(3 - 4i) + (5 + 3i) = 8 - I
","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-2","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 3","id":66,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q03.jpg","question_text":"3. Last year at RT University, the ratio of the number of students accepted to the number of students applying for admission was 2 to 7. RT University accepted 630 students last year. 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Three line segments intersect as shown in the figure below, forming angles with measures of 150°, 40°, and x°, respectively. 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If f(x) 3×2 + 7x — 8, then f(-3) = ?","section":"math","question_number":10,"form_id":"a09","category":"algebraic-and-function-expressions","readable_category":"Algebraic & Function Expressions","sub_category":"solve-function-expressions","readable_sub_category":"Solve Function Expressions","answer_choices":"Choice G","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$f(-3)=3(-3)^2+7(-3)-8=-2$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-10","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 11","id":74,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q11.jpg","question_text":"11. Two sides of a triangle are equal in length. The third side is 3 centimeters longer than either of the other 2 sides. 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The 220 graduating seniors of Madison- High School will sit in the center section of the school auditorium at the graduation ceremony. 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In the standard (x,y) coordinate plane, the point (3,-7) is the midpoint of the line segment with endpoints (9, -11) and:","section":"math","question_number":13,"form_id":"a09","category":"equation-of-a-line","readable_category":"Equation of a Line","sub_category":"distance-and-midpoint","readable_sub_category":"Distance & Midpoint","answer_choices":"Choice B","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$\\frac {9+x}{2}=3 \\\\$$\r\n$$\\frac {-11+y}{2}=-7 \\\\$$\r\n$$\\Rightarrow x=-3 ,\\ y=-3$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-13","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 14","id":77,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q14.jpg","question_text":"14. A community theater group performed at 5 local schools. For each school, the table below shows the total number of tickets sold and the total dollar amount collected from ticket sales. At School A, only 2 types of tickets were sold: premium tickets for $10 each and value tickets for $6 each. How many value tickets were sold at School A ?","section":"math","question_number":14,"form_id":"a09","category":"word-problems","readable_category":"Word Problems","sub_category":"2-variable-addition","readable_sub_category":"2 Variable Addition","answer_choices":"Choice J","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$t+v=200\\\\$$\r\n$$10t+6v=1400\\\\$$\r\n$$\\Rightarrow t=50,\\ v=150$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-14","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 15","id":78,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q15.jpg","question_text":"15. The theater group had to pay each school a facility charge. For use of its facility, School C charged the theater group 10% of the ticket sales and a fixed fee of $200. How much money did School C charge the theater group for use of its facility?","section":"math","question_number":15,"form_id":"a09","category":"word-problems","readable_category":"Word Problems","sub_category":"fixed-cost-and-variable-cost","readable_sub_category":"Fixed Cost + Variable Cost","answer_choices":"Choice E","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$10\\% \\times 1800+200=380$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-15","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 16","id":79,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q16.jpg","question_text":"16. What is the difference between the median and the mean number of tickets sold at the 5 schools?","section":"math","question_number":16,"form_id":"a09","category":"statistics","readable_category":"Statistics","sub_category":"mean-median-mode-combinations","readable_sub_category":"Mean, Median, Mode Combinations","answer_choices":"Choice K","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$median=250 \\\\$$\r\n$$mean=\\frac {200+250+300+150+275}{5}=235 \\\\$$\r\n$$\\Rightarrow median - mean = 250-235=15$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-16","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 17","id":80,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q17.jpg","question_text":"17. What is the area, in square decimeters, of a right triangle with side lengths of 10 dm, 26 dm, and 24 dm ?","section":"math","question_number":17,"form_id":"a09","category":"perimeter-area-volume","readable_category":"Perimeter, Area, Volume","sub_category":"triangles-squares-rectangles-circles","readable_sub_category":"Triangles, Squares, Rectangles, Circles","answer_choices":"Choice E","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$Area = \\frac{10\\times24}{2}=120 \\ dm^2$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-17","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 18","id":81,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q18.jpg","question_text":"18. The mean of a list of 7 numbers is 85. The first 6 numbers on the list are 82, 93, 68, 93, 70, and 98. What is the 7th number on the list?","section":"math","question_number":18,"form_id":"a09","category":"statistics","readable_category":"Statistics","sub_category":"mean-median","readable_sub_category":"Mean, Median","answer_choices":"Choice J","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$Mean = \\frac{82+93+68+93+70+x}{7}=85 \\\\$$\r\n$$\\Rightarrow x=91$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-18","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 19","id":82,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q19.jpg","question_text":"19. Which of the following is the sine of the smallest angle in a right triangle with side lengths 7, 24, and 25 inches, respectively?","section":"math","question_number":19,"form_id":"a09","category":"trigonometry","readable_category":"Trigonometry","sub_category":"pythagorean-theorem-and-sin-cos-tan","readable_sub_category":"Pythagorean Theorem & sin cos tan","answer_choices":"Choice A","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$\\sin A = \\frac{7}{25}$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-19","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 20","id":83,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q20.jpg","question_text":"20. In the figure shown below, all angles are right angles, and the side lengths given are in feet. What is the area, in square feet, of the figure?","section":"math","question_number":20,"form_id":"a09","category":"perimeter-area-volume","readable_category":"Perimeter, Area, Volume","sub_category":"triangles-squares-rectangles-circles","readable_sub_category":"Triangles, Squares, Rectangles, Circles","answer_choices":"Choice G","answer_image":"https://ahdjango.herokuapp.com/media/answers/A09_math_q20_a.jpg","answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"The longer length of the smaller rectangle (S2) = 12-5=7
\r\n$$Total\\ area = S1+S2=10 \\times 5 + 3 \\times 7=71$$
","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-20","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 21","id":84,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q21.jpg","question_text":"21. A triangle has a perimeter of 26 cm and sides of length x cm, (x + 3) cm, and (x + 5) cm. What is the value of x?","section":"math","question_number":21,"form_id":"a09","category":"perimeter-area-volume","readable_category":"Perimeter, Area, Volume","sub_category":"triangles-squares-rectangles-circles","readable_sub_category":"Triangles, Squares, Rectangles, Circles","answer_choices":"Choice A","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"x+(x+3)+(x+5)=26\r\n=> x=6","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-21","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 22","id":85,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q22.jpg","question_text":"22. A truck sprang a leak in its radiator, which held 480 ounces of fluid when it started to leak. Assuming the truck continues at 35 mph and its radiator leaks 4 ounces of fluid per minute, how many miles will the truck travel before the radiator is empty?","section":"math","question_number":22,"form_id":"a09","category":"word-problems","readable_category":"Word Problems","sub_category":"distance-speed-time","readable_sub_category":"Distance, Speed, Time","answer_choices":"Choice J","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$t=\\frac{480}{4}=120 \\ minutes = 2 \\ hours\\\\$$\r\n$$d=35 \\ mph \\times 2 \\ hours=70 \\ miles$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-22","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 23","id":86,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q23.jpg","question_text":"23. An ice cream shop sells ice cream cones with exactly 1 of 3 ice cream flavors in the cone. The 3 flavors are vanilla, chocolate, and strawberry. Last Saturday, the shop sold 42 cones. It sold I 1 more with chocolate than with vanilla and 2 more with vanilla than with strawberry. How many cones with strawberry ice cream did the shop sell that Saturday?","section":"math","question_number":23,"form_id":"a09","category":"algebraic-and-function-expressions","readable_category":"Algebraic & Function Expressions","sub_category":"systems-of-equations","readable_sub_category":"Systems of Equations","answer_choices":"Choice A","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"v+c+s=42c=v+11
\r\nv=s+2
\r\n=> c=s+13
\r\n=>s+2+s+13+s=42
\r\n=>s=9
","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-23","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 24","id":87,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q24.jpg","question_text":"24. In ABC below, D is the midpoint of CB, ZABC is a right angle, AB = 8 m, and AC = 10 m. What is AD, in meters?","section":"math","question_number":24,"form_id":"a09","category":"similar-triangles-and-types-of-triangles","readable_category":"Similar Triangles & Types of Triangles","sub_category":"similar-triangles","readable_sub_category":"Similar Triangles","answer_choices":"Choice G","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$BC=\\sqrt{AC^2-AB^2}=\\sqrt{10^2-8^2}=6\\\\$$\r\n$$BD=\\frac{BC}{2}=3\\\\$$\r\n$$\\Rightarrow AD=\\sqrt{BD^2+AB^2}=\\sqrt{3^2+8^2}=\\sqrt{73}$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-24","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 25","id":88,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q25.jpg","question_text":"25. Lyman has plotted 5 points in the standard (.v,y) coordinate plane below. He then plots a new point as follows: the x-coordinate of the new point is the mean of the .v-coordinates of the 5 points already plotted; the y-coordinate of the new point is the mean of the y-coordinates of the 5 points already plotted. Which of the following ordered pairs gives the coordinates of Lyman’s new point?","section":"math","question_number":25,"form_id":"a09","category":"graphing-properties","readable_category":"Graphing Properties","sub_category":"interpret-graphs-or-figures","readable_sub_category":"Interpret Graphs or Figures","answer_choices":"Choice C","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$x=\\frac{(-2)+(-1)+(-2)+1+4}{5}=0 \\\\$$\r\n$$y=\\frac{4+1+(-2)+(-1)+(-2)}{5}=0 $$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-25","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 26","id":89,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q26.jpg","question_text":"26. The 1st and 2nd terms of a certain geometric sequence are 10 and —5, respectively. What is the 5th term of the geometric sequence?","section":"math","question_number":26,"form_id":"a09","category":"sequences-and-patterns","readable_category":"Sequences and Patterns","sub_category":"geometric-sequences","readable_sub_category":"Geometric Sequences","answer_choices":"Choice H","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$10, -5, \\frac{5}{2}, -\\frac{5}{4}, \\frac{5}{8}, ...$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-26","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 27","id":91,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q27.jpg","question_text":"27. Alani works 8 hours per day 5 days each week at a custom embroidery shop. Each day Alani is paid either $1.00 per shirt that she stitches or $10.00 per hour, whichever daily amount is higher. Alani stitched the following numbers of shirts: 60 on Monday, 52 on Tuesday, 85 on Wednesday, 80 on Thursday, and 90 on Friday. What is Alani’s total pay for these 5 days?","section":"math","question_number":27,"form_id":"a09","category":"word-problems","readable_category":"Word Problems","sub_category":"1-variable-equations","readable_sub_category":"1 Variable Equations","answer_choices":"Choice C","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"Monday:
\r\nThe daily amount for 60 shirts is $$60 \\times 1= 60 \\ dollars$$
\r\nThe daily amount for 8 hours is $$8 \\times 10=80\\ dollars$$
\r\nThus the daily pay should be $80.
\r\nTuesday:
\r\nThe daily amount for 52 shirts is $$52 \\times1=52\\ dollars$$
\r\nThe daily amount for 8 hours is $$8 \\times10=80\\ dollars$$
\r\n\r\nThus the daily pay should be $80.
\r\nWednesday:
\r\nThe daily amount for 85 shirts is $$85 \\times1=85\\ dollars$$
\r\nThe daily amount for 8 hours is $$8 \\times10=80\\ dollars$$
\r\nThus the daily pay should be $85.
\r\nThursday:
\r\nThe daily amount for 80 shirts is $$80 \\times1=80\\ dollars$$
\r\nThe daily amount for 8 hours is $$8 \\times10=80\\ dollars$$
\r\nThus the daily pay should be $80.
\r\nFriday:
\r\nThe daily amount for 90 shirts is $$90 \\times1=90\\ dollars$$
\r\nThe daily amount for 8 hours is $$8 \\times10=80\\ dollars$$
\r\nThus the daily pay should be $90.
\r\nTherefore, the total pay is $80+$80+$85+$80+$90=$415
","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-27","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 28","id":92,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q28.jpg","question_text":"28. Which of the following most precisely describes the roots of the equation 5×2 + 7x + 2 = 0 ?","section":"math","question_number":28,"form_id":"a09","category":"quadratic-equations","readable_category":"Quadratic Equations","sub_category":"factoring","readable_sub_category":"Factoring","answer_choices":"Choice H","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"To find the roots of the equation, it can be rearranged as $$(x+1)(5x+2)=0$$
\r\nTherefore the roots are $$1\\ and\\ -\\frac{2}{5}$$ which are two rational roots.
","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-28","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 29","id":93,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q29.jpg","question_text":"29. Paula is planning a course for a bike race. The course is in the shape of a right triangle, as shown below. Participants will begin at A, ride directly to B, then directly to C, and directly back to A. Paula wants to put a rest stop at the halfway point on the course. How many miles past B will the rest stop be?","section":"math","question_number":29,"form_id":"a09","category":"trigonometry","readable_category":"Trigonometry","sub_category":"pythagorean-theorem-and-sin-cos-tan","readable_sub_category":"Pythagorean Theorem & sin cos tan","answer_choices":"Choice D","answer_image":"https://ahdjango.herokuapp.com/media/answers/A09_math_q29_a.jpg","answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$BC=\\sqrt{AB^2+AC^2}=13$$\r\nTotal distance of the course is AB+BC+AC=30
\r\nDistance of half the course is $$30\\div2=15$$
\r\nTherefore the stop should be 15-5=10 miles from B.
\r\nChoice D.","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-29","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 30","id":94,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q30.jpg","question_text":"30. Adams High School has 120 students, and 1/3 of thestudents are taking Literature. Of the students NOT taking Literature, I are taking Composition. No students are taking both Literature and Composition. How many students are taking Composition?","section":"math","question_number":30,"form_id":"a09","category":"ratios-proportions-percentages-fractions","readable_category":"Ratios, Proportions, Percentages, Fractions","sub_category":"percents-and-fractions","readable_sub_category":"Percents & Fractions","answer_choices":"Choice G","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"The number of students NOT taking Literature is $$120\\times (1-\\frac{1}{3})=80$$
\r\nThe number of students taking Composition is $$80\\times \\frac{1}{4}=20$$
","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-30","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 31","id":95,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q31.jpg","question_text":"31. For what value of x is the equation","section":"math","question_number":31,"form_id":"a09","category":"exponents-radicals-and-scientific-notation","readable_category":"Exponents, Radicals, & Scientific Notation","sub_category":"radical-expressions","readable_sub_category":"Radical Expressions","answer_choices":"Choice D","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$\\sqrt{x}+3=6 \\\\$$\r\n$$\\Rightarrow \\sqrt{x}=3 \\\\$$\r\n$$\\Rightarrow x=9$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-31","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 32","id":96,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q32.jpg","question_text":"32. In the right triangle AABC shown below, the length of","section":"math","question_number":32,"form_id":"a09","category":"trigonometry","readable_category":"Trigonometry","sub_category":"pythagorean-theorem-and-sin-cos-tan","readable_sub_category":"Pythagorean Theorem & sin cos tan","answer_choices":"Choice H","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$\\sin A = \\frac{3}{4}=\\frac{BC}{AB}=\\frac{12}{AB} \\\\$$\r\n$$\\Rightarrow AB=\\frac{12\\times4}{3}=16\\\\$$\r\n$$\\Rightarrow AC=\\sqrt{AB^2-BC^2}=\\sqrt{16^2-12^2}=\\sqrt{112}=4\\sqrt{7}$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-32","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 33","id":97,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q33.jpg","question_text":"33. What integer does 3(log2 16) equal?","section":"math","question_number":33,"form_id":"a09","category":"logarithms","readable_category":"Logarithms","sub_category":"logarithm-expressions","readable_sub_category":"Logarithm Expressions","answer_choices":"Choice A","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$3(\\log_2 16)=3(\\log_2 2^4)=3(4)=12$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-33","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 34","id":99,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q34.jpg","question_text":"34. A bag contains several marbles. On 3 successive draws with replacement, a red marble is drawn from the bag each time. Which of the following statements must be: true about the marbles in the bag?","section":"math","question_number":34,"form_id":"a09","category":"probability","readable_category":"Probability","sub_category":"one-event","readable_sub_category":"One Event","answer_choices":"Choice F","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"F. is apparently true, because if there are no red marbles, it is impossible to draw red marbles from the bag.
The other choices may not be true.
","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-34","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 35","id":100,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q35.jpg","question_text":"35. Students and adults from Western High School visited an amusement park on a field trip. The amusement park charged $25 for each adult ticket and $20 for each student ticket. Before the trip, the students were given this information about the Happy Dragon roller coaster: the average speed of the roller coaster is 50 miles per hour, and 1 ride on the roller coaster track is completed in 2.25 minutes. A graph showing the height above level ground, in feet, with respect to the time into the ride, in seconds, is given below. Which of the following values is closest to the total distance traveled, in miles, during 1. complete ride on the roller coaster track?","section":"math","question_number":35,"form_id":"a09","category":"equation-of-a-line","readable_category":"Equation of a Line","sub_category":"distance-and-midpoint","readable_sub_category":"Distance & Midpoint","answer_choices":"Choice B","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"Total distance travelled in 1 complete ride =\r\n$$ 50 \\ miles \\ per\\ hour \\ \\times 2.25\\ min = \\frac{50 \\ miles \\ \\times 2.25 \\min}{60\\ min}=1.875\\ miles\\approx1.9\\ miles$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-35","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 36","id":101,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q36.jpg","question_text":"36. The roller coaster is at a height of at least 235 feet for a total of 5 seconds during each complete ride. Which of the following is closest to the percent of the time during a complete ride that the roller coaster is at a height of at least 235 feet?","section":"math","question_number":36,"form_id":"a09","category":"ratios-proportions-percentages-fractions","readable_category":"Ratios, Proportions, Percentages, Fractions","sub_category":"percents-and-fractions","readable_sub_category":"Percents & Fractions","answer_choices":"Choice G","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$\\frac{5 \\ seconds}{2.25 \\ minutes \\times 60 \\ seconds}=0.037\\approx4\\%$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-36","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 37","id":102,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q37.jpg","question_text":"37. Which of the following values is closest to the average slope, in feet per second, of the graph on the interval between 40 seconds and 90 seconds?","section":"math","question_number":37,"form_id":"a09","category":"equation-of-a-line","readable_category":"Equation of a Line","sub_category":"equations-that-describe-a-line","readable_sub_category":"Equations that Describe a Line","answer_choices":"Choice E","answer_image":"https://ahdjango.herokuapp.com/media/answers/A09_math_q37_a.jpg","answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$The\\ slope \\approx \\frac{200\\ ft}{50\\ s} = 4$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-37","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 38","id":103,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q38.jpg","question_text":"38. The value of x5(0.5×2+ 2.5x + 6) is between which of the following numbers when x T 10 ?","section":"math","question_number":38,"form_id":"a09","category":"exponents-radicals-and-scientific-notation","readable_category":"Exponents, Radicals, & Scientific Notation","sub_category":"scientific-notation","readable_sub_category":"Scientific Notation","answer_choices":"Choice J","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$10^5(0.5\\times10^2+2.5\\times10+6)=10^5(50+25+6)=81\\times10^5=8.1\\times10^6 \\\\$$\r\n$$\\Rightarrow 8\\times10^6<8.1\\times10^6<9\\times10^6$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-38","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 39","id":104,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q39.jpg","question_text":"39. For which of the following data sets is the difference between the mean and the median the greatest?","section":"math","question_number":39,"form_id":"a09","category":"statistics","readable_category":"Statistics","sub_category":"mean-median-mode-combinations","readable_sub_category":"Mean, Median, Mode Combinations","answer_choices":"Choice D","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"A. { 10, 10, 10, 10}
\r\nMean = 10
\r\nMedian = 10
\r\nDifference between Mean and Median = 10
\r\nB. { 10, 10, 15, 20}
\r\nMean = 13.75
\r\nMedian = 12.5
\r\nDifference between Mean and Median = 1.25
\r\nC. { 10, 15, 15, 15}
\r\nMean = 13.75
\r\nMedian =15
\r\nDifference between Mean and Median = 1.25
\r\nD. { 10, 15, 15, 100}
\r\nMean = 35
\r\nMedian =15
\r\nDifference between Mean and Median = 20
\r\nE. { 10, 20, 90, 100}
\r\nMean = 55
\r\nMedian =55
\r\nDifference between Mean and Median = 0
","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-39","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 40","id":105,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q40.jpg","question_text":"40. Pablo has a deck and pool in his backyard. The deck’s shape is a rectangle with a semicircle removed and is shown shaded in the figure below. The lengths of the straight sides of the deck are given in feet. Pablo plans to cover the top of the deck with stain. To decide how much stain to purchase, he needs to find the area of the top of the deck. To the nearest square foot, what is the area of the top of the deck?","section":"math","question_number":40,"form_id":"a09","category":"perimeter-area-volume","readable_category":"Perimeter, Area, Volume","sub_category":"mixed-shapes","readable_sub_category":"Mixed Shapes","answer_choices":"Choice K","answer_image":"https://ahdjango.herokuapp.com/media/answers/A09_math_q40_a.jpg","answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"Diameter of the circle = 32-4-4 =24 feet
\r\nRadius of the circle = 24/2=12 feet
\r\nTherefore,
\r\n$$shaded \\ area = 20\\times32-\\frac{\\pi r^2}{2}=20\\times32-\\frac{\\pi 12^2}{2}=414 \\ foot^2$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-40","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 41","id":106,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q41.jpg","question_text":"41. A 3-foot-wide brick sidewalk is laid around a rectangular swimming pool. The outside edge of the sidewalk measures 30 feet by 40 feet, as shown in the figure below. What is the perimeter, in feet, of the swimming pciol?","section":"math","question_number":41,"form_id":"a09","category":"perimeter-area-volume","readable_category":"Perimeter, Area, Volume","sub_category":"triangles-squares-rectangles-circles","readable_sub_category":"Triangles, Squares, Rectangles, Circles","answer_choices":"Choice B","answer_image":"https://ahdjango.herokuapp.com/media/answers/A09_math_q41_a.jpg","answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"a=30-3-3=24 feet
\r\nb=40-3-3=34 feet
\r\nTherefore, $$p=(a+b)\\times2=(24+34)\\times2=116$$
","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-41","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 42","id":107,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q42.jpg","question_text":"42. Given the functions f(x) = X2anc.","section":"math","question_number":42,"form_id":"a09","category":"algebraic-and-function-expressions","readable_category":"Algebraic & Function Expressions","sub_category":"nested-functions","readable_sub_category":"Nested Functions","answer_choices":"Choice F","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$g(f(x))=\\frac{1}{4-f(x)}=\\frac{1}{4-x^2}$$\r\nChoice F.","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-42","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 43","id":108,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q43.jpg","question_text":"43. A circle has a circumference of 27E\\ feet. What is the area, in square feet, of the circle?","section":"math","question_number":43,"form_id":"a09","category":"perimeter-area-volume","readable_category":"Perimeter, Area, Volume","sub_category":"triangles-squares-rectangles-circles","readable_sub_category":"Triangles, Squares, Rectangles, Circles","answer_choices":"Choice C","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$C=2 \\pi r=2 \\pi \\sqrt{2} \\\\$$\r\n$$\\Rightarrow r=\\sqrt{2} \\\\$$\r\n$$\\Rightarrow S= \\pi r^2= \\pi (\\sqrt{2})^2=2\\pi$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-43","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 44","id":109,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q44.jpg","question_text":"44. In the standard (x,v) coordinate plane, the coordinates of the y-intercept of the graph of the function v = f(x) are (0,-2). What are the coordinates of the v-intercept of the graph of the function y = f(x) — 3 ?","section":"math","question_number":44,"form_id":"a09","category":"equation-of-a-line","readable_category":"Equation of a Line","sub_category":"equations-that-describe-a-line","readable_sub_category":"Equations that Describe a Line","answer_choices":"Choice F","answer_image":"https://ahdjango.herokuapp.com/media/answers/A09_math_q44_a.jpg","answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"The graph of the function y=f(x)-3 is the graph of f(x) being moved downwards for 3 units. Therefore point (0,-2) become (0,-5).","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-44","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 45","id":110,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q45.jpg","question_text":"45. Which of the following is an equation of a parabola that passes through the 3 points labeled in the standard (x,y) coordinate plane below?","section":"math","question_number":45,"form_id":"a09","category":"conics","readable_category":"Conics","sub_category":"parabola","readable_sub_category":"Parabola","answer_choices":"Choice A","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"Only Choice A satisfies that when x equals to 0, y would equal to 3, therefore passes through point (0,3).","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-45","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 46","id":111,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q46.jpg","question_text":"46. As x continually increases in value without bound, the","section":"math","question_number":46,"form_id":"a09","category":"sequences-and-patterns","readable_category":"Sequences and Patterns","sub_category":"geometric-sequences","readable_sub_category":"Geometric Sequences","answer_choices":"Choice H","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"When x become really large, x+3 will be almost be equal to x:\r\n$$\\frac{x}{x+3}\\approx\\frac{x}{x}=1$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-46","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 47","id":112,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q47.jpg","question_text":"47. Yulan will use a bag of 30 solid-colored marbles for a game in which each player randomly draws marbles from the bag. The number of marbles of each color is shown in the table below.","section":"math","question_number":47,"form_id":"a09","category":"probability","readable_category":"Probability","sub_category":"more-than-one-event","readable_sub_category":"More than One Event","answer_choices":"Choice B","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"The probability of drawing a black marble first is\r\n$$\\frac{6}{30}$$\r\nThe probability of drawing a green marble second is\r\n$$\\frac{2}{29}$$\r\nThe probability of the two events happening is\r\n$$\\frac{6}{30}\\times\\frac{2}{29}=\\frac{2}{145}$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-47","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 48","id":113,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q48.jpg","question_text":"48. The expression 2b + c b — 2c is undefined whenever b = ?","section":"math","question_number":48,"form_id":"a09","category":"graphing-properties","readable_category":"Graphing Properties","sub_category":"domain-range-asymptote-undefined","readable_sub_category":"Domain, Range, Asymptote, Undefined","answer_choices":"Choice K","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"The expression is undefined whenever b-2c=0, ie, b=2c.","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-48","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 49","id":114,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q49.jpg","question_text":"49. What number is halfway between and","section":"math","question_number":49,"form_id":"a09","category":"ratios-proportions-percentages-fractions","readable_category":"Ratios, Proportions, Percentages, Fractions","sub_category":"lcm-gcf-prime-numbers","readable_sub_category":"LCM, GCF, Prime Numbers","answer_choices":"Choice E","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$\\frac{\\frac{2}{5}+\\frac{8}{7}}{2}=\\frac{27}{35}$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-49","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 50","id":115,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q50.jpg","question_text":"50. A function f(x) is defined as f(x) = 3’2-‘2. What 2 real numbers satisfy f(x) = 1 ?","section":"math","question_number":50,"form_id":"a09","category":"exponents-radicals-and-scientific-notation","readable_category":"Exponents, Radicals, & Scientific Notation","sub_category":"exponent-expressions","readable_sub_category":"Exponent Expressions","answer_choices":"Choice H","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$3^{x^2-x-2}=1=3^0\\\\$$\r\n$$x^2-x-2=0\\\\$$\r\n$$(x-2)(x+1)=0\\\\$$\r\n$$\\Rightarrow x=2,-1$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-50","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 51","id":116,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q51.jpg","question_text":"51. The ellipse shown in the standard (x,y) coordinate plane below has equation 93)2 + `-Y 255,2 = 1. Which of the","section":"math","question_number":51,"form_id":"a09","category":"conics","readable_category":"Conics","sub_category":"ellipse","readable_sub_category":"Ellipse","answer_choices":"Choice D","answer_image":"https://ahdjango.herokuapp.com/media/answers/A09_math_q51_a.jpg","answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"The major radius p is 5; the minor radius q is 3.
\r\nThe focal length is thus:
\r\n$$f^2=p^2-q^2=5^2-3^2=16 \\\\$$\r\n$$f=4$$\r\nTherefore, the foci are (3,1) (3,9).
\r\n\r\nReference:
\r\nhttps://www.khanacademy.org/math/precalculus/conics-precalc/foci-of-an-ellipse/a/ellipse-foci-review
","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-51","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 52","id":117,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q52.jpg","question_text":"52. A basket contains 10 solid-colored balls–2 blue, 3 red, and 5 green. Each ball has a single number printed on it. The blue balls are numbered 1 and 2 (each number is used once), the red balls are numbered 1-3 (each number is used once), and the green balls are numbered 1-5 (each number is used once). A ball will be drawn at random from the basket. What is the probability that the ball that is drawn will he red or have a 3 printed on it?","section":"math","question_number":52,"form_id":"a09","category":"probability","readable_category":"Probability","sub_category":"one-event","readable_sub_category":"One Event","answer_choices":"Choice J","answer_image":"https://ahdjango.herokuapp.com/media/answers/A09_math_q52_a.jpg","answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$p=\\frac{3+1}{10}=\\frac{4}{10}$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-52","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 53","id":118,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q53.jpg","question_text":"53. In the figure below, the given side lengths of AABC are in inches. What is the area, in square inches, of /ABC ?","section":"math","question_number":53,"form_id":"a09","category":"trigonometry","readable_category":"Trigonometry","sub_category":"pythagorean-theorem-and-sin-cos-tan","readable_sub_category":"Pythagorean Theorem & sin cos tan","answer_choices":"Choice B","answer_image":"https://ahdjango.herokuapp.com/media/answers/A09_math_q53_a.jpg","answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$Area \\ of \\triangle ABC = \\frac{1}{2}\\cdot AB \\cdot h \\\\$$\r\n$$h= 12\\times \\sin{30^\\circ} \\\\$$\r\n$$\\Rightarrow Area \\ of \\triangle ABC =\\frac{1}{2}\\cdot AB \\cdot 12\\times \\sin{30^\\circ} = 39$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-53","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 54","id":119,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q54.jpg","question_text":"54. There are 66 calories in 15 grams of grated Parmesan cheese, and 59% of those calories are from fat. When measuring Parmesan cheese, 5 grams is equal to 1 tablespoon. Which of the following is closest to the number of calories from fat per tablespoon of grated Parmesan cheese? .","section":"math","question_number":54,"form_id":"a09","category":"ratios-proportions-percentages-fractions","readable_category":"Ratios, Proportions, Percentages, Fractions","sub_category":"percents-and-fractions","readable_sub_category":"Percents & Fractions","answer_choices":"Choice J","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$\\frac{59\\%\\times66}{15}\\times3=13.2$$\r\nChoice J.","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-54","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 55","id":120,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q55.jpg","question_text":"55. In the diagram below, B, F, and H are on AC, AE, and BF, respectively, and GH I BE. The area of square ABGF is -12-t the area of square ACDE. What percent of the area of ACDE does the shaded portion represent?","section":"math","question_number":55,"form_id":"a09","category":"perimeter-area-volume","readable_category":"Perimeter, Area, Volume","sub_category":"mixed-shapes","readable_sub_category":"Mixed Shapes","answer_choices":"Choice D","answer_image":"https://ahdjango.herokuapp.com/media/answers/A09_math_q55_a.jpg","answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"Area of shaded portion = $$\\frac{1}{4}\\times\\frac{1}{4}=\\frac{1}{16}=6.5\\%$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-55","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 56","id":121,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q56.jpg","question_text":"56. In a data set of 10 distinct values, the single largest value is replaced with a much greater value to form a new data set. Which of the following statements is true about the values of the mean and median for the new data set as compared to the mean and median of the original data set?","section":"math","question_number":56,"form_id":"a09","category":"statistics","readable_category":"Statistics","sub_category":"mean-median-mode-combinations","readable_sub_category":"Mean, Median, Mode Combinations","answer_choices":"Choice F","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"The median will stay the same because it will not be affected by the change in the largest value.
\r\nThe mean will go up because the sum is increased by the increase in the largest value.
","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-56","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 57","id":122,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q57.jpg","question_text":"57. Valley High School and Mountain High School have decided that selected students will attend a daytime theatrical performance that costs $5 for each teacher and $3 for each student. One teacher and 10 students from Valley High will attend, and 2 teachers and 25 students from Mountain High will attend. Which of the following matrix products represents the ticket costs. in dollars, for each high school?","section":"math","question_number":57,"form_id":"a09","category":"matrices","readable_category":"Matrices","sub_category":"multiplication","readable_sub_category":"Multiplication","answer_choices":"Choice A","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"The ticket cost is $$5\\times1+3\\times10$$ and $$5\\times2+3\\times25$$, respectively.","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-57","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 58","id":123,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q58.jpg","question_text":"58. Karie is inventing a new notation in math. She has decided to use n.L to denote the sum of the first a positive integers. For example, 51 means 5 + 4 + 3 + 2 + 1. Karie has written 3 statements that she is investigating as possible properties of","section":"math","question_number":58,"form_id":"a09","category":"number-types-and-properties","readable_category":"Number Types & Properties","sub_category":"complex-number","readable_sub_category":"Complex Number","answer_choices":"Choice F","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$I. n\\downarrow+(n+1)=(n+1)\\downarrow$$\r\n$$(1+2+3+...+n)+(n+1)=1+2+3+...+n+(n+1)=(n+1)\\downarrow\\\\$$\r\nTherefore, I. is true.\r\n$$II. n\\downarrow+n\\downarrow=(2n)\\downarrow$$\r\nLet's plug in n=3,\r\n$$1+2+3+1+2+3\\neq1+2+3+4+5+6$$\r\nTherefore, II. is false.\r\n$$III. (n^2)\\downarrow=(n\\downarrow)^2$$\r\nLet's plug in n=3,\r\n$$(3^2)\\downarrow=(3\\downarrow)^2\\\\$$\r\n$$1+2+3+...+9=45\\neq(1+2+3)^2=36$$\r\nTherefore, III. is false.","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-58","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 59","id":124,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q59.jpg","question_text":"59. Rey wants to make an open box as shown below, using a square piece of cardboard. He intends to cut a 2-inch square from each corner of the cardboard and fold the cardboard along the lines shown to form the sides. The resulting box will have a volume of 72 cubic inches. What are the dimensions, in inches, of the original piece of cardboard?","section":"math","question_number":59,"form_id":"a09","category":"perimeter-area-volume","readable_category":"Perimeter, Area, Volume","sub_category":"triangles-squares-rectangles-circles","readable_sub_category":"Triangles, Squares, Rectangles, Circles","answer_choices":"Choice E","answer_image":"https://ahdjango.herokuapp.com/media/answers/A09_math_q59_a.jpg","answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$(x-4)(x-4)\\times2=72\\\\$$\r\n$$x=10 \\\\$$\r\n$$\\Rightarrow 10 \\times10$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-59","main_question":"","skills":[]},{"title":"2018 April(A09) Math Question 60","id":125,"question_image":"https://ahdjango.herokuapp.com/media/questions/A09_math_q60.jpg","question_text":"60. Which of the following quadratic equations has the complex number (1 + V-1) as a solution?","section":"math","question_number":60,"form_id":"a09","category":"quadratic-equations","readable_category":"Quadratic Equations","sub_category":"factoring","readable_sub_category":"Factoring","answer_choices":"Choice K","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"Let's start with K. To find the roots of $$x^2-2x+2 = 0$$:\r\n$$\\begin{align}\r\nx_{1,2} & =\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a} \\\\\r\n& =\\frac{2\\pm\\sqrt{2^2-4(2)(1)}}{2}\\\\\r\n& =1\\pm\\sqrt{-1}\r\n\\end{align}$$","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?M(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))r.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))a.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>X(o,c(t));var D=(o,t)=>{var n={};for(var e in o)r.call(o,e)&&t.indexOf(e)<0&&(n[e]=o[e]);if(o!=null&&u)for(var e of u(o))t.indexOf(e)<0&&a.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=D(e,[\"components\"]);return mdx(MDXLayout,y(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"a09-math","nextjs_formid_section_q":"a09-math-60","main_question":"","skills":[]}],"title":"A09 Math"},"__N_SSG":true}