The equation of a circle in the standard (x,y) plane is:
\r\n$$(x-h)^{2}+(y-k)^{2}=r^{2}$$\r\nWhere (h,k) is the center of the circle and r is the radius.
\r\n\r\n$$r^{2}=144$$ \r\n\r\n$$=> r=12$$\r\nThe circle intersects with the x-axis at (0,12), (-12,0)
","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":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-13","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 14","id":2376,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q14.jpg","question_text":"","section":"math","question_number":14,"form_id":"d06","category":"quadratic-equations","readable_category":"Quadratic Equations","sub_category":"factoring","readable_sub_category":"Factoring","answer_choices":"Choice G","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$=(x-9)(x+4)$$","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":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-14","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 15","id":2377,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q15.jpg","question_text":"15. Two vectors are shown in the standard (x,y) coordinate plane below.\r\n\r\nOne of the following vectors in the standard (x,y) coordinate plane is the sum of these 2 vectors. Which one?","section":"math","question_number":15,"form_id":"d06","category":"graphing-properties","readable_category":"Graphing Properties","sub_category":"vectors","readable_sub_category":"Vectors","answer_choices":"Choice E","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"The parallelogram rule says that if we place two vectors so they have the same initial point, and then complete the vectors into a parallelogram, then the sum of the vectors is the directed diagonal that starts at the same point as the vectors.\r\n\r\n\r\nhttps://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vector-add-sub/v/parallelogram-rule-for-vector-addition","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":["parallelogram-rule-for-vector-addition"],"readable_tags":"Parallelogram rule for vector addition","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-15","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 16","id":2378,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q16.jpg","question_text":"16. A square and a rectangle have the same area. The length of the rectangle is 196 centimeters, and the width of the rectangle is 4 centimeters. What is the length, in centimeters, of a side of the square?","section":"math","question_number":16,"form_id":"d06","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":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"Area of square:\r\n$S^2=196 \\times 4\\ cm^2$
\r\nLength of a side of the square:\r\n$S=\\sqrt{196\\times4}=14\\times2=28$
","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":"d06-math","nextjs_formid_section_q":"d06-math-16","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 17","id":2379,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q17.jpg","question_text":"17. T-shirts are on sale for D dollars each, including tax. Valentina has N dollars with which to purchase T-shirts. After she purchases the maximum number she can, Q T-shirts, she has R dollars left. For all possible choices of D and N, which of the following equations models a correct relationship between D, N, Q, and R, as defined?","section":"math","question_number":17,"form_id":"d06","category":"word-problems","readable_category":"Word Problems","sub_category":"cost","readable_sub_category":"Cost","answer_choices":"Choice D","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"The cost of Q T-shirts is QD, and there are R dollars left, therefore N = QD+R.","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":"d06-math","nextjs_formid_section_q":"d06-math-17","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 18","id":2380,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q18.jpg","question_text":"18. At a sandwich shop, customers can order either a meat or a vegetarian sandwich on either white or wheat bread. Out of a total of 50 customers, 20 ordered a sandwich on white bread, 28 ordered a meat sandwich, and 12 ordered a meat sandwich on white bread. The given information is summarized in the table below.","section":"math","question_number":18,"form_id":"d06","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":"Vegetarian sandwich = 50 - 28 = 22.
\r\n\r\nVegetarian sandwich on white bread = 20 - 12 = 8.
\r\n\r\nTherefore, vegetarian sandwich on wheat bread = 22 - 8 = 14.
","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":"d06-math","nextjs_formid_section_q":"d06-math-18","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 19","id":2381,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q19.jpg","question_text":"19. A team of biologists tagged and released 90 deer in a forest. From the same forest 2 weeks later, the biologists collected a random sample of 30 deer, 5 of which were tagged. Let p be the proportion of deer in this forest that are tagged. What is pˆ, the sample proportion, for this sample?","section":"math","question_number":19,"form_id":"d06","category":"statistics","readable_category":"Statistics","sub_category":"general-statistics","readable_sub_category":"General Statistics","answer_choices":"Choice C","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$\\frac{5}{30}=\\frac{1}{6}$$","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":["sample-proportion"],"readable_tags":"Sample proportion","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-19","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 20","id":2382,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q20.jpg","question_text":"√•2 +√•8 +√•1•8 =?","section":"math","question_number":20,"form_id":"d06","category":"exponents-radicals-and-scientific-notation","readable_category":"Exponents, Radicals, & Scientific Notation","sub_category":"radical-expressions","readable_sub_category":"Radical Expressions","answer_choices":"Choice G","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$\\sqrt{2}+\\sqrt{8}+\\sqrt{18} \\\\$$\r\n$$=\\sqrt{2}+\\sqrt{4\\times2}+\\sqrt{9\\times2} \\\\$$\r\n\r\n$$=\\sqrt{2}+\\sqrt{4}\\sqrt{2}+\\sqrt{9}\\sqrt{2}=\\sqrt{2}+2\\sqrt{2}+3\\sqrt{2} \\\\$$\r\n\r\n$$=6\\sqrt{2}$$","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":"d06-math","nextjs_formid_section_q":"d06-math-20","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 21","id":2383,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q21.jpg","question_text":"21. Which of the following inequalities is equivalent to 3 − 2x > 7 − x ?","section":"math","question_number":21,"form_id":"d06","category":"inequalities","readable_category":"Inequalities","sub_category":"inequality-expressions","readable_sub_category":"Inequality Expressions","answer_choices":"Choice C","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var y=Object.defineProperty,D=Object.defineProperties;var M=Object.getOwnPropertyDescriptors;var n=Object.getOwnPropertySymbols;var e=Object.prototype.hasOwnProperty,u=Object.prototype.propertyIsEnumerable;var r=($,p,o)=>p in $?y($,p,{enumerable:!0,configurable:!0,writable:!0,value:o}):$[p]=o,x=($,p)=>{for(var o in p||(p={}))e.call(p,o)&&r($,o,p[o]);if(n)for(var o of n(p))u.call(p,o)&&r($,o,p[o]);return $},a=($,p)=>D($,M(p));var s=($,p)=>{var o={};for(var t in $)e.call($,t)&&p.indexOf(t)<0&&(o[t]=$[t]);if($!=null&&n)for(var t of n($))p.indexOf(t)<0&&u.call($,t)&&(o[t]=$[t]);return o};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(o){var t=o,{components:$}=t,p=s(t,[\"components\"]);return mdx(MDXLayout,a(x(x({},layoutProps),p),{components:$,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"$$3-2x>7-x $$\"),mdx(\"p\",null,\"$$ 3>7-x+2x$$\"),mdx(\"p\",null,\"$$ 3>7+x $$\"),mdx(\"p\",null,\"$$ 3-7>x$$\"),mdx(\"p\",null,\"$$ -4>x$$\"),mdx(\"p\",null,\"$$x<-4$$\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-21","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 22","id":2384,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q22.jpg","question_text":"22. Let a be positive and b be negative. If it can be determined, in which quadrant of the standard (x,y) coordinate plane is the point (−a,b2) located?","section":"math","question_number":22,"form_id":"d06","category":"graphing-properties","readable_category":"Graphing Properties","sub_category":"domain-range-asymptote-undefined","readable_sub_category":"Domain, Range, Asymptote, Undefined","answer_choices":"Choice G","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var y=Object.defineProperty,D=Object.defineProperties;var M=Object.getOwnPropertyDescriptors;var p=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,u=Object.prototype.propertyIsEnumerable;var $=(t,o,n)=>o in t?y(t,o,{enumerable:!0,configurable:!0,writable:!0,value:n}):t[o]=n,a=(t,o)=>{for(var n in o||(o={}))r.call(o,n)&&$(t,n,o[n]);if(p)for(var n of p(o))u.call(o,n)&&$(t,n,o[n]);return t},s=(t,o)=>D(t,M(o));var i=(t,o)=>{var n={};for(var e in t)r.call(t,e)&&o.indexOf(e)<0&&(n[e]=t[e]);if(t!=null&&p)for(var e of p(t))o.indexOf(e)<0&&u.call(t,e)&&(n[e]=t[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:t}=e,o=i(e,[\"components\"]);return mdx(MDXLayout,s(a(a({},layoutProps),o),{components:t,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"$$a > 0 \\u21D2 -a <0 $$\"),mdx(\"p\",null,\"$$b < 0 \\u21D2 b^2 > 0 $$\"),mdx(\"p\",null,\"Therefore the point is (-,+) and should be in the II quadrant.\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":["quandrants-of-the-standard-x-y-coordinate-plane"],"readable_tags":"Quandrants of the standard (x,y) coordinate plane","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-22","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 23","id":2385,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q23.jpg","question_text":"23. The mass of a certain type of bacteria grows exponentially, doubling every 20 minutes. What was the mass, in milligrams, of the bacteria exactly 2 hours after the mass first reached 10 milligrams?","section":"math","question_number":23,"form_id":"d06","category":"sequences-and-patterns","readable_category":"Sequences and Patterns","sub_category":"geometric-sequences","readable_sub_category":"Geometric Sequences","answer_choices":"Choice D","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var $=Object.defineProperty,c=Object.defineProperties;var h=Object.getOwnPropertyDescriptors;var o=Object.getOwnPropertySymbols;var s=Object.prototype.hasOwnProperty,m=Object.prototype.propertyIsEnumerable;var p=(e,t,n)=>t in e?$(e,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):e[t]=n,i=(e,t)=>{for(var n in t||(t={}))s.call(t,n)&&p(e,n,t[n]);if(o)for(var n of o(t))m.call(t,n)&&p(e,n,t[n]);return e},u=(e,t)=>c(e,h(t));var a=(e,t)=>{var n={};for(var r in e)s.call(e,r)&&t.indexOf(r)<0&&(n[r]=e[r]);if(e!=null&&o)for(var r of o(e))t.indexOf(r)<0&&m.call(e,r)&&(n[r]=e[r]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var r=n,{components:e}=r,t=a(r,[\"components\"]);return mdx(MDXLayout,u(i(i({},layoutProps),t),{components:e,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"We can also calculate any term in a Geometric Sequence using the Rule:\"),mdx(\"p\",null,\"$$x_n = a_1r^{(n-1)}$$\"),mdx(\"p\",null,\"The first term $a_1=10 mg$;\"),mdx(\"p\",null,\"The common ratio is 2: $r=2$;\"),mdx(\"p\",null,\"The number of terms excluding the first term is $2\\\\ hours \\\\times 60\\\\ \\\\frac{minutes}{hour} \\\\div 20\\\\ minutes =6$\"),mdx(\"p\",null,\"The total number of terms including the first term is $n=6+1=7$\"),mdx(\"p\",null,\"Therefore the 7th term is $a_7=10\\\\times2^{(7-1)}=640$\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":["exponential-growth"],"readable_tags":"Exponential growth","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-23","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 24","id":2386,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q24.jpg","question_text":"24. One day will be randomly selected from the 7 days in a week. Then 1 month will be randomly selected from the 12 months in a year. What is the probability that the selected day will be Tuesday and the selected month will be January?","section":"math","question_number":24,"form_id":"d06","category":"probability","readable_category":"Probability","sub_category":"more-than-one-event","readable_sub_category":"More than One Event","answer_choices":"Choice F","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var s=Object.defineProperty,y=Object.defineProperties;var D=Object.getOwnPropertyDescriptors;var p=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,e=Object.prototype.propertyIsEnumerable;var c=(t,n,o)=>n in t?s(t,n,{enumerable:!0,configurable:!0,writable:!0,value:o}):t[n]=o,$=(t,n)=>{for(var o in n||(n={}))r.call(n,o)&&c(t,o,n[o]);if(p)for(var o of p(n))e.call(n,o)&&c(t,o,n[o]);return t},u=(t,n)=>y(t,D(n));var f=(t,n)=>{var o={};for(var a in t)r.call(t,a)&&n.indexOf(a)<0&&(o[a]=t[a]);if(t!=null&&p)for(var a of p(t))n.indexOf(a)<0&&e.call(t,a)&&(o[a]=t[a]);return o};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(o){var a=o,{components:t}=a,n=f(a,[\"components\"]);return mdx(MDXLayout,u($($({},layoutProps),n),{components:t,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"$$P_{Tue}=\\\\frac{1}{7} $$\"),mdx(\"p\",null,\"$$P_{Jan}=\\\\frac{1}{12} $$\"),mdx(\"p\",null,\"$$=>P_{Tue+Jan}=\\\\frac{1}{7}\\\\times\\\\frac{1}{12}=\\\\frac{1}{84} $$\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":["probability"],"readable_tags":"Probability","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-24","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 25","id":2387,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q25.jpg","question_text":"25. The average weight of Juan, Jim, and Malik is exactly 160 pounds. The average weight of Juan, Jim, Malik, and Harry is exactly 150 pounds. How many pounds does Harry weigh?","section":"math","question_number":25,"form_id":"d06","category":"statistics","readable_category":"Statistics","sub_category":"mean-median","readable_sub_category":"Mean, Median","answer_choices":"Choice B","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var J=Object.defineProperty,m=Object.defineProperties;var M=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var i=Object.prototype.hasOwnProperty,r=Object.prototype.propertyIsEnumerable;var t=(n,a,p)=>a in n?J(n,a,{enumerable:!0,configurable:!0,writable:!0,value:p}):n[a]=p,$=(n,a)=>{for(var p in a||(a={}))i.call(a,p)&&t(n,p,a[p]);if(u)for(var p of u(a))r.call(a,p)&&t(n,p,a[p]);return n},s=(n,a)=>m(n,M(a));var e=(n,a)=>{var p={};for(var o in n)i.call(n,o)&&a.indexOf(o)<0&&(p[o]=n[o]);if(n!=null&&u)for(var o of u(n))a.indexOf(o)<0&&r.call(n,o)&&(p[o]=n[o]);return p};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(p){var o=p,{components:n}=o,a=e(o,[\"components\"]);return mdx(MDXLayout,s($($({},layoutProps),a),{components:n,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"$$Average\\\\ weight_{(Juan,\\\\ Jim,\\\\ Malik)}=\\\\frac{Juan+Jim+Malik}{3}=160\\\\ pounds$$\"),mdx(\"p\",null,\"$$=>Juan+Jim+Malik=160\\\\ pounds \\\\times3=480\\\\ pounds$$\"),mdx(\"p\",null,\"$$Average\\\\ weight_{(Juan,\\\\ Jim,\\\\ Malik,\\\\ Harry)}=\\\\frac{Juan+Jim+Malik+Harry}{4}=150\\\\ pounds$$\"),mdx(\"p\",null,\"$$=>Juan+Jim+Malik+Harry=150\\\\ pounds \\\\times4=600\\\\ pounds$$\"),mdx(\"p\",null,\"$$=>Harry=600\\\\ pounds-480\\\\ pounds=120 \\\\ pounds$$\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":["average"],"readable_tags":"Average","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-25","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 26","id":2388,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q26.jpg","question_text":"26. What is the value of the expression _log6(36)+_log3(9)+ ?","section":"math","question_number":26,"form_id":"d06","category":"logarithms","readable_category":"Logarithms","sub_category":"logarithm-expressions","readable_sub_category":"Logarithm Expressions","answer_choices":"Choice H","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var i=Object.defineProperty,l=Object.defineProperties;var y=Object.getOwnPropertyDescriptors;var p=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,u=Object.prototype.propertyIsEnumerable;var c=(o,t,e)=>t in o?i(o,t,{enumerable:!0,configurable:!0,writable:!0,value:e}):o[t]=e,$=(o,t)=>{for(var e in t||(t={}))r.call(t,e)&&c(o,e,t[e]);if(p)for(var e of p(t))u.call(t,e)&&c(o,e,t[e]);return o},s=(o,t)=>l(o,y(t));var a=(o,t)=>{var e={};for(var n in o)r.call(o,n)&&t.indexOf(n)<0&&(e[n]=o[n]);if(o!=null&&p)for(var n of p(o))t.indexOf(n)<0&&u.call(o,n)&&(e[n]=o[n]);return e};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(e){var n=e,{components:o}=n,t=a(n,[\"components\"]);return mdx(MDXLayout,s($($({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"Since $6^2=36$, $log_6(36)=2$.\"),mdx(\"p\",null,\"Since $3^2=9$, $log_3(9)=2$.\"),mdx(\"p\",null,\"Therefore, $(log_6(36))(log_3(9))=2\\\\times2=4$\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-26","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 27","id":2389,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q27.jpg","question_text":"27. Each of 2 identical number cubes, shown below, has a different integer, 1 through 6, on each face. Consider the sample space determined by rolling these number cubes and adding the 2 integers on the faces that land on top. What is the positive difference between the greatest sum and the least sum in this sample space?","section":"math","question_number":27,"form_id":"d06","category":"word-problems","readable_category":"Word Problems","sub_category":"2-variable-addition","readable_sub_category":"2 Variable Addition","answer_choices":"Choice B","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var i=Object.defineProperty,m=Object.defineProperties;var y=Object.getOwnPropertyDescriptors;var n=Object.getOwnPropertySymbols;var s=Object.prototype.hasOwnProperty,u=Object.prototype.propertyIsEnumerable;var a=(e,t,o)=>t in e?i(e,t,{enumerable:!0,configurable:!0,writable:!0,value:o}):e[t]=o,r=(e,t)=>{for(var o in t||(t={}))s.call(t,o)&&a(e,o,t[o]);if(n)for(var o of n(t))u.call(t,o)&&a(e,o,t[o]);return e},$=(e,t)=>m(e,y(t));var c=(e,t)=>{var o={};for(var p in e)s.call(e,p)&&t.indexOf(p)<0&&(o[p]=e[p]);if(e!=null&&n)for(var p of n(e))t.indexOf(p)<0&&u.call(e,p)&&(o[p]=e[p]);return o};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(o){var p=o,{components:e}=p,t=c(p,[\"components\"]);return mdx(MDXLayout,$(r(r({},layoutProps),t),{components:e,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"The greatest sum$=6+6=12$.\"),mdx(\"p\",null,\"The least sum$=1+1=2$.\"),mdx(\"p\",null,\"Therefore, the positive difference $=12-2=10$\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-27","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 28","id":2390,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q28.jpg","question_text":"28. What angle measure, in radians, is equal to 30° ?","section":"math","question_number":28,"form_id":"d06","category":"angles","readable_category":"Angles","sub_category":"circles","readable_sub_category":"Circles","answer_choices":"Choice F","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var $=Object.defineProperty,f=Object.defineProperties;var y=Object.getOwnPropertyDescriptors;var a=Object.getOwnPropertySymbols;var c=Object.prototype.hasOwnProperty,e=Object.prototype.propertyIsEnumerable;var i=(p,t,o)=>t in p?$(p,t,{enumerable:!0,configurable:!0,writable:!0,value:o}):p[t]=o,r=(p,t)=>{for(var o in t||(t={}))c.call(t,o)&&i(p,o,t[o]);if(a)for(var o of a(t))e.call(t,o)&&i(p,o,t[o]);return p},s=(p,t)=>f(p,y(t));var u=(p,t)=>{var o={};for(var n in p)c.call(p,n)&&t.indexOf(n)<0&&(o[n]=p[n]);if(p!=null&&a)for(var n of a(p))t.indexOf(n)<0&&e.call(p,n)&&(o[n]=p[n]);return o};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(o){var n=o,{components:p}=n,t=u(n,[\"components\"]);return mdx(MDXLayout,s(r(r({},layoutProps),t),{components:p,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"$360\\xB0=2\\\\pi\\\\ radians$\"),mdx(\"p\",null,\"$\\\\frac{2\\\\pi}{360\\xB0}=\\\\frac{x}{30\\xB0}$\"),mdx(\"p\",null,\"$=> x=30\\\\times\\\\frac{2\\\\pi}{360\\xB0}=\\\\frac{\\\\pi}{6}$\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":["degrees-and-radians"],"readable_tags":"Degrees and radians","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-28","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 29","id":2391,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q29.jpg","question_text":"29. For one school week, Hannah recorded the following temperatures, in degrees Fahrenheit, so she could investigate the difference between the high and low temperature each day.\r\n\r\nDay\r\nMonday Tuesday Wednesday Thursday Friday\r\nLow High\r\n−3° 26° −5° 32° −7° 22° 03° 40° 02° 40°\r\n\r\nTo the nearest degree, what was the mean of the differences in daily high and low temperatures for these 5 days?","section":"math","question_number":29,"form_id":"d06","category":"statistics","readable_category":"Statistics","sub_category":"mean-median","readable_sub_category":"Mean, Median","answer_choices":"Choice E","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var d=Object.defineProperty,$=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var o=Object.getOwnPropertySymbols;var a=Object.prototype.hasOwnProperty,f=Object.prototype.propertyIsEnumerable;var h=(e,t,n)=>t in e?d(e,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):e[t]=n,p=(e,t)=>{for(var n in t||(t={}))a.call(t,n)&&h(e,n,t[n]);if(o)for(var n of o(t))f.call(t,n)&&h(e,n,t[n]);return e},i=(e,t)=>$(e,c(t));var u=(e,t)=>{var n={};for(var r in e)a.call(e,r)&&t.indexOf(r)<0&&(n[r]=e[r]);if(e!=null&&o)for(var r of o(e))t.indexOf(r)<0&&f.call(e,r)&&(n[r]=e[r]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var r=n,{components:e}=r,t=u(r,[\"components\"]);return mdx(MDXLayout,i(p(p({},layoutProps),t),{components:e,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"Difference between the high and low temperature of Monday $=26\\xB0-(-3\\xB0)=29\\xB0$;\"),mdx(\"p\",null,\"Difference between the high and low temperature of Tuesday $=32\\xB0-(-5\\xB0)=37\\xB0$;\"),mdx(\"p\",null,\"Difference between the high and low temperature of Wednesday $=22\\xB0-(-7\\xB0)=29\\xB0$;\"),mdx(\"p\",null,\"Difference between the high and low temperature of Thursday $=40\\xB0-3\\xB0=37\\xB0$;\"),mdx(\"p\",null,\"Difference between the high and low temperature of Friday $=40\\xB0-2\\xB0=38\\xB0$;\"),mdx(\"p\",null,\"Therefore, the mean of the differences $=\\\\frac{29\\xB0+37\\xB0+29\\xB0+37\\xB0+38\\xB0}{5}=34\\xB0$\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-29","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 30","id":2392,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q30.jpg","question_text":"30. A family’s budgeted items are expressed as a fraction of their weekly income in the chart below.","section":"math","question_number":30,"form_id":"d06","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":"","mdcontent":{"compiledSource":"var y=Object.defineProperty,D=Object.defineProperties;var M=Object.getOwnPropertyDescriptors;var c=Object.getOwnPropertySymbols;var f=Object.prototype.hasOwnProperty,p=Object.prototype.propertyIsEnumerable;var e=(o,r,t)=>r in o?y(o,r,{enumerable:!0,configurable:!0,writable:!0,value:t}):o[r]=t,n=(o,r)=>{for(var t in r||(r={}))f.call(r,t)&&e(o,t,r[t]);if(c)for(var t of c(r))p.call(r,t)&&e(o,t,r[t]);return o},u=(o,r)=>D(o,M(r));var s=(o,r)=>{var t={};for(var a in o)f.call(o,a)&&r.indexOf(a)<0&&(t[a]=o[a]);if(o!=null&&c)for(var a of c(o))r.indexOf(a)<0&&p.call(o,a)&&(t[a]=o[a]);return t};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(t){var a=t,{components:o}=a,r=s(a,[\"components\"]);return mdx(MDXLayout,u(n(n({},layoutProps),r),{components:o,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"$1-(\\\\frac{3}{8}+\\\\frac{1}{4}+\\\\frac{1}{8}+\\\\frac{1}{12}+\\\\frac{1}{16}+\\\\frac{1}{24})=\\\\frac{1}{16}$\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-30","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 31","id":2393,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q31.jpg","question_text":"31. What is the 322nd digit after the decimal point in the repeating decimal 0.1357 ?","section":"math","question_number":31,"form_id":"d06","category":"number-types-and-properties","readable_category":"Number Types & Properties","sub_category":"rational-and-irrational-numbers-and-integers","readable_sub_category":"Rational & Irrational Numbers and Integers","answer_choices":"Choice C","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var d=Object.defineProperty,u=Object.defineProperties;var g=Object.getOwnPropertyDescriptors;var n=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;var s=(e,t,o)=>t in e?d(e,t,{enumerable:!0,configurable:!0,writable:!0,value:o}):e[t]=o,p=(e,t)=>{for(var o in t||(t={}))r.call(t,o)&&s(e,o,t[o]);if(n)for(var o of n(t))a.call(t,o)&&s(e,o,t[o]);return e},c=(e,t)=>u(e,g(t));var h=(e,t)=>{var o={};for(var i in e)r.call(e,i)&&t.indexOf(i)<0&&(o[i]=e[i]);if(e!=null&&n)for(var i of n(e))t.indexOf(i)<0&&a.call(e,i)&&(o[i]=e[i]);return o};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(o){var i=o,{components:e}=i,t=h(i,[\"components\"]);return mdx(MDXLayout,c(p(p({},layoutProps),t),{components:e,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"The repeating decimal repeats itself in blocks of 4 (with the repeating group being 1357).\"),mdx(\"p\",null,\"$$322\\\\div4=80...2$$\"),mdx(\"p\",null,\"Before the 322nd digit, there are 80 blocks of \\u201C1357\\u201D, which makes digit 3 the 2nd digit after the 80 blocks.\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":["repeating-decimal"],"readable_tags":"Repeating decimals","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-31","main_question":"","skills":[{"title":"Repeating decimal","mdcontent":{"compiledSource":"var f=Object.defineProperty,c=Object.defineProperties;var u=Object.getOwnPropertyDescriptors;var a=Object.getOwnPropertySymbols;var n=Object.prototype.hasOwnProperty,s=Object.prototype.propertyIsEnumerable;var i=(e,t,p)=>t in e?f(e,t,{enumerable:!0,configurable:!0,writable:!0,value:p}):e[t]=p,o=(e,t)=>{for(var p in t||(t={}))n.call(t,p)&&i(e,p,t[p]);if(a)for(var p of a(t))s.call(t,p)&&i(e,p,t[p]);return e},h=(e,t)=>c(e,u(t));var m=(e,t)=>{var p={};for(var r in e)n.call(e,r)&&t.indexOf(r)<0&&(p[r]=e[r]);if(e!=null&&a)for(var r of a(e))t.indexOf(r)<0&&s.call(e,r)&&(p[r]=e[r]);return p};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(p){var r=p,{components:e}=r,t=m(r,[\"components\"]);return mdx(MDXLayout,h(o(o({},layoutProps),t),{components:e,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"A decimal number with a digit (or group of digits) that repeats forever.\"),mdx(\"p\",null,'Often show by \"...\"'),mdx(\"p\",null,\"Examples:\"),mdx(\"p\",null,\"1/3 = 0.333... (the 3 repeats forever)\"),mdx(\"p\",null,'1/7 = 0.142857142857... ( the \"142857\" repeats forever)'),mdx(\"p\",null,\"77/600 = 0.128333... (the 3 repeats forever)\"),mdx(\"p\",null,\"The part that repeats can also be shown by placing dots over the first and last digits of the repeating pattern, or by a line over the pattern.\"),mdx(\"p\",null,mdx(\"a\",o({parentName:\"p\"},{href:\"https://www.mathsisfun.com/definitions/recurring-decimal.html\"}),\"https://www.mathsisfun.com/definitions/recurring-decimal.html\")))}MDXContent.isMDXComponent=!0;\n","scope":{}}}]},{"title":"2021 June(D06) Math Question 32","id":2394,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q32.jpg","question_text":"32. You and a friend each have a can full of water. You start pouring the water from your can into an empty bucket at a constant rate of 4 ounces per second. While you are still pouring water, 3 seconds after you started, your friend starts pouring the water from her can into the same bucket at a constant rate of 2 ounces per second. How many seconds after you first started pouring the water into the bucket will it contain 24 ounces of water?","section":"math","question_number":32,"form_id":"d06","category":"word-problems","readable_category":"Word Problems","sub_category":"distance-speed-time","readable_sub_category":"Distance, Speed, Time","answer_choices":"Choice G","answer_image":"https://ahdjango.herokuapp.com/media/answers/d06-math-q32a.png","answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var D=Object.defineProperty,M=Object.defineProperties;var X=Object.getOwnPropertyDescriptors;var u=Object.getOwnPropertySymbols;var a=Object.prototype.hasOwnProperty,p=Object.prototype.propertyIsEnumerable;var s=(o,t,n)=>t in o?D(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,r=(o,t)=>{for(var n in t||(t={}))a.call(t,n)&&s(o,n,t[n]);if(u)for(var n of u(t))p.call(t,n)&&s(o,n,t[n]);return o},y=(o,t)=>M(o,X(t));var c=(o,t)=>{var n={};for(var e in o)a.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&&p.call(o,e)&&(n[e]=o[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:o}=e,t=c(e,[\"components\"]);return mdx(MDXLayout,y(r(r({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"After 5 seconds, the total amount of water both you and your friend pour is 24 ounces.\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-32","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 33","id":2395,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q33.jpg","question_text":"33. A package of candy contains pieces each of which is 1 of 6 possible colors: brown, red, green, yellow, orange, and blue. In each package, 1/3 of the pieces are brown and the remaining pieces have an even\r\ndistribution of the other 5colors. 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Which of the following intervals is the range of the functionf(x)=−(x−3)2 +4?","section":"math","question_number":34,"form_id":"d06","category":"conics","readable_category":"Conics","sub_category":"parabola","readable_sub_category":"Parabola","answer_choices":"Choice G","answer_image":"https://ahdjango.herokuapp.com/media/answers/d06-math-q34a.png","answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var D=Object.defineProperty,M=Object.defineProperties;var X=Object.getOwnPropertyDescriptors;var a=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,u=Object.prototype.propertyIsEnumerable;var c=(t,n,o)=>n in t?D(t,n,{enumerable:!0,configurable:!0,writable:!0,value:o}):t[n]=o,p=(t,n)=>{for(var o in n||(n={}))r.call(n,o)&&c(t,o,n[o]);if(a)for(var o of a(n))u.call(n,o)&&c(t,o,n[o]);return t},s=(t,n)=>M(t,X(n));var y=(t,n)=>{var o={};for(var e in t)r.call(t,e)&&n.indexOf(e)<0&&(o[e]=t[e]);if(t!=null&&a)for(var e of a(t))n.indexOf(e)<0&&u.call(t,e)&&(o[e]=t[e]);return o};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(o){var e=o,{components:t}=e,n=y(e,[\"components\"]);return mdx(MDXLayout,s(p(p({},layoutProps),n),{components:t,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"Draw the graph of the function and you can see the range.\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":["parabola","range"],"readable_tags":"Parabola, Range","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-34","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 35","id":2397,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q35.jpg","question_text":"35. Anoki made a scale drawing of his rectangular classroom. The classroom is 7.5 meters by 9.0 meters. In his scale drawing, Anoki made the length of the shorter side of the classroom 9.0 centimeters. 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In rhombus ABCD shown below, AC = 5 feet and BD = 6 feet. 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One number is 25% of a second number, and the second number is 70% of a third number. 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The monthly rent charged for a store at Center Street Mall is $2 per square foot of floor area. The floor plan of a store at Center Street Mall is shown in the figure below, with right angles as indicated and all distances given in feet. How much monthly rent is charged for this store?","section":"math","question_number":38,"form_id":"d06","category":"perimeter-area-volume","readable_category":"Perimeter, Area, Volume","sub_category":"mixed-shapes","readable_sub_category":"Mixed Shapes","answer_choices":"Choice K","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var f=Object.defineProperty,i=Object.defineProperties;var u=Object.getOwnPropertyDescriptors;var p=Object.getOwnPropertySymbols;var a=Object.prototype.hasOwnProperty,s=Object.prototype.propertyIsEnumerable;var $=(e,t,o)=>t in e?f(e,t,{enumerable:!0,configurable:!0,writable:!0,value:o}):e[t]=o,n=(e,t)=>{for(var o in t||(t={}))a.call(t,o)&&$(e,o,t[o]);if(p)for(var o of p(t))s.call(t,o)&&$(e,o,t[o]);return e},m=(e,t)=>i(e,u(t));var c=(e,t)=>{var o={};for(var r in e)a.call(e,r)&&t.indexOf(r)<0&&(o[r]=e[r]);if(e!=null&&p)for(var r of p(e))t.indexOf(r)<0&&s.call(e,r)&&(o[r]=e[r]);return o};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(o){var r=o,{components:e}=r,t=c(r,[\"components\"]);return mdx(MDXLayout,m(n(n({},layoutProps),t),{components:e,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"Area of rectangle $=60\\\\times30=1800$\"),mdx(\"p\",null,\"Area of trapezoid$=\\\\frac{1}{2}(18+30+27+33)\\\\times 36 \\\\times \\\\frac{1}{2}=1944$\"),mdx(\"p\",null,\"Area of store $1800+1944=3744$\"),mdx(\"p\",null,\"Therefore, monthly rent $=\\\\$ 2 \\\\times 3744= \\\\$ 7488$\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":["trapezoid-area","rectangle-area"],"readable_tags":"Trapezoid area, Rectangle area","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-38","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 39","id":2401,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q39.jpg","question_text":"39. Mrs. Neeson, a science teacher, told her students that 30.0% of their final semester grades will come from their homework averages, and the remaining 70.0% will come from their test averages. She also said that the final exam will count for 20.0% of the test average. What percent of the science final semester grade is the final exam grade?","section":"math","question_number":39,"form_id":"d06","category":"ratios-proportions-percentages-fractions","readable_category":"Ratios, Proportions, Percentages, Fractions","sub_category":"percents-and-fractions","readable_sub_category":"Percents & Fractions","answer_choices":"","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var p=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,s=Object.prototype.propertyIsEnumerable;var a=(t,o,n)=>o in t?M(t,o,{enumerable:!0,configurable:!0,writable:!0,value:n}):t[o]=n,u=(t,o)=>{for(var n in o||(o={}))r.call(o,n)&&a(t,n,o[n]);if(p)for(var n of p(o))s.call(o,n)&&a(t,n,o[n]);return t},y=(t,o)=>X(t,c(o));var D=(t,o)=>{var n={};for(var e in t)r.call(t,e)&&o.indexOf(e)<0&&(n[e]=t[e]);if(t!=null&&p)for(var e of p(t))o.indexOf(e)<0&&s.call(t,e)&&(n[e]=t[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:t}=e,o=D(e,[\"components\"]);return mdx(MDXLayout,y(u(u({},layoutProps),o),{components:t,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"$20\\\\% \\\\times 70\\\\% = 14\\\\%$\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-39","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 40","id":2402,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q40.jpg","question_text":"40. A rectangle with an area of 30 square inches has length and width, in inches, that are both integers. 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Some information about each condo is given below. The couple assumes that the market value of either condo will increase exponentially at a rate of 4% per year.","section":"math","question_number":41,"form_id":"d06","category":"exponents-radicals-and-scientific-notation","readable_category":"Exponents, Radicals, & Scientific Notation","sub_category":"scientific-notation","readable_sub_category":"Scientific Notation","answer_choices":"Choice C","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var p=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,s=Object.prototype.propertyIsEnumerable;var a=(t,o,n)=>o in t?M(t,o,{enumerable:!0,configurable:!0,writable:!0,value:n}):t[o]=n,u=(t,o)=>{for(var n in o||(o={}))r.call(o,n)&&a(t,n,o[n]);if(p)for(var n of p(o))s.call(o,n)&&a(t,n,o[n]);return t},y=(t,o)=>X(t,c(o));var D=(t,o)=>{var n={};for(var e in t)r.call(t,e)&&o.indexOf(e)<0&&(n[e]=t[e]);if(t!=null&&p)for(var e of p(t))o.indexOf(e)<0&&s.call(t,e)&&(n[e]=t[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:t}=e,o=D(e,[\"components\"]);return mdx(MDXLayout,y(u(u({},layoutProps),o),{components:t,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"$210,000-189,900=20,100=2.01\\\\times10^4$\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":false,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-41","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 42","id":2404,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q42.jpg","question_text":"42. The couple will consider the price per square foot of each condo. Let x and y be the price per square foot, rounded to the nearest $1, of Condo X and Condo Y, respectively. One of the following comparisons is true. Which one?","section":"math","question_number":42,"form_id":"d06","category":"ratios-proportions-percentages-fractions","readable_category":"Ratios, Proportions, Percentages, Fractions","sub_category":"proportions-and-ratios","readable_sub_category":"Proportions & Ratios","answer_choices":"Choice J","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var c=Object.defineProperty,D=Object.defineProperties;var M=Object.getOwnPropertyDescriptors;var a=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,s=Object.prototype.propertyIsEnumerable;var u=(o,p,t)=>p in o?c(o,p,{enumerable:!0,configurable:!0,writable:!0,value:t}):o[p]=t,e=(o,p)=>{for(var t in p||(p={}))r.call(p,t)&&u(o,t,p[t]);if(a)for(var t of a(p))s.call(p,t)&&u(o,t,p[t]);return o},$=(o,p)=>D(o,M(p));var y=(o,p)=>{var t={};for(var n in o)r.call(o,n)&&p.indexOf(n)<0&&(t[n]=o[n]);if(o!=null&&a)for(var n of a(o))p.indexOf(n)<0&&s.call(o,n)&&(t[n]=o[n]);return t};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(t){var n=t,{components:o}=n,p=y(n,[\"components\"]);return mdx(MDXLayout,$(e(e({},layoutProps),p),{components:o,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"$x=92$\"),mdx(\"p\",null,\"$y=\\\\frac{189900}{1726}\\\\approx110$\"),mdx(\"p\",null,\"\\\\$92 is \\\\$18 less than $110.\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-42","main_question":"2403","skills":[],"mainQImg":"https://ahdjango.herokuapp.com/media/questions/d06_math_q41.jpg"},{"title":"2021 June(D06) Math Question 43","id":2405,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q43.jpg","question_text":"43. The annual property tax for Condo X is 2% of its assessed value. 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In the standard (x,y) coordinate plane, the 3 lines with equations y= _3_x−3, y=−_2_x+2, and x=0 bound a triangular region. What is the area, in square coordinate units, of that triangular region? 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The volume of a solid object is equal to the volume of water it displaces when completely submerged in water. A solid object will be placed in a rectangular tank that has a base of 35 cm by 30 cm and is filled with water to a uniform depth of 13 cm. When the object is completely submerged, the new depth of the water in the tank is 15 cm. 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In coordinate units, the radius of the smaller circle is 2, and the radius of the larger circle is 4. Points A(−4,0), B, and C(4,0) are on the larger circle. 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A 3rd circle, not shown, is the image resulting from applying the 1st transformation listed below to the smaller circle and then applying the 2nd transformation listed below to the result of the 1st transformation.\r\n1st: A dilation with center O and scale factor 2 2nd: A translation of 8 coordinate units to the\r\nright\r\nThe 3rd circle has how many points in common with the larger circle?","section":"math","question_number":49,"form_id":"d06","category":"graphing-properties","readable_category":"Graphing Properties","sub_category":"reflection-rotation-symmetry-translation","readable_sub_category":"Reflection, Rotation, Symmetry, Translation","answer_choices":"Choice B","answer_image":"https://ahdjango.herokuapp.com/media/answers/d06_math_q49a.png","answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var u=Object.defineProperty,l=Object.defineProperties;var m=Object.getOwnPropertyDescriptors;var r=Object.getOwnPropertySymbols;var c=Object.prototype.hasOwnProperty,p=Object.prototype.propertyIsEnumerable;var h=(t,e,o)=>e in t?u(t,e,{enumerable:!0,configurable:!0,writable:!0,value:o}):t[e]=o,a=(t,e)=>{for(var o in e||(e={}))c.call(e,o)&&h(t,o,e[o]);if(r)for(var o of r(e))p.call(e,o)&&h(t,o,e[o]);return t},i=(t,e)=>l(t,m(e));var s=(t,e)=>{var o={};for(var n in t)c.call(t,n)&&e.indexOf(n)<0&&(o[n]=t[n]);if(t!=null&&r)for(var n of r(t))e.indexOf(n)<0&&p.call(t,n)&&(o[n]=t[n]);return o};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(o){var n=o,{components:t}=n,e=s(n,[\"components\"]);return mdx(MDXLayout,i(a(a({},layoutProps),e),{components:t,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"After the transformations, the new circle and the larger circle will be tangent to each other - they have one common point.\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-49","main_question":"2410","skills":[],"mainQImg":"https://ahdjango.herokuapp.com/media/questions/d06_math_q48.jpg"},{"title":"2021 June(D06) Math Question 50","id":2412,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q50.jpg","question_text":"50. 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Which of the following is an equation of OB ?","section":"math","question_number":51,"form_id":"d06","category":"algebraic-and-function-expressions","readable_category":"Algebraic & Function Expressions","sub_category":"write-function-expressions","readable_sub_category":"Write Function Expressions","answer_choices":"Choice C","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var M=Object.defineProperty,X=Object.defineProperties;var c=Object.getOwnPropertyDescriptors;var p=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,u=Object.prototype.propertyIsEnumerable;var y=(t,o,n)=>o in t?M(t,o,{enumerable:!0,configurable:!0,writable:!0,value:n}):t[o]=n,a=(t,o)=>{for(var n in o||(o={}))r.call(o,n)&&y(t,n,o[n]);if(p)for(var n of p(o))u.call(o,n)&&y(t,n,o[n]);return t},s=(t,o)=>X(t,c(o));var D=(t,o)=>{var n={};for(var e in t)r.call(t,e)&&o.indexOf(e)<0&&(n[e]=t[e]);if(t!=null&&p)for(var e of p(t))o.indexOf(e)<0&&u.call(t,e)&&(n[e]=t[e]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var e=n,{components:t}=e,o=D(e,[\"components\"]);return mdx(MDXLayout,s(a(a({},layoutProps),o),{components:t,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"Slope $=tan \\\\theta = tan 45\\xB0 =1$\"),mdx(\"p\",null,\"$\\\\therefore y=x$\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":["linear-equations"],"readable_tags":"Linear equations","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-51","main_question":"2410","skills":[],"mainQImg":"https://ahdjango.herokuapp.com/media/questions/d06_math_q48.jpg"},{"title":"2021 June(D06) Math Question 52","id":2368,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q52.jpg","question_text":"A sequence is given by","section":"math","question_number":52,"form_id":"d06","category":"sequences-and-patterns","readable_category":"Sequences and Patterns","sub_category":"arithmetic-sequences","readable_sub_category":"Arithmetic Sequences","answer_choices":"Choice J","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var D=Object.defineProperty,i=Object.defineProperties;var m=Object.getOwnPropertyDescriptors;var r=Object.getOwnPropertySymbols;var p=Object.prototype.hasOwnProperty,c=Object.prototype.propertyIsEnumerable;var s=(o,t,e)=>t in o?D(o,t,{enumerable:!0,configurable:!0,writable:!0,value:e}):o[t]=e,a=(o,t)=>{for(var e in t||(t={}))p.call(t,e)&&s(o,e,t[e]);if(r)for(var e of r(t))c.call(t,e)&&s(o,e,t[e]);return o},d=(o,t)=>i(o,m(t));var u=(o,t)=>{var e={};for(var n in o)p.call(o,n)&&t.indexOf(n)<0&&(e[n]=o[n]);if(o!=null&&r)for(var n of r(o))t.indexOf(n)<0&&c.call(o,n)&&(e[n]=o[n]);return e};const makeShortcode=o=>function(e){return console.warn(\"Component \"+o+\" was not imported, exported, or provided by MDXProvider as global scope\"),mdx(\"div\",a({},e))},Chart=makeShortcode(\"Chart\"),layoutProps={},MDXLayout=\"wrapper\";function MDXContent(e){var n=e,{components:o}=n,t=u(n,[\"components\"]);return mdx(MDXLayout,d(a(a({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}),mdx(Chart,{mdxType:\"Chart\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-52","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 53","id":2414,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q53.jpg","question_text":"53. In the figure below, the distances between 2 pairs of cities are shown, as well as the angle formed at Ewing, which has a measure of 127°. 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Which of the following expressions is equivalent to __1___ − __1___ ?\r\nx−a x+a","section":"math","question_number":54,"form_id":"d06","category":"algebraic-and-function-expressions","readable_category":"Algebraic & Function Expressions","sub_category":"simplify-algebraic-expressions","readable_sub_category":"Simplify Algebraic Expressions","answer_choices":"Choice F","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var y=Object.defineProperty,D=Object.defineProperties;var M=Object.getOwnPropertyDescriptors;var p=Object.getOwnPropertySymbols;var e=Object.prototype.hasOwnProperty,u=Object.prototype.propertyIsEnumerable;var c=(o,t,a)=>t in o?y(o,t,{enumerable:!0,configurable:!0,writable:!0,value:a}):o[t]=a,r=(o,t)=>{for(var a in t||(t={}))e.call(t,a)&&c(o,a,t[a]);if(p)for(var a of p(t))u.call(t,a)&&c(o,a,t[a]);return o},s=(o,t)=>D(o,M(t));var x=(o,t)=>{var a={};for(var n in o)e.call(o,n)&&t.indexOf(n)<0&&(a[n]=o[n]);if(o!=null&&p)for(var n of p(o))t.indexOf(n)<0&&u.call(o,n)&&(a[n]=o[n]);return a};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(a){var n=a,{components:o}=n,t=x(n,[\"components\"]);return mdx(MDXLayout,s(r(r({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"$=\\\\frac{x+a-x+a}{x^2-a^2}=\\\\frac{2a}{x^2-a^2}$\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-54","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 55","id":2416,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q55.jpg","question_text":"55. One of the following equations represents the ellipse shown below in the standard (x,y) coordinate plane. 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One of the following equations is that of a parabola\r\nwith x-intercepts −5 and _3_ in the standard (x,y) 4\r\ncoordinate plane. Which equation?","section":"math","question_number":56,"form_id":"d06","category":"quadratic-equations","readable_category":"Quadratic Equations","sub_category":"foil","readable_sub_category":"FOIL","answer_choices":"Choice J","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var c=Object.defineProperty,m=Object.defineProperties;var y=Object.getOwnPropertyDescriptors;var $=Object.getOwnPropertySymbols;var e=Object.prototype.hasOwnProperty,r=Object.prototype.propertyIsEnumerable;var s=(p,t,x)=>t in p?c(p,t,{enumerable:!0,configurable:!0,writable:!0,value:x}):p[t]=x,n=(p,t)=>{for(var x in t||(t={}))e.call(t,x)&&s(p,x,t[x]);if($)for(var x of $(t))r.call(t,x)&&s(p,x,t[x]);return p},a=(p,t)=>m(p,y(t));var u=(p,t)=>{var x={};for(var o in p)e.call(p,o)&&t.indexOf(o)<0&&(x[o]=p[o]);if(p!=null&&$)for(var o of $(p))t.indexOf(o)<0&&r.call(p,o)&&(x[o]=p[o]);return x};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(x){var o=x,{components:p}=o,t=u(o,[\"components\"]);return mdx(MDXLayout,a(n(n({},layoutProps),t),{components:p,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"$(x+5)(x-\\\\frac{3}{4})=0$\"),mdx(\"p\",null,\"$=> (x+5)(x-\\\\frac{3}{4})\\\\times4=0$\"),mdx(\"p\",null,\"$=> (x+5)(4x-3)=0$\"),mdx(\"p\",null,\"$=> 4x^2-3x+5\\\\times4x-5\\\\times3=0$\"),mdx(\"p\",null,\"$=> 4x^2+17x-15=0$\"),mdx(\"p\",null,\"$=> 4x^2+17x-15=y$\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-56","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 57","id":2418,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q57.jpg","question_text":"57. There are 100 fractions in the following set. Each fraction after the first is found by adding 3 to the preceding fraction’s numerator and denominator. What is the product of these 100 fractions?","section":"math","question_number":57,"form_id":"d06","category":"ratios-proportions-percentages-fractions","readable_category":"Ratios, Proportions, Percentages, Fractions","sub_category":"percents-and-fractions","readable_sub_category":"Percents & Fractions","answer_choices":"Choice E","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var f=Object.defineProperty,i=Object.defineProperties;var u=Object.getOwnPropertyDescriptors;var t=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,s=Object.prototype.propertyIsEnumerable;var l=(c,e,a)=>e in c?f(c,e,{enumerable:!0,configurable:!0,writable:!0,value:a}):c[e]=a,o=(c,e)=>{for(var a in e||(e={}))r.call(e,a)&&l(c,a,e[a]);if(t)for(var a of t(e))s.call(e,a)&&l(c,a,e[a]);return c},m=(c,e)=>i(c,u(e));var p=(c,e)=>{var a={};for(var n in c)r.call(c,n)&&e.indexOf(n)<0&&(a[n]=c[n]);if(c!=null&&t)for(var n of t(c))e.indexOf(n)<0&&s.call(c,n)&&(a[n]=c[n]);return a};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(a){var n=a,{components:c}=n,e=p(n,[\"components\"]);return mdx(MDXLayout,m(o(o({},layoutProps),e),{components:c,mdxType:\"MDXLayout\"}),mdx(\"p\",null,\"$\\\\frac{1}{\\\\cancel{4}}\\\\times\\\\frac{\\\\cancel{4}}{\\\\cancel{7}}\\\\times\\\\frac{\\\\cancel{7}}{\\\\cancel{10}}\\\\times ... \\\\times \\\\frac{\\\\cancel{295}}{\\\\cancel{298}} \\\\times \\\\frac{\\\\cancel{298}}{301}=\\\\frac{1}{301}$\"))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":["finding-patterns"],"readable_tags":"Finding patterns","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-57","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 58","id":2360,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q58.jpg","question_text":"58. If2x =7and2y =14,thenx−y=?","section":"math","question_number":58,"form_id":"d06","category":"exponents-radicals-and-scientific-notation","readable_category":"Exponents, Radicals, & Scientific Notation","sub_category":"exponent-expressions","readable_sub_category":"Exponent Expressions","answer_choices":"Choice H","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"","mdcontent":{"compiledSource":"var s=Object.defineProperty,D=Object.defineProperties;var M=Object.getOwnPropertyDescriptors;var a=Object.getOwnPropertySymbols;var y=Object.prototype.hasOwnProperty,$=Object.prototype.propertyIsEnumerable;var c=(o,t,n)=>t in o?s(o,t,{enumerable:!0,configurable:!0,writable:!0,value:n}):o[t]=n,p=(o,t)=>{for(var n in t||(t={}))y.call(t,n)&&c(o,n,t[n]);if(a)for(var n of a(t))$.call(t,n)&&c(o,n,t[n]);return o},e=(o,t)=>D(o,M(t));var u=(o,t)=>{var n={};for(var r in o)y.call(o,r)&&t.indexOf(r)<0&&(n[r]=o[r]);if(o!=null&&a)for(var r of a(o))t.indexOf(r)<0&&$.call(o,r)&&(n[r]=o[r]);return n};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(n){var r=n,{components:o}=r,t=u(r,[\"components\"]);return mdx(MDXLayout,e(p(p({},layoutProps),t),{components:o,mdxType:\"MDXLayout\"}),mdx(\"p\",null,`$$\n\\\\frac{2^x}{2^y}=2^{x-y}=\\\\frac{7}{14}=\\\\frac{1}{2}=2^{-1} $$\n$$\\\\Rightarrow x-y=-1\n$$`))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":[],"readable_tags":"","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-58","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 59","id":2359,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q59.jpg","question_text":"59. The table indicates the grade (10 or 11) and high school (North or South) of the 270 students enrolled in Algebra II in the Green City School District.\r\nSuppose 2 of these students will be chosen at random to represent the Algebra II classes at a local STEM (Science, Technology, Engineering, and Mathematics) event. Which of the following expressions gives the probability that both chosen students will be from the same grade and the same high school?","section":"math","question_number":59,"form_id":"d06","category":"probability","readable_category":"Probability","sub_category":"one-event","readable_sub_category":"One Event","answer_choices":"Choice A","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"The number of ways the 2 chosen students are from Grade 10, North \\(= {}_{47} C_{2}=\\frac{47!}{2!}\\)
\r\n\r\n\r\nThe number of ways the 2 chosen students are from Grade 10, South = \\({}_{93} C_{2}=\\frac{93!}{2!}\\)
\r\n\r\n\r\nThe number of ways the 2 chosen students are from Grade 11, North = \\({}_{73} C_{2}=\\frac{73!}{2!}\\)
\r\n\r\n\r\nThe number of ways the 2 chosen students are from Grade 11, South = \\({}_{57} C_{2}=\\frac{57!}{2!}\\)
\r\n\r\n\r\nThe total number of ways 2 students are chosen = \\({}_{270} C_{2}=\\frac{270!}{2!}\\)
\r\n\r\n\r\n$$\\therefore\tP(same\\ grade\\ and\\ same\\ school) \\approx \\frac{\\frac{47!}{2!}+\\frac{93!}{2!}+\\frac{73!}{2!}+\\frac{57!}{2!}}{\\frac{270!}{2!}}$$","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":["probability"],"readable_tags":"Probability","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-59","main_question":"","skills":[]},{"title":"2021 June(D06) Math Question 60","id":2358,"question_image":"https://ahdjango.herokuapp.com/media/questions/d06_math_q60.jpg","question_text":"60. A certain company has 120 employees, 85 of whom have business degrees. Of the employees with business degrees, 75 are certified public accountants (CPAs). There are 14 employees who are not CPAs and also do not hold a business degree. One employee of the company will be selected at random to be interviewed for a television news program. What is the probability that the selected employee will be a CPA ?\r\n(Note: A business degree is NOT required to be a CPA.)","section":"math","question_number":60,"form_id":"d06","category":"probability","readable_category":"Probability","sub_category":"one-event","readable_sub_category":"One Event","answer_choices":"Choice J","answer_image":null,"answer_image2":null,"answer_image3":null,"answer_image4":null,"explanation":"$$10+75+14+x=120$$ \r\n\r\n$$x=21$$\r\n\r\n\r\nThe number of employees who are CPAs is \\(21+75=96\\).\r\n\r\n\r\nTherefore the probability is \\(P=96/120\\).","mdcontent":{"compiledSource":"var D=Object.defineProperty,i=Object.defineProperties;var m=Object.getOwnPropertyDescriptors;var r=Object.getOwnPropertySymbols;var a=Object.prototype.hasOwnProperty,c=Object.prototype.propertyIsEnumerable;var s=(o,n,e)=>n in o?D(o,n,{enumerable:!0,configurable:!0,writable:!0,value:e}):o[n]=e,p=(o,n)=>{for(var e in n||(n={}))a.call(n,e)&&s(o,e,n[e]);if(r)for(var e of r(n))c.call(n,e)&&s(o,e,n[e]);return o},d=(o,n)=>i(o,m(n));var u=(o,n)=>{var e={};for(var t in o)a.call(o,t)&&n.indexOf(t)<0&&(e[t]=o[t]);if(o!=null&&r)for(var t of r(o))n.indexOf(t)<0&&c.call(o,t)&&(e[t]=o[t]);return e};const makeShortcode=o=>function(e){return console.warn(\"Component \"+o+\" was not imported, exported, or provided by MDXProvider as global scope\"),mdx(\"div\",p({},e))},Venn=makeShortcode(\"Venn\"),layoutProps={},MDXLayout=\"wrapper\";function MDXContent(e){var t=e,{components:o}=t,n=u(t,[\"components\"]);return mdx(MDXLayout,d(p(p({},layoutProps),n),{components:o,mdxType:\"MDXLayout\"}),mdx(Venn,{mdxType:\"Venn\"}))}MDXContent.isMDXComponent=!0;\n","scope":{}},"tags":["sets","probability","venn-diagram"],"readable_tags":"Probability, Sets, Venn diagram","free_to_read":true,"nextjs_formid_section":"d06-math","nextjs_formid_section_q":"d06-math-60","main_question":"","skills":[{"title":"Venn diagrams","mdcontent":{"compiledSource":"var m=Object.defineProperty,p=Object.defineProperties;var d=Object.getOwnPropertyDescriptors;var o=Object.getOwnPropertySymbols;var r=Object.prototype.hasOwnProperty,h=Object.prototype.propertyIsEnumerable;var w=(a,t,e)=>t in a?m(a,t,{enumerable:!0,configurable:!0,writable:!0,value:e}):a[t]=e,c=(a,t)=>{for(var e in t||(t={}))r.call(t,e)&&w(a,e,t[e]);if(o)for(var e of o(t))h.call(t,e)&&w(a,e,t[e]);return a},s=(a,t)=>p(a,d(t));var y=(a,t)=>{var e={};for(var n in a)r.call(a,n)&&t.indexOf(n)<0&&(e[n]=a[n]);if(a!=null&&o)for(var n of o(a))t.indexOf(n)<0&&h.call(a,n)&&(e[n]=a[n]);return e};const layoutProps={},MDXLayout=\"wrapper\";function MDXContent(e){var n=e,{components:a}=n,t=y(n,[\"components\"]);return mdx(MDXLayout,s(c(c({},layoutProps),t),{components:a,mdxType:\"MDXLayout\"}),mdx(\"p\",null,mdx(\"a\",c({parentName:\"p\"},{href:\"https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-data/two-way-tables/v/two-way-frequency-tables-and-venn-diagrams\"}),\"https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-data/two-way-tables/v/two-way-frequency-tables-and-venn-diagrams\")))}MDXContent.isMDXComponent=!0;\n","scope":{}}}]}],"title":"D06 Math"},"__N_SSG":true}