ACT Form 67F Math Answer Explanation


Choice D

$$6\times$10=$60$$ $$$60\div(6-1)=$12$$

2011 April(67F) Math Question 2

Word Problems Practice

- Cost

2. A calculator has a regular price of $$8.95 before taxes.
It goes on sale at 20% below the regular price Before taxes are added, what is the sale price of the calculator?

Choice G

$$$58.95\times0.8=$47.16$$

Choice C

$$30:44=70:x$$ $$44\times70=30x$$ $$x=102.66$$

Choice F

$$(5+2-(-3)(2+(-3))$$ $$=(5+2+3)(2-3)$$ $$=(10)(-1)$$ $$=-10$$

Choice A

To maximize the value of x, you must minimize the value of

$$y^{2}$$ $$y^{2}=0,\ x^{2}=256$$ $$x=\pm\sqrt{256}=\pm16$$

The positive 16 is the answer.

Choice J

If Antoine rode the roller coaster, he must be more than 4 feet tall.

Choice C

$$N(4)=\frac{1200\times4^{2}+10}{4^{2}+1}$$ $$=\frac{1200\times16+10}{16+1}$$ $$=\frac{19200}{17}$$ $$\approx 1130$$

Choice J

$$3x^{5}\cdot7x^{9}=(3\cdot7)(x^{5}\cdot x^{9})$$ $$=21x^{14}$$

2011 April(67F) Math Question 9

Probability Practice

- One Event

9. A bag contains 5 yellow jellybeans, 4 red jellybeans, and 3 green jellybeans, all of the same shape and size When 1 jellybean is randomly picked from the bag, what is the probability that it is green?

Choice B

$$\frac{3}{5+4+3}=\frac{3}{12}=\frac{1}{4}$$

Choice G

$$35=5\times7$$ $$56=2^{3}\times7$$ $$16=2^{4}$$ $$\Rightarrow2^{4}\times5\times7=16\times5\times7=560$$

2011 April(67F) Math Question 11

Angles Practice

- Collinear Points & Triangles

11. Marisa's design for a rectangular stained glass window with 7 triangles is shown below. The 2 white triangles are congruent(△ABC ≅ △DEC)and will be a different color than the other 5 triangles, The design includes the measures of ∠CAB, ∠ACB, and ∠DCE. What is the measure of ∠CED?

Choice B

Because triangles ABC and DEC are congruent,

$$\angle CAB=\angle CDE$$ $$\angle CDE= 180° – 45° – 70° = 65°$$

Choice F

$$=\frac{\frac{57}{7}}{\frac{15}{14}}$$ $$=\frac{57}{7}\times\frac{14}{15}$$ $$=\frac{114}{15}$$ $$=\frac{38}{5}$$

Choice D

$$x + y = 15 ---(1)$$ $$x – y = 9---(2)$$ $$(1)+(2)$$ $$2x=24$$ $$x=12$$ $$y=3$$ $$xy=12(3)=36$$

Choice J

1. Draw A as a point on a circle.

2. Draw B 6 units counterclockwise from A.

3. Draw C 2 units clockwise from point A, between A and B in the clockwise direction.

4. Draw D 9 units clockwise from A, between C and B in the clockwise direction.

Now your points are in the correct order, A, C, B, D in the clockwise direction.

2011 April(67F) Math Question 15

Statistics Practice

- Mean, Median

15. To determine a students overall test score for the semester. Ms. Rainwater deletes the lowest test score and calculates the average of the remaining test scores Galen took all 5 tests and earned the following scores in Ms. Rainwater's class this semester:81, 83, 88, 92 and 99. What overall test score did Galen earn in Ms. Rainwater's class this semester?

Choice D

$$\frac{(83 + 88 + 92 + 99)}{4}=90.5$$

Choice K

$$ Slope-intercept (y = mx + b) form$$ $$ 6x – 2 = y \Rightarrow y = 6x – 2$$

2011 April(67F) Math Question 17

Quadratic Equations Practice

- Factoring

17. What is the sum of the 2 solutions of the equation
x2-3x-28=0?

Choice B

$$ \Rightarrow (x – 7)(x + 4) = 0$$ $$ x=7,-4$$ $$ 7+(-4)=3$$

Choice G

$$=\mid-20+18\mid=\mid-2\mid=2$$

Choice C

$$\frac{3}{8}=0.375$$ $$\frac{5}{16}=0.3125$$ $$\frac{11}{32}=0.34375$$

Choice K

$$Slope=\frac{(y2 – y1)}{(x2 – x1)}$$ $$=\frac{10-8}{-2-3}$$ $$=\frac{2}{-5}$$

Choice E

$$a + a + b …

Choice H

$$\frac{250}{875}$$ $$=0.286 $$

Choice B

$$37-13=24$$ $$24=3\times8$$ $$13,16,19,22,25,28,31,34,37$$

The question …

2011 April(67F) Math Question 24

Quadratic Equations Practice

- FOIL

24.For x2≠49,

Choice F

$$x^{2}\neq49\Rightarrow x\neq\pm7$$ $$x^{2}-49=(x+7)(x-7)$$ $$\Rightarrow\frac{(x-7)(x-7)}{(x+7)(x-7)}$$ $$=\frac{(x-7)}{(x+7)}$$

2011 April(67F) Math Question 25

Perimeter, Area, Volume Practice

- Mixed Shapes

25. The sides of one triangle are 12 inches, 14 inches, and 15 inches long, respectively. In a second triangle similar to the first, the shortest side is 8 inches long.
To the nearest tenth of an inch, what is the length of the longest side of the second triangle?

Choice C

$$12:8=15:x$$ $$8\times15=12x$$ $$x=10$$

Choice H

When x -2, (x + …

2011 April(67F) Math Question 27

Perimeter, Area, Volume Practice

- Other Shapes

27. A pentagon has 1 side of length z cm , 2 sides of length
(z + 2)cm each, I side of length 5 cm, and I side of length 3z cm. What is the perimeter, in centimeters, of the pentagon?

Choice B

$$z + 2(z + 2) …

Choice G

67f

B is 10 blocks east …

Choice E

$$b=6c \Rightarrow c=\frac{1}{6}b$$ $$a=2c=2(\frac{1}{6}b)=\frac{1}{3}b$$

2011 April(67F) Math Question 30

Word Problems Practice

- Temperature

30. For a certain plant, the recommended nighttime temperature range in degrees Fahrenheit is
59°≤ F ≤68°. Given the formula C=5/9(F-32)
where C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit, what is the corresponding nighttime temperature range in degrees Celsius for the plant?

Choice J

$$\frac{5}{9}(59-32)=\frac{5}{9}\times27=15$$ $$\frac{5}{9}(68-32)=\frac{5}{9}\times36=20$$ $$\Rightarrow 15° \leq …

2011 April(67F) Math Question 31

Angles Practice

- Other Shapes

31. In parallelogram ABCD below, the measure of ∠BCD is98° and the measure of ∠ CDB is38°. What is the measure of ∠BDA?

Choice C

By parallel line properties,

$$\angle …

Choice J

67f

$$6\times6\times5=180$$

2011 April(67F) Math Question 33

Perimeter, Area, Volume Practice

- Other Shapes

33. Rhombus RHOM is shown in the figure below.
HR=5 m and HM= 6 m, then what is the length, in meters, of OR

Choice E

67f

The triangle is a 3-4-5 …

Choice H

67f

Shade any square whose reflection …

Choice C

$$4x(x)=80$$ $$\Rightarrow 4x^{2}=80$$ $$\Rightarrow x=\sqrt{20}$$ …

2011 April(67F) Math Question 36

Perimeter, Area, Volume Practice

- Other Shapes

36. Ms. Luciano's Algebra I class is describing the volume of geometric figures in terms of variables, She draws a rectangular prism that has a length of (x+2)meters, a width of (x-2)
meters, and a height of (r +1)meters Which of the following is an expression for the volume, in cubic meters, of the rectangular prism?

Choice K

The volume of this rectangular …

Choice B

$$t = 10f – 20$$ …

Choice G

$$Tangent=\frac{opposite}{adjacent}$$ $$\tan25°=\frac{x}{100}$$ $$x=100\tan25°=100\times0.47=47$$

Choice E

67f

3-4-5 triangle (6-8-10)

2011 April(67F) Math Question 40

Perimeter, Area, Volume Practice

- Mixed Shapes

40. Each edge of a cube is 4 inches long. Each edge of a second cube is triple the length of each edge of the first cube. The volume of the second cube is how many cubic inches bigger than the volume of the first cube?

Choice J

$$4^{3}=64$$ $$4\times3=12$$ $$12^{3}=1728$$

The volume …

2011 April(67F) Math Question 41

Conics Practice

- Circles

41. A particular circle in the standard (x, y) coordinate plane has an equation of (x-8)+y2=15. What are the radius of the circle, in coordinate units, and the coordinates of the center of the circle?

Choice E

$$(x-h)^{2}+(y-k)^{2}=r^{2}$$

Based on this equation, …

Choice J

The perimeter of a rectangle …

2011 April(67F) Math Question 43

Perimeter, Area, Volume Practice

- Mixed Shapes

43. The picnic shelter must be at least 10 feet from any edge of the park, On graph paper with the distance between grid lines representing 10 feet, a city engineer makes a scale drawing of the park, as shown below.
The region where the picnic shelter CANNOT be built is shown shaded. The corners of both the park and the region where the picnic shelter may be built are at the intersections of grid lines. The corners of the picnic shelter must also be at the intersections of grid lines How many different locations in the park are possible for the placement of the picnic shelter?

Choice A

There are 2 possible vertical …

Choice F

The current area of the …

2011 April(67F) Math Question 45

Trigonometry Practice

- Graphing Trig Functions

45. The graphs of f(x)=cos x and g(x)= cos(x-π/4) are shown in the standard (x, y) coordinate plane below.
After one of the following pairs of transformations is applied to the graph of f(x), the image of the graph of f(x)is the graph of &(r)。 Which pair is it?

Choice E

Compared to y = cos …

Choice K

$$0\lt p\lt q$$

(F)\ 0\lt …

Choice D

$$a=b\times0.25$$ $$\frac{b\times1.35}{b\times0.25}=\frac{1.35}{0.25}=5.4$$

Choice H

67f

$$\sin^{2}\theta+\cos^{2}\theta-4$$ $$=1-4$$ $$=-3$$

Choice E

67f

Therefore, the line of reflection …

2011 April(67F) Math Question 50

Angles Practice

- Circles

50. What is the length, in inches, of a 144 are of a circle whose circumference is 60 inches?

Choice H

$$\frac{x}{144°}=\frac{60}{360°}$$ $$x=144\times\frac{60}{360}=24$$

Choice B

The plane section of such …

2011 April(67F) Math Question 52

Logarithms Practice

- Logarithm Expressions

52. If b is a positive number such that log(1/81)=-4, then
b=?

Choice F

$$\log x=y \Rightarrow a^{y}=x$$ $$b^{4}=81$$ …

Choice D

f(x + a) + b …

2011 April(67F) Math Question 54

Angles Practice

- Parallel Lines

54. In the figure below, parallel lines a and b intersect parallel lines c and d. If it can be determined, what is the sum of the degree measures of ∠1 and ∠2?

Choice F

Based on parallel line properties, …

Choice D

To maximize the value of P(x,y), you must maximize the value of 4x + 3y.

At point B, P(x,y) = 4 • 0 + 3 • 4 = 12.

At point C, P(x,y) =4 • 4 + 3 • 0 = 16.

The value of P(x,y) is higher at point C then at point B and points B and C are connected by a straight line delineating an edge of the shaded region, no other points along this line or anywhere else in the shaded region can have a higher value than point C.

Choice F

(F) Look at the graph of P(x,y) above question 55 and compare it to the graph in 56 that labels the quadrants. P(x,y) contains points in quadrants I and II only.

Choice A

67f

Tangent is defined as opposite/adjacent. …

Choice K

If f(x)=0 when x=3, (x …

Choice C

$$\frac{5}{1000000}=5\cdot 10^{-6}$$

2011 April(67F) Math Question 60

Quadratic Equations Practice

- FOIL

60. Given a >b and (a-b)>(a-b), then(a+ b)must be:

Choice F

$$(a^{2}-b^{2})=(a+b)(a-b)$$ $$(a – b)\gt (a …