ACT Form 73C Math Answer Explanation


Choice C

$$a(4-a)-5(a+7)=4a-a^2-5a-35=-a^2-a-35$$

Choice G

$$\frac{1}{4}=0.25 \\$$ $$ \Rightarrow 0.03 \leq 0.2 \leq 0.25 \\$$ $$ \Rightarrow 0.03 \leq 0.2 \leq \frac{1}{4}$$

2015 June(73C) Math Question 3

Quadratic Equations Practice

- Factoring

3. If x^2 + 4 =29,then x^2— 4 =?

Choice C

$$x^2=29-4=25 \\$$ $$ \Rightarrow x^2-4=25-4=21$$

2015 June(73C) Math Question 4

Angles Practice

- Vertex Angles & Bisectors

4. In the figure below, QRS is equilateral, side QR is bisected by T, and side QS is bisected by U. What is the degree measure of TUS ?

Choice H

Since T and U bisect QR and QS, respectively, TU//RS. Thus, $$\angle TUQ=\angle S=60° \\$$ $$ \Rightarrow \angle TUS=180°-\angle TUQ=180°-60°=120°$$

Choice C

73c

The line is going downwards. Therefore the slope is negative.

Choice K

$$\sqrt{81}=9 \\ $$ $$\sqrt{99}\approx\sqrt{100}=10$$ $$ \\ 9 \leq 9.2371 \leq 10 \\$$ $$ \Rightarrow 81\leq the \ number \leq 99$$

2015 June(73C) Math Question 7

Probability Practice

- One Event

7. A bag contains 10 pieces of flavored candy: 4 lemon, 3 strawberry, 2 grape, and 1 cherry. One piece of candy will be randomly picked from the bag. What is the probability the candy picked is NOT grape flavored?

Choice E

$$p=\frac{10-2}{10}=\frac{4}{5}$$

Choice K

$$\frac{x_{A}+(-3)}{2}=1 \\$$ $$ \Rightarrow x_{A}=5 \\$$ $$ \frac{y_{A}+4}{2}=2 \\$$ $$ \Rightarrow y_{A}=0 $$

Choice B

$$2x+8=116 \\ $$ $$\Rightarrow x=54$$

Choice H

$$500+200x=$2,200 \\$$ $$ \Rightarrow x=$8.50$$

2015 June(73C) Math Question 11

Quadratic Equations Practice

- FOIL

11. Which of the following expressions is equivalent to (3x + 6)(2x — 1) ?

Choice D

$$(3x+6)(2x-1)=6x^2-3x+12x-6=6x^2+9x-6$$

2015 June(73C) Math Question 12

Word Problems Practice

- 1 Variable Equations

12. Carrie's Chocolate Shop and Tamika's Treat Shop both sell candy in boxes. The table below lists the price (the total amount the customer pays) of each box of candy sold at the shops. For each shop, there is a linear relationship between the price of a box of candies and the number of candies in that box. These are the only numbers of candies that can be purchased at the shops. Jeremy has $10.00 in quarters to spend on candy. What is the maximum number of quarters he would have left after paying for a box of 25 candies at Tamika's Treat Shop? (Note: Each quarter is worth $0.25.)

Choice J

A box of 25 candies at Tamika's Treat costs $4.25. Thus the money left is $10.00 - $4.25 = $5.75, which is 23 quarters: $$\frac{$5.75}{$0.25}=23$$

2015 June(73C) Math Question 13

Statistics Practice

- Mean, Median

13. At Tamika's Treat Shop, what is the average price per candy in a box of 20, to the nearest $0.01 ?

Choice B

$$\frac{$3.75}{20}=$0.1875\approx $0.19$$

Choice F

Only the equation in F fulfils all the given prices and the number of candies given in the table.

Choice E

The opposite of 'at least 1' is 'no one'.

2015 June(73C) Math Question 16

Angles Practice

- Collinear Points & Triangles

16. In the figure below, vertices D and F of ADEF lie on CG, the measure of LCDE is 148°, and the measure of EFG is 140°. What is the measure of DEF ?

Choice E

$$\frac{9\times9\times12}{3\times3\times3}=36$$

Choice J

$$f(-4)=-4(-4)^{3}-4(-4)^{2} =-4(-64)-4(16) =256-64 =192$$

Choice A

$$x+2y=4 \\ $$ $$-2x+y=7 \\$$ $$\Rightarrow x=-2, \ y=3$$

Choice G

73c

$$x=\sqrt{8^2+9^2}\approx12 \\$$ $$Perimeter = 8+10+12+19=49\approx50$$

Choice C

$$5\times7-4\times6=11$$

Choice H

$$\frac{BC}{AB}=\frac{BD}{BE} \\$$ $$ \Rightarrow \frac{BC}{3}=\frac{12}{4} …

2015 June(73C) Math Question 23

Inequalities Practice

- Inequality Expressions

23. Given that x <= 4 and x + y >= 5, what is the LEAST value that y can have?

Choice D

When x=4, y can have …

2015 June(73C) Math Question 24

Angles Practice

- Other Shapes

24. The circle shown below has diameter AD, and points B and C lie on the circle. The measure of ZCAD is 300, and the measure of minor arc CD is 60°. What is the measure of minor arc AC ?

Choice J

73c

2015 June(73C) Math Question 25

Word Problems Practice

- Interesection

25. One caution sign flashes every 4 seconds, and another caution sign flashes every 10 seconds. At a certain instant, the 2 signs flash at the same time. How many seconds elapse until the 2 signs next flash at the same time?

Choice D

Let the number of times …

Choice K

Since a and b are …

2015 June(73C) Math Question 27

Conics Practice

- Circles

27. Graphed in the same standard (x,y) coordinate plane are a circle and a parabola. The circle has radius 3 and center (0,0). The parabola has vertex (-3,-2), has a vertical axis of symmetry, and passes through (-2,-1). The circle and the parabola intersect at how many

Choice C

73c

Choice H

$$40\%\times250=60\%x \\$$ $$ \Rightarrow x=166 …

2015 June(73C) Math Question 29

Inequalities Practice

- Inequality Expressions

29. Which of the following inequalities is equivalent to —2x— 6y> 2y— 4 ?

Choice A

$$-2x-6y>2y-4 \\$$ $$ \Rightarrow …

Choice F

$$ \tan\alpha=\frac{\sin\alpha}{\cos\alpha} \\$$ $$ \Rightarrow …

Choice B

$$3k+5k+3k+5k=96 \ cm \\ $$ …

Choice G

$$d^2=\frac{16\times8}{2} \\$$ $$ \Rightarrow d=8 …

Choice B

$$\frac{3.6}{12}=30 \%$$

Choice F

73c

$$JD=\sqrt{5^2+12^2}=13$$

Choice B

$$length \ of arc\ \widehat{CD}=\frac{2\pi …

Choice H

12 - 3.6 = 8.4

Choice A

4 - 1 = 3

2015 June(73C) Math Question 38

Probability Practice

- One Event

38. At a local post office, on average, 3 customers are in line when the post office closes each day. The probability, P, that exactly n customers are in line when the post office closes can be modeled by the equation P=. Given that e-3 0.05, which of the following values is closest to the probability that exactly 2 customers are in line when the post office

Choice J

$$P=\frac{3^ne^{-3}}{n!}=\frac{3^2\times0.05}{2!}\approx0.23$$

Choice B

The amplitude of f(x)=cos(x) is …

Choice H

$$\frac{4}{3}\pi x^3=12 \\ \Rightarrow x=\sqrt[3]{\frac{9}{\pi}}$$

2015 June(73C) Math Question 41

Statistics Practice

- Mean, Median

41. For 20 quiz scores in a typing class, the table below gives the frequency of the scores in each score interval. Which score interval contains the median of the scores?

Choice D

The median will be the …

Choice H

$$\tan40°=\frac{height}{50}\\$$ $$ \Rightarrow height=50\times\tan40°=42$$

Choice B

Sea Horse: $$\frac{255-50-50}{0.25}=620$$ Ocean Blue: …

2015 June(73C) Math Question 44

Statistics Practice

- General Statistics

44. The table below gives experimental data values for variables x and y. Theory predicts that y varies directly with x. Based on the experimental data, which of the following values is closest to the constant of variation? (Note: The variable y varies directly with the variable x provided that y = kx for some nonzero constant k, called the constant of variation.)

Choice G

0.05 fits the data best.

Choice A

$$2x-5y=-5 \\ $$ $$\Rightarrow 2x+5=5y …

Choice J

$$\frac{x}{2\frac{1}{2}}=\frac{2\frac{1}{4}}{1\frac{1}{2}} \\$$ $$ \Rightarrow x= …

Choice E

$$\frac{12x^6}{3x^2}-\frac{9x^2}{3x^2}=4x^4-3$$

2015 June(73C) Math Question 48

Matrices Practice

- Multiplication

48. Four matrices are given bwlow. Which of the following matrix products is undefined?

2015 June(73C) Math Question 49

Angles Practice

- Circles

49. A circle, 2 chords. and some lengths, in centimeters, are shown in the figure below, which is not drawn to scale. What is the value of x ? (Note: When two chords intersect, the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord.)

Choice D

$$2x=5\times7 \\$$ $$ \Rightarrow x=17.5$$

Choice F

73c

$$\frac{[5+(5+x)]\cdot x}{2}=12 \\$$ $$ \Rightarrow …

Choice B

The square of a number …

2015 June(73C) Math Question 52

Quadratic Equations Practice

- Factoring

52. Given that (x + 2) and (x — 1) are factors of the quadratic expression below, what are the values of a and b ?

Choice K

$$(x-1)(x+2)=x^{2}+x-2$$ $$x^{2}+x-2=x^{2}+(a+2)x+a+b$$ $$\require{cancel}$$ $$\cancel{x^{2}}+x-2=\cancel{x^{2}}+(a+2)x+a+b$$ $$\Rightarrow …

2015 June(73C) Math Question 53

Quadratic Equations Practice

- Factoring

53. The height above the ground, h units, of an object seconds after being thrown from the top of a building is given by the equation h = —2t2 + 10: + 48. An equivalent factored form of this equation shows that the object:

Choice E

73c

Since the given equation is …

Choice J

The slopes of two lines …

2015 June(73C) Math Question 55

Inequalities Practice

- Intersection of Lines

55. The shaded portion of the graph in the standard(x,y) coordinate plane below represents the solution set of one of the following systems of linear inequalities. Which one?

Choice A

The shaded area lies below …

Choice K

$$(\sqrt{3})^{j}=27^{k}$$ $$(3^{\frac{1}{2}})^{j}=(3^{3})^{k}$$ $$\frac{j}{2}=3k$$ $$j=2\times3k$$ $$\frac{j}{k}=6$$ …

Choice A

For an arithmetic sequence, the …

Choice F

$$sin\theta=\frac{1}{4}$$ $$\Rightarrow sin(\frac{1}{4})^{-1}=\theta$$ $$arc\ length=2\pi …

Choice D

The asymptote of a function …

2015 June(73C) Math Question 60

Conics Practice

- Ellipse

60. A right circular cone is intersected by a plane that is not parallel to the base and does not intersect the base or vertex, ps shown in the figure below. One of the following figures shows the shape of the intersection. Which figure is it?

Choice F

73c

Conic sections are the result …