ACT Form 69F Math Answer Explanation


Choice C

$$14+9=23$$ $$23\times2=46$$

Choice F

$$\frac{8}{-4}=-2$$ $$\frac{-16}{8}=-2$$ $$-64\times(-2)=128$$

Choice A

$$(8+3-(-5))(3+(-5))$$ $$=(8+3+5)(3-5)$$ $$=16(-2)$$ $$=-32$$

Choice G

$$\frac{34-10}{2}=12$$

Choice E

$$-2x+3=-21$$ $$-2x=-21-3=-24$$ $$x=\frac{-24}{-2}=12$$

2011 June(69F) Math Question 6

Statistics Practice

- Mean, Median

6. What is the mean of the list of numbers below?
62,100,93,62,72,78,50,85,62,36

Choice J

$$62+100+93+62+72+78+50+85+62+36=700$$ $$\frac{700}{10}=70$$

Choice E

$$1\frac{2}{3}+\frac{3}{4}=1\frac{8}{12}+\frac{9}{12}$$ $$=1\frac{17}{12}$$ $$=2\frac{5}{12}$$

Choice H

69f

$$6:10=x:90$$ $$10x=6\times90=540$$ $$x=54$$

Choice C

$$$35\times4+0.375\times300$$ $$=$140+$112.5$$ $$=$252.5$$

2011 June(69F) Math Question 10

Quadratic Equations Practice

- FOIL

10. The expression(7c- 2d)(2c+ d) is equivalent to

Choice J

$$=7c(2c+d)-2d(2c+d)$$ $$=14c^{2}+7cd-4dc-2d^{2}$$ $$=14c^{2}+3cd-2d^{2}$$

Choice B

$$3x+5y-13=0$$ $$5y=13-3x$$ $$y=\frac{13-3x}{5}$$

2011 June(69F) Math Question 12

Word Problems Practice

- Distance, Speed, Time

12. The speed of one bus exceeds 3 times the speed of another bus by 20 mph. The speed of the slower bus is k mph. Which of the following expressions represents the speed of the faster bus, in miles per hour?

Choice K

“3 times the speed” of …

2011 June(69F) Math Question 13

Word Problems Practice

- Temperature

13. At 2:00 a m, the temperature is -15°F. For the next
3 hours, the temperature decreases 2°F per hour. What is the temperature at 5:00 a m.?

Choice A

$$-15-2\times3=-15-6=-21$$

Choice J

From 2 hours to 4 hours, her distance traveled does not increase. Therefore, her car must have been stopped.

$$250-100=150$$

Choice B

$$r=\frac{6}{2}=3$$ $$h=1.5$$ $$\pi \approx 3.14$$ $$\pi r^{2}h=3.14\times 3^{2}\times(1.5)=42.39$$

Choice F

$$f(-1)=\mid-1\mid^{3}-1=1^{3}-1=1-1=0$$

Choice C

$$332\times1.25=415$$

Choice F

$$6a-4a+5b-4b+4c+2c=2a+b+6c$$

Choice B

$$\frac{6+14}{2}=10$$

Choice K

$$6\times6=36$$

Choice C

69f

Choice G

If “the x-coordinate of point …

2011 June(69F) Math Question 23

Word Problems Practice

- % Concentration

23. Beverly is using a punch recipe that calls for 2 parts ginger ale to I part fruit juice by volume. Bever planning to make 12 liters of this punch for a party How many liters of fruit juice does Beverly need in order to make 12 liters of this punch?

Choice C

You must add these parts …

Choice F

$$\frac{4c}{5}-\frac{1}{2}=-\frac{25}{2}$$ $$\frac{4c}{5}=-\frac{25}{2}+\frac{1}{2}$$ $$\frac{4c}{5}=-\frac{24}{2}$$ $$4c\times2=5\times(-24)$$ $$8c=-120$$ …

Choice B

69f

$$\overline{AC}=r+4r=5r$$ $$\overline{AB}:\overline{AC}=r:5r=1:5$$

Choice F

$$y=mx+b$$ $$3y=-8x+5$$ $$y=-\frac{8}{3}x+5$$ $$m=-\frac{8}{3}$$

2011 June(69F) Math Question 27

Probability Practice

- Combinations

27. The Kingston High School multimedia room has
108 seats, which are all arranged in rows. The number of seats in each row is 3 less than the number of rows How many rows of seats are in the multimedia room?

Choice C

Let r = number of …

Choice H

69f

$$90°\lt\theta\lt180°$$

It is in the …

Choice C

Because the length of the …

Choice G

$$1\times316+2\times271=858$$

Choice E

$$12d:30d:40d=64:24:18$$ $$[64,24,18]=576$$

Choice K

If the board is 1.5 …

2011 June(69F) Math Question 33

Conics Practice

- Circles

33. In the standard (x, y) coordinate plane, the equation of a circle is x+y=100. At what 2 points does the circle intersect the y-axis?

Choice A

This equation is

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

where …

Choice H

$$(-mp)(mp^{9})^{4}$$ $$=(-m)(m^{4})(p)(p^{9\times4})$$ $$=(-m^{5})(p{37})$$

Choice A

$$0.578578578...$$

Because the decimal repeats …

2011 June(69F) Math Question 36

Probability Practice

- More than One Event

36. A jar contains exactly 12 gumballs, each of which is a solid color. There are 5 blue and 7 white gumballs Chris will draw one gumball at random and then without replacement, will draw another gumball from the jar at random. Which of the following expressions gives the probability that Chris will draw 2 blue gumballs?

Choice K

His probability of drawing a …

Choice E

$$red=green+15,\ green=blue+9$$ $$red=blue+9+15=blue+24$$ $$red+green+blue=72$$ $$\Rightarrow …

Choice H

$$(14+24)10\times\frac{1}{2}$$ $$=38\times10\times\frac{1}{2}$$ $$=380\times\frac{1}{2}$$ $$=190$$ $$190\times$1.75=$332.5$$

Choice A

The slope of OC is …

2011 June(69F) Math Question 40

Word Problems Practice

- 2 Variable Addition

40. The junior class at Silverwood High School sponsored a costume party. Each student wearing a costume paid
2 admission, and each student NOT wearing a costume paid $5 admission. An amount of $489 was collected from the 150 students who paid admission.
How much of the amount was collected from students NOT wearing a costume?

Choice G

$$Pay\ $2:\ x$$ $$Pay\ $5:\ …

Choice D

$$i=\sqrt{-1},\ i^{2}=-1$$ $$\sqrt{-27}=\sqrt{27}i=3\sqrt{3}i$$ $$\sqrt{-48}=\sqrt{48}i=4\sqrt{3}i$$ $$\sqrt{-48}+\sqrt{-27}$$ …

Choice K

$$tangent=\frac{opposite}{adjacent}$$ $$\tan67°=\frac{x}{7.5}$$ $$x=7.5\tan67°$$

2011 June(69F) Math Question 43

Angles Practice

- Circles

43. For any circle with 2 secants drawn from P to the circle, as shown in the figure below, the lengths of the segments of the secants are determined by a(a+b)=c(c+d).
In the figure below, A, B, D, and E are on the circle Point B is on secant segment AC, and D is on secant segment CE. The lengths of AB, BC, and CD are given in meters. What is the length, in meters, of DE

Choice B

In the diagram,

$$a = …

2011 June(69F) Math Question 44

Angles Practice

- Other Shapes

44. While lifting weights, a person sits on an incline weight bench and pushes the weights straight up, as shown in the figure below on the left. The weight bench is shown below on the right. The angle between the horizontal seat and the backrest is 110 what is the measure of the angle between the backrest and the vertical path of the weights?

Choice J

69f

This line then forms an …

2011 June(69F) Math Question 45

Conics Practice

- Parabola

45. In the standard (x, y) coordinate plane, the graph of x is shifted 5 units down and 4 units right. Which of the following is an equation of the translated graph?

Choice D

To shift this graph down …

Choice G

69f

$$\frac{60}{2}-5=25$$ $$\frac{100}{2}+10=60$$ $$25^{2}+60^{2}=625+3600=4225$$ $$4225=65^{2}$$

2011 June(69F) Math Question 47

Angles Practice

- Circles

47. A sector of a circle has an area equal to 5/12 of the area of the circle. What is the measure of the sectors central angle?

Choice D

$$360°\times\frac{5}{12}=150°$$

2011 June(69F) Math Question 48

Statistics Practice

- Mean, Median

48. List B consists of all the integers in List a below and also 3 integers a, b, and c, where a s 17, b=c, and b ≥ 42. what is the median of the integers in List B?
List A:12,16,17,29,29,35,41,42,47,4

Choice J

69f

$$\frac{35+41}{2}=38$$

Choice D

$$2x-a\leq3 \Rightarrow x\leq\frac{3+a}{2}$$ $$2x-a\geq-3 \Rightarrow …

Choice J

The greatest power of 17,23,61 …

Choice E

Based on the diagram, the …

Choice G

69f

$$f(5)=3$$ $$g(f(5))=g(3)=-5$$

Choice C

69f

$$45°:45°:90°$$ $$=1:1:\sqrt{2}$$ $$=x:x:x\sqrt{2}$$ $$30°:60°:90°$$ $$=1:\sqrt{3}:2$$ …

Choice K

$$a+b=5$$ $$ab=6$$ $$a,b=2,3$$ $$\Rightarrow \frac{3}{2}+\frac{2}{3}=\frac{9+4}{6}=\frac{13}{6}$$

2011 June(69F) Math Question 55

Matrices Practice

- Addition & Subtraction

55. Given the matrix equation shown below, what is = b/a?
(Note: Whenever n is a positive integer, the notation n!
represents the product of the integers from n to 1. For example,3!=3·2·1)

Choice A

$$a= 3! + 2! = …

2011 June(69F) Math Question 56

Inequalities Practice

- Intersection of Lines

56. Graphed in the standard (x, coordinate plane below is the solution set for a system of 3 linear inequalities For values of x and y that satisfy this system, what is the maximum value of 6x- 2y?

Choice K

To find the maximum value …

Choice C

If the second pyramid has …

Choice G

$$x^{2}=5^{2}+5^{2}-2\cdot5\cdot5\cos\theta$$ $$x^{2}=25+25-50\cos\theta$$ $$50\cos\theta=50-x^{2}$$ $$\cos\theta=\frac{50-x^{2}}{50}$$

Choice D

SAS Triangle Congruence Theorem : …

2011 June(69F) Math Question 60

Quadratic Equations Practice

- Factoring

60. What is the value of c if x+2 is a factor of
2x3+2x2-2cx+4?

Choice K

If x + 2 is …