# Conquering ACT Math and Science 4th

## Educators  ### Problem 1

In triangle $A B C$ below, the measure of angle $B$ is 70 degrees, and the measure of angle $A$ is half the measure of angle $B .$ What is the measure of angle $C ?$
A. $65^{\circ}$
?. $70^{\circ}$
C. $75^{\circ}$
D. $80^{\circ}$
E. $85^{\circ}$ Lily A.

### Problem 2

Twenty-one students agreed to contribute an equal amount of money to buy a gift for their teacher. If a total of $\$ 70.40$had been collected after 16 students paid their shares, what was the total price of the gift? F.$\$54.40$
G. $\$ 92.40$H.$\$188.00$
J. $\$ 1,126.40$K.$\$1,478.40$ Lily A.

The minimum fine for driving in excess of the speed limit is $\$ 25 .$An additional$\$6$ is added to the minimum fine for each mile per hour $(\mathrm{mph})$ in excess of the speed limit. Omar was issued a $\$ 103$fine for speeding in a 55-mph speed limit zone. For driving at what speed, in$\mathrm{mph},$was Omar fined? A. 13 B. 52 C. 62 D. 68 E. 72 Lily A. Numerade Educator ### Problem 4 In a circuit,$E=I R,$where$E=$number of volts,$I=$number of amperes, and$R=$number of ohms. How much resistance, in ohms, does a circuit possess if the number of volts is 24 and the current is 8 amperes? F. 2 G. 3 H. 4 J. 24 K. 32 Lily A. Numerade Educator ### Problem 5 In the figure below, line$s$is parallel to line$t,$and line$p$is a transversal crossing both lines$s$and$t .$Which of the following lists 3 angles that are equal in measure? A. angle$a$, angle$b$, angle$c$B. angle$a$, angle$c$, angle$d$C. angle$a$, angle$c$, angle$f$D. angle$a$, angle$d$, angle$e$E. angle$b$, angle$d$, angle$e$ James K. Numerade Educator ### Problem 6 What value of$a$makes$\frac{2}{3} a+5=11$true? F. 4 G.$5 \frac{1}{3}$H. 9$10 \frac{2}{3}$K. 24 Lily A. Numerade Educator ### Problem 7$\frac{35.65}{0.05}=?$A. 0.713 B. 7.13 C. 71.30 D. 713.0 E. 7,130.0 Lily A. Numerade Educator ### Problem 8 What is the slope of the line that is perpendicular to the line given by the equation$3 y+6 x=-5 ?$F. -2 G.$\frac{-5}{3}$H.$\frac{-1}{2}$J.$\frac{1}{2}$K. 3 Lily A. Numerade Educator ### Problem 9 If$x=-4,$then$24+3-x^{2}=?$A. 11 B. 25 C. 29 D. 31 E. 43 Lily A. Numerade Educator ### Problem 10 A pair of shoes that originally costs$\$75.00$ is on sale at $40 \%$ off. If the sales tax on the shoes is $7 \%$ of the purchase price, how much would it cost to buy the pair of shoes at the sale price?
F. $\$ 33.15$G. \$40.00
H. $\$ 42.90$J.$\$45.00$
K. $\$ 48.15$ Lily A. Numerade Educator ### Problem 11 Which of the following graphs represents$x>7 ?$A. B. C. D. E. James K. Numerade Educator ### Problem 12 If the ratio of$2 p$to$11 r$is 1 to$6,$what is the ratio of$6 p$to$11 r ?$F. 1 to 18 G. 3 to 6 H. 3 to 33 J. I to 6 K. 3 to 22 Lily A. Numerade Educator ### Problem 13 Which of the following equations could be used to determine the value of$x ?$A.$13 \sin x=5$B. 12 tan$x=5$C.$12 \cos x=13$D.$5 \tan x=12$E.$\frac{\cos x}{5}=12$ James K. Numerade Educator ### Problem 14 A rectangular soccer field has an area of 4,500 square meters. The length of the field is 10 meters more than twice the width. Which of the following equations could be used to find the width$w,$in feet, of the soccer field? F.$w^{2}=4,500-10 w$G.$2(w+10)+w=4,500$H.$w+10(2 w)=4,500$J.$w(2 w+10)=4,500$K.$w\left(w^{2}+10\right)=4,500$ Lily A. Numerade Educator ### Problem 15 While riding his bike at a rate of 14 miles per hour (mph), Alan takes 1.20 hours to ride the entire length of a trail. How many hours would it take him to complete the same ride if he rode at 8 mph? A. 1.40 B. 1.75 C. 2.10 D. 2.55 E. 9.60 Lily A. Numerade Educator ### Problem 16 Last year on his vegetable farm, Phil planted carrots in a squareshaped plot, with sides measuring 18 feet. This year, he changed this plot into a rectangular design with the same area as the original square section. If the new width of this section is 12 feet, what is its length, in feet? F. 18 G. 21 H. 27 J. 30 K. 36 Lily A. Numerade Educator ### Problem 17 An apartment complex has 30 apartments that each rent for$\$320$ per month. If $70 \%$ of the apartments are rented for 6 months, how much rent will be charged in total for those apartments for the 6 months?
A. $\$ 6,720$B.$\$9,600$
C. $\$ 22,450$D.$\$40,320$
E. $\$ 57,600$ Lily A. Numerade Educator ### Problem 18 In the figure below,$W, X,$and$Z$are collinear. If the measure of angle$Y$is$87^{\circ}$and the measure of angle$Y X W$is$128^{\circ},$what is the measure of angle$Z$? F.$35^{\circ}$G.$41^{\circ}$H.$52^{\circ}$J.$78^{\circ}$K.$139^{\circ}$ James K. Numerade Educator ### Problem 19 What is the value of$x$in the solution for the system of equations below? $\begin{array}{l} -2 x+3 y=30 \\ 4 x-\frac{1}{4} y=-14 \end{array}$$\mathbf{A} \cdot-27$B. -16 C. -9 D. -4 E. -3 Lily A. Numerade Educator ### Problem 20 What is the product of the complex numbers$(-2 i+5)$and$(2 i+5) ?$F. 3 G. 21 H. 29 J.$20 i-21$K.$20 i+21$ Lily A. Numerade Educator ### Problem 21 For all$x,-5 x(x-2)-\left(4 x-7 x^{2}\right)+(-3 x)=?$A.$-12 x^{2}-11 x$B.$-12 x^{2}+9 x$C.$2 x^{2}+3 x$D.$2 x^{2}+9 x$E.$12 x^{2}+11 x$ Lily A. Numerade Educator ### Problem 22$4^{-3}$is equivalent to: F. 64 G. 12 H.$\frac{1}{64}$J. -4 K. -64 Lily A. Numerade Educator ### Problem 23 If$x=\frac{5}{2}$is one solution of the equation$2 x^{2}+k x-20=0,$what is the value of$k ?$A. -5 B. -3 C. 2 D. 3 E. 8 Lily A. Numerade Educator ### Problem 24 In triangle$Q R S$shown below,$\overline{R T}$bisects angle$Q R S$. The measure of angle$Q R S$is$118^{\circ},$and angle$Q$measures$44^{\circ} .$What is the measure of angle$R T S ?$F.$77^{\circ}$G.$90^{\circ}$H.$103^{\circ}$J.$109^{\circ}$K.$118^{\circ}\$ James K.

### Problem 25

Emily wants to enclose an area of her backyard for her dogs. She has 52 feet of fencing. The width of the enclosed area can be between 9 and 12 feet. If she wants to use all of the fencing, what are the possible dimensions for the length of the enclosed area, in feet?
A. Between 13 and 15
B. Between 14 and 17
C. Between 28 and 34
D. Between 40 and 43
E. All of the fencing cannot be used. Lily A.