ACT Math Full mixed practice — Free with Answer Explanations

Question 1

What is the median of the data set ${4, 9, 2, 7, 5, 1, 8}$ ?

A.

4

B.

5

C.

5.14

D.

6

Question 2

A taxi charges a flat fee of $\$ 2.50 $pl u s$ $1.75$ per mile. Which equation gives the total cost $C$ for a ride of $m$ miles?

A.

C = 2.50 m + 1.75

B.

C = 1.75 m + 2.50

C.

C = (2.50 + 1.75) m

D.

C = 2.50 \times 1.75 m

Question 3

The function $f (x) = 2^{x}$ is transformed to $g (x) = 2^{x - 3} + 5$ . Compared to $f$ , the graph of $g$ is:

A.Shifted left 3 units and up 5 unitsB.Shifted right 3 units and down 5 unitsC.Shifted right 3 units and up 5 unitsD.Stretched vertically by 5 and shifted right 3 units

Question 4

A store sells two products. Product X has a profit of $\$ 5 $p er u ni t an d P r o d u c t Y ha s a p r o f i t o f$ $8$ per unit. The store can produce at most 200 units total, and must produce at least 60 units of Product X. If the store produces $x$ units of X and $y$ units of Y, which constraint set correctly models the situation?

A.

x + y \leq 200

;

x \geq 60

;

x, y \geq 0

B.

x + y = 200

;

x \geq 60

;

x, y \geq 0

C.

x + y \leq 200

;

x \leq 60

;

x, y \geq 0

D.

5 x + 8 y \leq 200

;

x \geq 60

;

x, y \geq 0

Question 5

A circle has a radius of 5. What is its area?

A.

10 π

B.

25 π

C.

50 π

D.

5 π

Question 6

Two pipes fill a pool. Pipe A can fill the pool alone in 6 hours; Pipe B alone in 4 hours. Working together, how many hours does it take to fill the pool?

A.

5

hoursB.

\frac{12}{5}

hoursC.

10

hoursD.

\frac{24}{5}

hours

Question 7

A car's value depreciates by 15% each year. The car was purchased for $\$ 24{,}000 $. W hi c h e x p r ess i o n g i v es t h ec a r^{'} s v a l u e$ V $a f t er$ t$ years?

A.

V = 24000 - 0.15 t

B.

V = 24000 (1.15)^{t}

C.

V = 24000 (0.85)^{t}

D.

V = 24000 (0.15)^{t}

Question 8

A cylindrical can has a radius of 3 cm and a height of 10 cm. A second cylindrical can has the same volume but a radius of 5 cm. What is the height of the second can, in cm?

A.

3.6

cmB.

6

cmC.

7.2

cmD.

5

cm

Question 9

A recipe requires $\frac{3}{4}$ cup of sugar to make 24 cookies. A baker wants to make 60 cookies. How many cups of sugar are needed?

A.

\frac{15}{8}

cupsB.

\frac{9}{4}

cupsC.

2

cupsD.

\frac{5}{4}

cups

Question 10

Solve for $x$ : $lo g_{3} (x) = 4$

A.

x = 12

B.

x = 7

C.

x = 81

D.

x = 64

Question 11

A population of bacteria doubles every 3 hours. Starting with 500 bacteria, approximately how many bacteria are there after 12 hours?

A.

2, 000

B.

6, 000

C.

8, 000

D.

16, 000

Question 12

A farmer wants to fence a rectangular area along a river. He has 120 meters of fence and does not need to fence the side along the river. What is the maximum area he can enclose?

A.

900

m²B.

1, 600

m²C.

1, 800

m²D.

3, 600

m²

Question 13

A car travels 150 miles in 2.5 hours. At this same rate, how many miles will it travel in 4 hours?

A.

200

milesB.

225

milesC.

240

milesD.

250

miles

Question 14

For what values of $x$ is the quadratic $x^{2} - 5 x + 6 < 0$ ?

A.

x < 2

or

x > 3

B.

x < - 3

or

x > - 2

C.

2 < x < 3

D.

- 3 < x < - 2

Question 15

What is the value of $x$ if $3 x - 7 = 14$ ?

A.

x = 3

B.

x = 7

C.

x = 9

D.

x = 21

Question 16

A company's profit $P$ (in thousands of dollars) is modeled by $P = - 2 t^{2} + 12 t - 10$ , where $t$ is years after founding. In which year does the company reach maximum profit?

A.Year 3B.Year 6C.Year 2D.Year 5

Question 17

The expression $sin^{2} θ + cos^{2} θ$ equals:

A.

0

B.

2

C.

sin (2 θ)

D.

1

Question 18

A phone plan costs $\$ 30 $p er m o n t h pl u s$ $0.10$ per text message. Last month, Jake paid $\$ 47.50$. How many text messages did Jake send?

A.

170

B.

175

C.

180

D.

77.5

Question 19

The height $h$ (in feet) of a projectile launched upward is given by $h (t) = - 16 t^{2} + 80 t + 6$ , where $t$ is time in seconds. At what time does the projectile hit the ground?

A.

t = 5

secondsB.

t \approx 5.07

secondsC.

t = 2.5

secondsD.

t \approx 4.93

seconds

Question 20

A runner completes the first half of a race at 8 mph and the second half at 12 mph. What is the runner's average speed for the entire race?

(Note: the race is split by distance, not time.)

A.

10

mphB.

9.6

mphC.

9

mphD.

11

mph

Question 21

In right triangle $A B C$ with the right angle at $C$ , if $sin A = \frac{3}{5}$ , what is $cos A$ ?

A.

\frac{3}{4}

B.

\frac{4}{5}

C.

\frac{3}{5}

D.

\frac{5}{4}

Question 22

Water is pumped into a tank at 12 gallons per minute and drained at 5 gallons per minute. If the tank starts empty and holds at most 350 gallons, after how many minutes will the tank be full?

A.

29.2

minutesB.

50

minutesC.

70

minutesD.

40.6

minutes

Question 23

A store marks up items by 40% to set the retail price, then offers a 25% coupon. A customer buys an item whose wholesale cost was $\$ 80$. What does the customer pay?

A.

\

68$B.

\

80$C.

\

84$D.

\

96$

Question 24

A 10-foot ladder leans against a wall. The base of the ladder is 6 feet from the wall. How high up the wall does the ladder reach?

A.

4

feetB.

6

feetC.

8

feetD.

136

feet

Question 25

A store sells notebooks for $\$ 3.50$ each. During a sale, the price is reduced by 20%. How much does a customer pay for 4 notebooks at the sale price?

A.

\

11.20$B.

\

12.60$C.

\

14.00$D.

\

10.00$

Question 26

A store increases a price by 30%, then later decreases that new price by 30%. Compared to the original price, the final price is:

A.Equal to the original priceB.

9%

less than the originalC.

9%

more than the originalD.

6%

less than the original

Question 27

What is the slope of the line passing through $(2, 5)$ and $(6, 13)$ ?

A.

1

B.

2

C.

4

D.

\frac{1}{2}

Question 28

A ball is dropped from a height of 200 feet. Each time it bounces, it reaches 60% of its previous height. What is the height of the ball after its 3rd bounce?

A.

43.2

feetB.

72

feetC.

120

feetD.

48

feet

Question 29

A savings account earns 4% annual interest, compounded annually. If $\$ 1{,}000$ is deposited today, what is the balance after 3 years?

A.

\

1{,}120.00$B.

\

1{,}124.86$C.

\

1{,}040.00$D.

\

1{,}120.60$

Question 30

A class of 30 students took a test. The average score was 74. Then 5 more students took the same test and scored an average of 82. What is the overall average score of all 35 students?

A.

78

B.

75.14

C.

76

D.

74.5