Practice Math ACT

Math ACT Practice Test

60 questions, just like the real thing :)​

By: J.Nelson

Multiple Choice

If $$5x+2=7x-7$$  , then $$x=?$$  

• $$\frac{2}{9}$$  

• $$\frac{1}{3}$$  

• $$\frac{2}{3}$$  

• $$\frac{3}{2}$$  

• $$\frac{9}{2}$$  

Multiple Choice

The expression x[(y-w)+z] is equivalent to:

• xy-xw+xz

• xy-w+z

• xy+xw+xz

• xy-xw-xz

• xy-w+xz

Multiple Choice

The toxicity level of a lake is found by dividing the amount of dissolved toxins the lake water currently has per liter by the maximum safe amount of dissolved toxins that the water can hold per liter and then converting it to a percentage. If the river currently has 0.86 milligrams of dissolved toxins per liter of water and the maximum safe amount of dissolved toxins is 1.04 milligrams per liter, what is the toxicity level of the lake water, to the nearest percentage?

• 86%

• 84%

• 83%

• 80%

• 79%

Multiple Choice

A rectangular pasture that measures 250 meters by 300 meters is completely fenced around its borders. What is the approximate length, in meters, of the surrounding fence?

• 75,000

• 1,100

• 750

• 600

• 550

Multiple Choice

So far, Michael has earned the following scores on five 100 point tests this semester: 72, 94, 85, 83, 97. What score must he earn on the sixth 100 point test of the semester if he wants to make an 88 point average for the six tests?

• 100

• 97

• 88

• 85

• He cannot make an average of 88.

Multiple Choice

Which two numbers should be placed in the blanks below so that the difference between consecutive numbers is the same?

19, __, __, 55

• 20, 53

• 27, 50

• 30, 48

• 31, 43

• 34, 42

Multiple Choice

Mrs. Cook is a teacher whose salary is $23,125 for a 185-day school year. In Mrs. Cook's school district, substitute teachers are paid at a rate of $90 per day. If a substitute is paid to teach Mrs. Crook's class in her absence one day, how much less does the school district pay in salary by paying a substitute teach instead of paying Mrs. Cook for that day?

• $215

• $125

• $90

• $45

• $35

Multiple Choice

If a marble is randomly chosen from a bag that contains exactly 6 purple marbles, 4 blue marbles, and 10 green marbles, what is the probability that the marble will NOT be green?

• $$\frac{1}{5}$$  

• $$\frac{3}{10}$$  

• $$\frac{1}{3}$$  

• $$\frac{1}{2}$$  

• $$\frac{3}{5}$$  

Multiple Choice

Zach has 3 pairs of shoes, 8 shirts, and 5 pairs of jeans. How many distinct outfits -- each consisting of a pair of shoes, a shirt, and a pair of jeans -- can Zach select?

• 240

• 120

• 40

• 16

• 8

Multiple Choice

$$4x^2y\cdot2x^3y\cdot3xy^2\$$  is equivalent to:

• $$9x^6y^2$$  

• $$9x^6y^4$$  

• $$12xy^{10}$$  

• $$24x^6y^2$$  

• $$24x^6y^4$$  

Multiple Choice

Which of the following is a solution to the equation $$x^2-25x=0$$  

• -25

• -5

• 5

• 25

• 125

Multiple Choice

Craig ran $$2\ \frac{2}{3}$$   miles on Wednesday and $$3\ \frac{1}{4}$$  miles on Thursday. What was the total distance Craig ran during those two days, in miles?

• $$5\ \frac{3}{12}$$  

• $$5\ \frac{2}{7}$$  

• $$5\ \frac{3}{7}$$  

• $$5\ \frac{9}{12}$$  

• $$5\ \frac{11}{12}$$  

Multiple Choice

The ratio of the side lengths for a triangle is exactly 9:12:15. In another triangle, which is similar to the first, the shortest side is 18 inches long. To the nearest hundredth of an inch, what is the length of the longest side of the other triangle?

• 18.25

• 24.00

• 25.5

• 30.00

• Cannot be determined from the given information

Multiple Choice

The formula for volume V of a sphere with radius r is $$V=\frac{4}{3}\pi^3$$  . If the radius of a spherical rubber ball is $$2\ \frac{3}{4}$$  inches, what si the volume, to the nearest cubic inch?

• 8

• 11

• 56

• 77

• 87

Multiple Choice

For the triangle $$\Delta PQR$$   shown, what is sin R?

• $$\frac{r}{q}$$  

• $$\frac{r}{p}$$  

• $$\frac{p}{r}$$  

• $$\frac{q}{r}$$  

• $$\frac{p}{q}$$  

Multiple Choice

If x and y are positive integers such that the greatest common factor of $$x^2y^2$$  and $$xy^3$$   is 50, then which of the following could equal y?

• 50

• 25

• 10

• 5

• 2

Multiple Choice

If x is a real number such that $$x^3=729$$  , then $$x^2+\sqrt[]{x}=?$$  

• 738

• 732

• 90

• 84

• 12

Multiple Choice

A circle in the standard (x,y) coordinate plane is tangent to the x-axis at 4 and tangent to the y-axis at 4. Which of the following is an equation of the circle?

• $$\left(x-4\right)^2+\left(y-4\right)^2=16$$  

• $$\left(x+4\right)^2+\left(y+4\right)^2=16$$  

• $$\left(x-4\right)^2+\left(y-4\right)^2=4$$  

• $$x^2+y^2=16$$  

• $$x^2+y^2=4$$  

Multiple Choice

What expression must the center cell of the table below contain so that the sums of each row and each column are equivalent?

• 2x

• 3x

• 4x

• 5x

• 6x

Multiple Choice

At a plant, 160,000 tons of petrochemicals are required to produce 100,00 tons of plastic. How many tons of the petrochemicals are required to produce 5,00 tones of plastic?

• 8,000

• 10,000

• 16,000

• 80,000

• 100,000

Multiple Choice

A chord 20 inches long is 4 inches from the center of a circle, as shown below. What is the radius of the circle, to the nearest tenth of an inch?

• 4.0

• 10.7

• 10.8

• 11.0

• 21.6

Multiple Choice

Workers for a roofing company lean a 20 foot ladder against a building. The side of the building is perpendicular to the level ground so that the base of the ladder is 5 feet away from the base of the building. To the nearest foot, how far up the building does the ladder reach?

• 5

• 10

• 18

• 19

• 20

Multiple Choice

Point C is to be graphed in a quadrant of the standard (x,y) coordinate plane.

If the x-coordinate and the y-coordinate of point C are to have the same signs, then point must be located in:

• Quadrant I or II

• Quadrant I or III

• Quadrant I or IV

• Quadrant II or IV

• Quadrant III or IV

Multiple Choice

What is the x-coordinate of the point in the standard (x,y) coordinate plane at which the two lines $$y\ =\ 2x-1$$  and $$y=x+2$$   intersect?

• -2

• 0

• 1

• 3

• 4

Multiple Choice

A square is circumscribed about a circle with a 6 foot radius, as shown below. What is the area of the square, in square feet?

• 12

• 36

• 72

• 144

• 288

Multiple Choice

If a rectangle measures 12 meters by 16 meters, what is the length, in meters, of the diagonal of the rectangle?

• 14

• 18

• 20

• 22

• 28

Multiple Choice

Which of the following is a set of all real numbers x, such that $$x+1>x+8$$  ?

• the set containing zero

• the set containing all real numbers

• the set containing all positive numbers

• the set containing all negative numbers

• the empty set

Multiple Choice

For all pairs of real numbers P and Q where P=2Q+9, Q=?

• $$2P-9$$  

• $$\frac{P+9}{2}$$  

• $$\frac{P}{2}+9$$  

• $$\frac{P}{2}-9$$  

• $$\frac{P-9}{2}$$  

Multiple Choice

The ratio of the radii of two circles is 5:12. What is the ratio of their circumferences?

• 5:12

• $$5:12\pi$$  

• $$10:12\pi$$  

• 10:24

• 25:144

Multiple Choice

Of the 777 graduating seniors in a certain high school, approximately $$\frac{1}{3}$$   are going to a trade school, and approximately $$\frac{2}{7}$$   of those going to a trade school are going to an art or design institute. Which of the following is the closet estimate for the number of graduating seniors going to an art or design institute?

• 74

• 75

• 110

• 219

• 256

Multiple Choice

What is the slope-intercept form of $$4x-y+7=0$$  

• $$y=-4x-7$$  

• $$y=-4x+7$$  

• $$y=x+\frac{4}{7}$$  

• $$y=4x-7$$  

• $$y=4x+7$$  

Multiple Choice

Parallelogram PQRS, with dimensions in feet, is shown in the diagram. What is the area of the parallelogram, in square feet?

• 48

• 96

• 120

• 144

• 180

Multiple Choice

The distance D, in feet, that a ball can be catapulted is given by the equation $$D=\frac{2}{3}T+10$$  , where T is the applied torque in newtons. What amount of torque, in newtons, must be applied for the ball's distance to be 170 meters?

• 160

• 200

• 240

• 320

• 480

Multiple Choice

If $$a=b-3$$  , then $$\left(b-a\right)^2=?$$  

• -81

• -27

• -9

• 9

• 27

Multiple Choice

Points B and C lie on line segment AD, as shown below. Line segment AD is 40 units long, line segment AC is 15 units lone, and line segment BD is 30 units long. How many units long, if it can be determined, is line segment BC?

• 20

• 15

• 10

• 5

• Cannot be determined from the given information

Multiple Choice

What is the average number of students enrolled per section in English 1?

• 17

• 18

• 19

• 20

• 21

Multiple Choice

The school owns 35 anthologies, which students are required to have during their English classes. There are 4 anthologies currently being re-covered, and 1 anthology is currently missing. For which of the following class periods, if any, are there NOT enough anthologies available for each student to have his or her own anthology?

• Period 1

• Period 1 & 2

• Period 1 & 3

• Period 2 & 3

• There are enough anthologies for each class period.

Multiple Choice

After polling a class of 20 science students by a show of hands, you find that 12 students enjoy chemistry while 17 students enjoy biology. Given that information, what is the maximum number of students in this class who enjoy both chemistry and biology?

• 0

• 5

• 12

• 17

• 29

Multiple Choice

For all positive integers X, Y, and Z, which of the following expressions is equivalent to $$\frac{Y}{Z}$$  

• $$\frac{Y}{Z}+\frac{X}{Y}$$  

• $$\frac{Y\cdot Z}{Z\cdot Y}$$  

• $$\frac{Y+X}{Z+X}$$  

• $$\frac{Y\cdot X}{Z\cdot X}$$  

• $$\frac{Y\cdot Y}{Z\cdot Z}$$  

Multiple Choice

If 120% of a number is 360, what is 50% of the number?

• 120

• 150

• 260

• 300

• 480

Multiple Choice

The hypotenuse of the right triangle $$\Delta LMN$$   shown below is 18 feet long. The sine of angle L is $$\frac{5}{6}$$  . About how many feet long is line segment MN?

• 11

• 12

• 15

• 18

• Cannot be determined from the given information.

Multiple Choice

If $$x=3t-8$$   and $$y=4+t$$  , which of the following equations expresses y in terms of x?

• $$y=4x-4$$  

• $$y=\frac{x-20}{3}$$  

• $$y=\frac{x+3}{20}$$  

• $$y=\frac{x}{3-4}$$  

• $$y=\frac{x+20}{3}$$  

Multiple Choice

Hexagons have 9 diagonals, as illustrated. How many diagonals do octagons have?

• 8

• 16

• 20

• 32

• 40

Multiple Choice

Jennifer wants to draw a circle graph showing the favorite candies of her friends. When she polled her friends, asking each his or her favorite candy, 30% of her friends said chocolate, 25% of her friends said peppermint, 15% of her friends side licorice, 15% of her friends side gum, and the remaining friends said some other type of candy. If she groups the other candies chosen by the remaining friends in the same sector, what will the degree measure of this sector be?

• 12

• 24

• 26

• 48

• 54

Multiple Choice

The number of students participating in afterschool programs at a certain high school can be shown by the following matrix.

Quizbow(30), Band(60), Chorus(40), Debate(30)

The principal estimates the ratio of the number of program awards that will be earned to the number of students participating with the following,

Quizbow: 0.2

Band: 0.3

Chorus: 0.5

Debate: 0.4

Given the data, what is the principal's estimate of the number of programs awards that will be earned for these afterschool programs?

• 60

• 56

• 52

• 48

• 36

Multiple Choice

After a hurricane, coastal workers removed an estimated 8,000 cubic yards of sand from the downtown area. If this sand was spread in an even layer over a rectangular segment of beach, as shown below, about how many yards deep would that new layer of sand be?

• Less than 1

• Between 1 and 2

• Between 2 and 3

• Between 3 and 4

• More than 4

Multiple Choice

What is the distance in the standard (x,y) coordinate plane between points (1,2) and (4,6)?

• 4

• 5

• 7

• 10

• 13

Multiple Choice

In the figure, VWXY is a trapezoid, Z lies on line VY, and angle measures are as marked. What is the measure of angle WYX?

• 25

• 30

• 45

• 55

• 65

Multiple Choice

In the set of complex numbers, where $$i^2=-1$$  .

$$\frac{i}{i-1}\cdot\frac{i+1}{i+1}=?$$  

• $$-i$$  

• $$\frac{i}{-2}$$  

• $$\frac{i-1}{-2}$$  

• $$\frac{1}{-2}$$  

• $$\frac{i^2+i}{i^2-2i-1}$$  

Multiple Choice

If $$f\left(x\right)=x^2+x+4$$  , then $$f\left(x+h\right)=?$$  

• $$x^2+x+h^2+h+4$$  

• $$x^2+x+2h+4$$  

• $$x^2+2xh+x+h^2+h+4$$  

• $$x^2+x+h+4$$  

• $$h^2+h+2x+4$$  

Multiple Choice

An abandoned area of town has the shape and dimensions of the blocks given below. All borders run either north-south or east -west. A survey or has set his equipment halfway between point M and Point O. Which of the following is the location of the surveyor from point L?

• $$9\ \frac{1}{2}$$  blocks east and $$4\ \frac{1}{2}$$  blocks north

• $$9$$  blocks east and $$5$$  blocks north

• $$10\ \frac{1}{2}$$  blocks east and $$4\ \frac{1}{2}$$  blocks north

• $$10\ \frac{1}{2}$$  blocks east and $$5\ \frac{1}{2}$$  blocks north

• 12 blocks east and 9 blocks norht

Multiple Choice

Which of the following systems of inequalities is represented by the shaded region of the graph below?

• $$y\le x\ and\ x\ge1$$  

• $$y\le-x+1\ and\ x\ge2$$  

• $$y\le-x+1\ and\ x\ge1$$  

• $$y\le x-1\ and\ x\ge2$$  

• $$y\le x+1\ and\ x\ge-2$$  

Multiple Choice

If $$\sin\theta=\frac{4}{5}\ and\ \frac{\pi}{2}<\theta<\pi$$  , then $$\cos\theta=?$$  

• $$\frac{-4}{5}$$  

• $$\frac{-3}{4}$$  

• $$\frac{-3}{5}$$  

• $$\frac{3}{5}$$  

• $$\frac{5}{3}$$  

Multiple Choice

A triangle, $$\Delta PQR$$  , is reflected across the x-axis to have the image $$\Delta P'Q'R'$$  in the standard (x,y) coordinate plane; this, P reflects to P'. The coordinates of point P are (a,b). Which of the following coordinates best describes the location of point P'?

• (a,b)

• (a,-b)

• (-a,b)

• (-a,-b)

• Cannot be determined from the given information

Multiple Choice

What is $$\cos\ \frac{\pi}{12}$$  , given that $$\frac{\pi}{12}=\ \frac{\pi}{3}-\frac{\pi}{4}$$   and $$\cos\ \left(\alpha-\beta\right)$$  = $$\left(\cos\alpha\ \right)\ \left(\cos\beta\right)$$  + $$\left(\sin\alpha\right)\left(\sin\beta\right)$$  ? (Note: You may use the table of values)

• $$-\frac{1}{2}$$  

• $$\frac{1}{2}$$  

• $$\frac{\sqrt[]{2}}{2}$$  

• $$\frac{\sqrt[]{2}-\sqrt[]{6}}{4}$$  

• $$\frac{\sqrt[]{2}+\sqrt[]{6}}{4}$$  

Multiple Choice

The larger of two numbers exceeds twice the smaller number by 6. The sum of twice the larger number and 4 times the smaller number is 70. If x is the smaller number, which equation below determines the correct value of x?

• 2(2x-4)+6x=70

• 2(2x+6)+4x=70

• 2(2x-6)+4x=70

• 4(2x+6)+2x=70

• 4(2x-6)+2x=70

Multiple Choice

In the figure shown, each pair of intersecting line segments meets at a right angle, and all the lengths given are in inches. What is the perimeter in inches, of the figure?

• 70

• 75

• 80

• 90

• 95

Multiple Choice

Which of the following statements describes the total number of dots in the first n rows of the triangular arrangement illustrated.

• The total is equal to 2n, where n is the number of rows

• The total is equal is $$n^2$$  , where n is the number of rows

• The total is equal to n!, where n is the number of rows

• The total is equal to $$2^o$$  , where n is the number of rows

• The total is equal to $$2^n-n!$$  , where n is the number of rows

Multiple Choice

A certain parabola in the standard (x,y) coordinate plane opens downwards and has a vertex NOT at the origin (0,0). Which of the following equations could describe the parabola?

• $$x=5y^2$$  

• $$y=2\left(x+3\right)^2+5$$  

• $$x=-2\left(y+2\right)^2+4$$  

• $$y=-3x^2$$  

• $$y=-4\left(x+1\right)^2-3$$  

Multiple Choice

The graph below shows the 2012 estimate of the five largest cities in the United States, to the nearest 1 million. According to the graph, the population of Houston makes up what fraction of the total population living in all five cities? Key: 1 smile face = 1 million people

• $$\frac{1}{11}$$  

• $$\frac{1}{10}$$  

• $$\frac{2}{19}$$  

• $$\frac{3}{19}$$  

• $$\frac{4}{19}$$