Free ACT Math Test Practice Questions with Answers
sample 2

Math questions, with answers and detailed solutions, similar to the questions in the ACT math test. The answers are at the bottom of the page.

  1. What is the greatest common factor of 45, 135 and 270?
    A) 5
    B) 9
    C) 15
    D) 25
    E) 45
  2. What is the value of 2x + 1/2 when 5x - 3 = -3x + 5
    A) -1/2
    B) -1/4
    C) 1
    D) 2 and 1/2 (mixed number)
    E) Value cannot be calculated
  3. The width W of a rectangle is 2 inches less than half its length L. Express the perimeter P of the rectangle in terms of the length L.
    A) 3L - 4
    B) 4L - 4
    C) 4L
    D) 3L - 2
    E) 2L - 2
  4. The total surface area of all six sides of the rectangular box below is equal to 80 square inches. What is the volume of the rectangular box in inches cubed?

    act problem 52.


    A) 40
    B) 48
    C) 12
    D) 30
    E) 16

  5. The points (-4 , -4), (-1 , -2) and (x , -8) are the vertices of a right triangle with the right angle at (-1 , -2). Find the value of x.
    A) 0
    B) 2
    C) 3
    D) -1
    E) -4
  6. In the figure below, L1 and L2 are parallel lines. The correct relationship between angles y and x is

    act problem, sample 2, problem 6 .


    A) y = x
    B) x + y = 180o
    C) x + y = 360o
    D) y = x + 90o
    E) y - x = 180180o
  7. If (x + y)2 = 144 and x2 - y2 = 24, then what is x if x and y are both positive?
    A) 7
    B) 5
    C) 12
    D) 2
    E) 8
  8. How many 3 digit numbers can we make using the digits 4, 5, 7 and 9 and where repetition is allowed?
    A) 34
    B) 33
    C) 44
    D) 12
    E) 43
  9. A boat travels 10 miles East and then 24 miles South to an island. How many miles are there from the point of departure of the boat to the island?
    A) 34
    B) 14
    C) 26
    D) 2√119
    E) 44
  10. What is the slope of any line perpendicular to the line -5x + 3y = 9?
    A) -3/5
    B) 5/3
    C) 3/5
    D) -5/3
    E) -1/5
  11. Which of the following is a factor of the polynomial -2x2 + 7x - 6?
    A) -2x - 3
    B) 2x + 2
    C) x - 6
    D) 2x - 2
    E) -2x + 3
  12. √(-9)(-4) + √(-4) = ?
    A) 6 + 2i
    B) 6 - 2i
    C) 8
    D) 4
    E) 2 + 6i
  13. Find the linear function f such that f(2) = 5 and f(3) = -5.
    A) f(x) = 2x + 1
    B) f(x) = -10x - 5
    C) f(x) = 3x - 1
    D) f(x) = -10x + 25
    E) f(x) = -10x - 25
  14. A circular garden has an area of 100π feet squared. What is the circumference of the garden in feet?
    A) 20
    B) 10π
    C) 20π
    D) 400π
    E) 2500π
  15. If 5/x = 10 and 2/y = 6 then x/y = ?
    A) 5/3
    B) 3/2
    C) 3/5
    D) 2/3
    E) 5/2
  16. If 2m-3 / 42m = 8, then 2m - 1 = ?
    A) 0
    B) 1
    C) 2
    D) -5
    E) -9
  17. In the figure below, ABC is a right triangle. Points B, C and D are collinear; points D, E and F are also collinear and so are points B, A and F. The length of segments DC and DE are equal. What is the size, in degrees, of angle AFE?

    act problem, sample 2, problem 17.


    A) 50o
    B) 40o
    C) 30o
    D) 45o
    E) 55o
  18. Which of the following is an equation of a line perpendicular to the line with equation 3x - 6y = 9?
    A) y = 2
    B) 3x + 6y = 9
    C) x - 2y = 3
    D) 2x + 2y = 3
    E) 2x + y = 7
  19. If a and b are any real numbers, then which of the following expressions is always positive?
    A) |a|
    B) |a + b|
    C) |a - b| + 1/2
    D) a2 + b2
    E) (a + b)2
  20. The geometric figure below consists of a right triangle and 2 semicircles. The diameters of the semicircles are the sides of the triangle. What is the area of the shaded region in square centimeters if the length of the hypotenuse of the triangle is 8 centimeters?

    act problem, sample 2, problem 20.


    A) 64
    B) 8π
    C) 64π
    D) 10π
    E) 16
  21. The mean of the numbers a, b, c, d and e is 23. The mean of the numbers a, b, c, d, e and f is 22. What is the value of f?
    A) 23
    B) 18
    C) 22
    D) 22.5
    E) 20
  22. Which of the following equations corresponds to the graph shown below?

    act problem, sample 2, problem 22 .


    A) y = (x - 3)2 - 1
    B) y = -(x - 3)2 + 1
    C) y = (x - 3)2 + 1
    D) y = x - 3
    E) y = -(x - 3)2 - 1
  23. Functions f and g are defined by f(x) = x2 + x and g(x) = √(x + 6). What is the value of g(f(2))?
    A) 3
    B) -3
    C) 7
    D) 6
    E) -6
  24. The sum of three consecutive integers is equal to 192. What is the product of these numbers?
    A) 216000
    B) 7077888
    C) 576
    D) 110592
    E) 262080
  25. What are the x-coordinates of the points intersection of the line with equation y = x + 1 and the circle with equation x2 + y2 = 5
    A) -2 , 0
    B) 1 , 2
    C) -2 , 1
    D) -2 , -1
    E) 1 , 3
  26. (1/2)sin(2x)(1 + cot2(x)) =
    A) tan(x)
    B) sin(x)
    C) cos(x)
    D) cot(x)
    E) sec(x)
  27. Find the area of the rectangle ABCD shown in the figure below.

    act problem, sample 2, problem 27.


    A) 2500 / √2
    B) 2500
    C) 2500 / √3
    D) 1250
    E) 5000
  28. Solve for x: logx(1024) = -5
    A) 1/4
    B) 4
    C) 1/2
    D) 1/8
    E) 2
  29. Simplify: 6 3√32 + 2 3√108
    A) 32
    B) 18 3√2
    C) 36 3√2
    D) 18 3√4
    E) 36 3√4
  30. Evaluate: 1 / (-5)2
    A) - 1 / 25
    B) 1 / 25
    C) 25
    D) -25
    E) 1 / 10