Free ACT Math Test Practice Questions with Answers #answers #to #homework


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Free ACT Math Test Practice Questions with Answers
sample 1

60 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. 4 x 10 -5 =
    A) – 40,000
    B) – 200
    C) 0.0004
    D) 0.00004
    E) 0.20

  2. Which of the following is equivalent to (x)(x)(x)(x 3 ), for all x?
    A) 4x
    B) 6x
    C) x 6
    D) 4x 6
    E) 4x 4

  3. There are 15 balls in a box: 8 balls are green, 4 are blue and 3 are white. Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a blue ball is selected at random from the box?
    A) 3/13
    B) 4/15
    C) 3/15
    D) 4/13
    E) 2/13
  4. The length of a rectangle is 3 times its width. If the width of the rectangle is 5 inches, what is the rectangle’s area, in square inches?
    A) 15
    B) 20
    C) 30
    D) 75
    E) 40

    For all x 2, (2x 2 + 2x – 12) / (x – 2) simplifies to
    A) 2(x – 2)
    B) x + 3
    C) 2(x + 3)(x – 2)
    D) x – 2
    E) 2(x + 3)

  5. If the hypotenuse of a right triangle is 10 inches long and one of its legs is 5 inches long, how long is the other leg?
    A) 5
    B) 5 3
    C) 5 5
    D) 75
    E) 10 – 5
  6. In the standard (x,y) coordinate plane, the graph of (x + 3) 2 + (y + 5) 2 = 16 is a circle. What is the circumference of the circle, expressed in coordinate units?
    A) 4
    B) 5
    C) 3
    D) 8
    E) 25
  7. How many solutions are there to the equation x 2 – 7 = 0?
    A) 1
    B) 2
    C) 4
    D) 7
    E) 14
  8. A circle with center (4,-5) is tangent to the y-axis in the standard (x,y) coordinate plane. What is the radius of this circle?
    A) 4
    B) 5
    C) (41)
    D) 16
    E) 25
  9. Angle A is an acute angle and sin(A) = 11/14. What is the value of cos(A)?
    A) 3/14
    B) 3 / 14
    C) 5 3 / 14
    D) (3/14)
    E) 5/14

  10. What are the values of a and b. if any, where – a|b + 4| 0.
    A) a 0 and b -4
    B) a 0 and b 4
    C) a 0 and b -4
    D) a 0 and b -4
    E) a 0 and b -4
  11. In a shipment of televisions, 1/50 of the televisions are defective. What is the ratio of defective to non defective televisions?
    A) 1/200
    B) 1/50
    C) 1/49
    D) 49/1
    E) 50/1
  12. Which of the following is divisible (with no remainder) by 4?
    A) 214133
    B) 510056
    C) 322569
    D) 952217
    E) 214395
  13. A particle travels 1 x 10 6 meters per second in a straight line for 5 x 10 -6 seconds. How many meters has it traveled?
    A) 2 x 10 11
    B) 5 x 10 12
    C) 5 x 10 -12
    D) 5
    E) 5 x 10 -36
  14. The length of sides AB and AC in the triangle below are equal. What is the measure of angle A?

    A) 70 o
    B) 55 o
    C) 40 o
    D) 110 o
    E) 20 o

  15. In the figure below ABC is an equilateral triangle. AH is perpendicular to BC and has a length of 2 3 inches. What is the area, in square inches, of triangle ABC.

    A) 12
    B) 2 3
    C) 4 3
    D) 8 3
    E) cannot be determined from the given information

  16. If 8y = 3x – 11, then x =
    A) (88/3) y
    B) (8/3) y + 11
    C) (8/3) y – 11
    D) (8y – 11)/3
    E) (8y + 11)/3
  17. Which of the statements describes the solution set for -2(x + 8) = -2x + 20?
    A) x = – 2 only
    B) x = 0 only
    C) x = 20 only
    D) There are no solution for this equation.
    E) All real numbers are solutions of this equation.
  18. When graphed in the (x,y) coordinate plane, at what point do the lines 2x + 3y = 5 and x = -2 intersect?
    A) (-2,0)
    B) (-2,5)
    C) (0,5/3)
    D) (0,5)
    E) (-2,3)
  19. The area of a trapezoid is 0.5 h (b1 + b2), where h is the altitude, and b1 and b2 are the lengths of the parallel bases. If a trapezoid has an altitude of 15 inches, an area of 105 square inches, and one of the bases 22 inches, what is the perimeter, in inches, of the trapezoid?
    A) 8
    B) 45
    C) 60
    D) 30
    E) This trapezoid does not exist.
  20. If you drove at average speed of 66 miles per hour, what distance, in miles, did you drive in 99 minutes?
    A) 1.5
    B) 0.7
    C) 65.34
    D) 108.9
    E) 150
  21. If x and y are any real numbers such that 0 x 2 y. which of these must be true?
    A) x (xy)/2 y
    B) 0 xy 2x
    C) x xy 2
    D) 0 xy 2
    E) xy y
  22. In the right triangle ABC below, what is the cosine of angle A?
  23. The graph of y = 2/(x – 3) is shown below

    Among the following, which is the best possible graphical representation of y = -2/|x – 3|

    .

  24. What is the slope of the line
    4x = -3y + 8
    A) 4
    B) -3/4
    C) -4/3
    D) 2
    E) 8
  25. In the figure below, B is on AD. BAC and ACB measure 26� and 131� respectively. What is the measure of CBD?

    .

  26. Which of the following is equal to 45
    A) 15
    B) 5 3
    C) 9 5
    D) 3 5
    E) 3

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