Sample Test

Free Sample Test

Here is a free sample test from our ACT Math Power Download.

Before attempting this free sample test, you should try our free practice problems.

Question 1:  How many 3 letter combinations can possibly be made from this set of letters: L M N P Q R?

  • Remember the formula for combinations: (N!) ÷ [(N − S)! × S!]
  • In our question, S = 3 and N = 6 (because there are six letters in the set).
  • When you see the exclamation point (N!) in the equation, it means you need to multiply that number by each number which is successively lower than it. So for example, 3! = 3 × 2 × 1





Question 2:  Find the midpoints of a line on a two-dimensional graph that runs through the points (−6, 8) and (2, −2).

  • You need a formula for the midpoint of (x1, y1) and (x2, y2).
  • The midpoint formula is: (x1 + x2) ÷ 2 , (y1 + y2) ÷ 2

Question 3:  What is the equation 4 = log5625 equivalent to?

Question 4:  (5x − 2y)2 = ?

  • You should use the FOIL method: First − Outside − Inside − Last
  • If you do not remember how to do the FOIL method, refer back to the algebra page.

Question 5:  The radius of circle B is 0.7 and the radius of circle C is 0.4. How much larger is the area of circle B than circle C?

  • The area of a circle is calculated by multiplying the square of the radius by π.





Question 6:  The radius of circle Q is 0.9. What is the circumference of the circle?

Question 7:   What are the x and y intercepts of the following?: 6x2 + 2y = 54

Question 8:  How many 2 letter permutations can be made from this character set: ? ! $

  • Permutations take into account the order of items in each set, so the set ? ! is distinct from the set ! ? and the set $ ! is distinct from ! $, for example.
  • The formula for permutations is: N! ÷ (N − S)!

Question 9: In a two-dimensional linear graph, x = 2 and y = 15. The y intercept is 6. Calculate the slope (m) of the line.

  • Remember to use the slope formula: y = mx + b

Question 10:  Consider cone Z, with diameter of 16 and height of 9. Calculate the volume of the cone.

  • Here is the formula to calculate the volume of a cone: (π × radius2 × height) ÷ 3

Question 11:  Rectangle D has a length of 5 units and a width of 7 units. What is the area of rectangle D?

Question 12:  Find the area of a right triangle with a height is 6 and a base of 3.

Question 13:  Calculate the perimeter of this rectangle: length = 4 units and width = 5 units

Question 14: (x2 − 4) ÷ (x − 2) = ?

Question 15:  If 6x − 3(x + 4) = 0, then x = ?

Now check your answers.

If you had problems with this free sample test, you may want to have another look at the following:

Algebra questions

Geometry exercises

Trigonometry equations