ACT Math Sample Questions Page
Here are some free ACT math sample questions from our ACT Math Download.
Look at the formulas and the hints at the bottom of this page before you do the questions.
1) How many 3 letter combinations can possibly be made from this set:
L M N P Q R?
2) Find the midpoints of a line on a two-dimensional graph that runs through the points (−6, 8) and (2, −2).
3) What is the equivalent of the equation 4 = log5625?
4) Expand the polynomial: (5x − 2y)2
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?
6) The radius of circle Q is 0.9. What is the circumference of the circle?
7) What are the x and y intercepts of the following? 6x2 + 2y = 54
8) How many 2 letter permutations can be made from the character set:
? ! $
9) In a two-dimensional linear graph, x = 2 and y = 15. The y intercept is 6. Calculate the slope (m) of the line.
10) Consider cone Z, with diameter of 16 and height of 9. Calculate the volume of the cone.
11) Rectangle D has a length of 5 units and a width of 7 units. What is the area of rectangle D?
12) Find the area of a right triangle with a height is 6 and a base of 3.
13) Calculate the perimeter of this rectangle: length = 4 units and width = 5 units
14) (x2 − 4) ÷ (x − 2) = ?
15) If 6x − 3(x + 4) = 0, then x = ?
After doing these ACT math questions, you should try our free practice problems.
ACT Math Sample Questions Page – Hints
Have a look at these hints before you try the ACT math sample questions at the top of the page. Then check your answers by clicking on the link above.
Combinations
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
Midpoints
You need a formula for the midpoint of (x1, y1) and (x2, y2).
The midpoint formula is: (x1 + x2) ÷ 2 , (y1 + y2) ÷ 2
Expanding polynomials
You should use the FOIL method: First − Outside − Inside − Last
(a + b)2 = (a + b)(a + b)
First: (a + b)(a + b) = a × a = a2
Outside: (a + b)(a + b) = a × b = ab
Inside: (a + b)(a + b) = b × a – ba = ab
Last: (a + b)(a + b) = b × b = b2
Add the above for the result: a2 + ab + ab + b2 = a2 + 2ab + b2
Circle area & radius
The area of a circle is calculated by multiplying the square of the radius by π.
Permutations
Permutations take into account the order of items in each set, so the set ? ! is distinct from the set ! ? and the set ! 3 is distinct from 3 !, for example.
The formula for permutations is: N! ÷ (N − S)!
Slope-intercept
Remember to use the formula: y = mx + b
Cone Volume
Here is the formula to calculate the volume of a cone:
(π × radius2 × height) ÷ 3
More exercises
If you had problems with these ACT math sample questions, you may want to have another look at these other exercises:
