Algebra Questions with Solutions
Try our algebra questions below in order to prepare for the algebra part of the ACT test.
- Free Questions on Absolute Value
- Free Questions on Inequalities
- Free Questions on Exponent Laws
- Free Questions on Functions
- Free Questions on Probability
- Free Questions on Matrices
- Free Questions on Multiple Solutions
- Free Questions on Imaginary Numbers
Algebra Questions – Further Examples
This section has algebra questions with solutions for you to study for the ACT math exam.
It provides the formulas you need to know and study in order to calculate absolute values, combinations, permutations, functions, and basic algebraic expressions.
Have a look at the formulas below. You may want to make a note of them on a piece of paper.
Alternatively, you might like to print out our cheat sheet, which shows the formulas most commonly used on the math section of the exam.
Then go to the algebra questions in the free sample of our download to check your progress with the practice test questions.
Absolute value is always a positive number. | − x | = x
Combinations and permutations:
The amount of combinations of sets of S that can be made from a group containing N items can be calculated using this formula:
(N!) ÷ [(N − S)! × S!]
You need use this formula to calculate the amount of permutations of size S taken from N items:
N! ÷ (N − S)!
Logarithmic functions are just another way of expressing exponents.
x = logyZ is always the same as: yx = Z
The use of the FOIL method is one of the most important things you will need to know in order to answer many algebra questions.
Look at the example algebra question below on the FOIL method.
Example: (3x − 2y)2 = ?
When you see practice questions for algebra like this one from our sample test, you should use the FOIL method.
This means that you multiply the terms in the parentheses in this order:
First − Outside − Inside − Last
Now study the solution below so that you know how to answer algebra questions like this one.
(3x − 2y)2 = (3x − 2y)(3x − 2y)
So, the first terms in each set of parentheses are 3x and 3x: (3x − 2y)(3x − 2y)
FIRST: 3x × 3x = 9x2
The terms on the outside are 3x and −2y: (3x − 2y)(3x − 2y)
OUTSIDE: 3x × −2y = −6xy
The terms on the inside of each set of parentheses are −2y and 3x: (3x − 2y)(3x − 2y)
INSIDE: −2y × 3x = −6xy
The last terms in each set are −2y and −2y: (3x − 2y)(3x − 2y)
LAST: −2y × −2y = 4y2
All of these individual parts are put together for your final answer to the algebra question:
9x2 − 6xy − 6xy + 4y2 = 9x2 − 12xy2 + 4y2
These types of algebra questions, as well as geometry and trigonometry problems, are included in our Practice Math Questions Download.