# Free Math Aptitude Test Practice: 2023 Prep Guide

Few hours of practice make all the difference.

Ace that Test!

Basic math skills are probably the most common component in pre-employment aptitude testing. Math skills are important in the recruitment world for two main reasons. The first is that many jobs require basic knowledge of math concepts and the ability to perform job-related tasks. The second reason is that math skills were found to be an indicator of logic, reasoning, and general aptitude, and prove to have benefits for employee productivity overall. So, regardless of your position, expect your aptitude test to include math questions.

#### Did you know?

**Math Aptitude Tests** help to assess your skills in the following areas: (1) arithmetic, (2) pre-algebra, (3) algebra, (4) word problems, and (5) number series. **Passing grades vary, but usually require scores over 70%. **Candidates who haven’t taken a math class in a while may find it beneficial to practice beforehand.

**What Is Included in Math Aptitude Tests?**

The most fundamental math skills that are assessed are basic understanding of mathematical computations and concepts such as basic arithmetic (addition, subtraction, multiplication, division), calculating percentages, and converting numbers into fraction and decimal forms. In addition, it is very common to assess basic algebra skills. These include the computation of an unknown variable based on the value of other variables, making equations, and simplifying mathematical terms. These skills may be assessed directly by asking the candidate to solve and evaluate mathematical expressions, by including the mathematical concepts in word problems, or by applying math while interpreting information, tables, and graphs.

#### iPREP: Concise. Focused. What you need.

##### Sign up

Immediate access

##### Practice

Online self-paced

##### Pass

Ace that Test!

**Which Types of Math Questions Are Included in the Assessments?**

The following categories of questions are the most common among math hiring tests. Not every math aptitude test will include questions of each category but every assessment is likely to include a few of these:

**Arithmetic**

Arithmetic focuses on the basic study of numbers and their basic operations – addition, subtraction, multiplication, and division.

**Pre-Algebra**

This broad area of mathematics is the foundation for many more complex phases. The majority of questions in math aptitude tests fall into this category and include the following:

- Different types of numbers such as integers, fractions, and decimals
- Factorization of natural numbers and properties of operations such as associativity and distributivity
- Exponents/powers and radicals/roots
- Evaluation of expressions and the application of the standard order of operations, including the use of parentheses (PEMDAS)
- Basics of equations and the manipulation of equations
- Fundamentals of the Cartesian plane

**Basic Algebra**

Algebra is a huge field in mathematics; however, aptitude tests assess its basic structures, which can usually still be found in everyday applications of math. They include:

- Understanding, simplification, and evaluation of algebraic expressions
- Linear equations and inequalities
- Graphing lines and slopes
- Systems of linear equations
- Quadratics (basics), polynomials, and factorization of quadratics

**Word Problems**

This specific type of mathematical questions is a textual problem, which assesses the ability to apply abstract mathematical concepts to “real-world” situations. The situation can usually be translated into either an arithmetic or algebraic expression and the answer is found by applying the adequate solving techniques.

**Number Series / Sequences**

Numerical series problems are problems that require you to find the missing number in a sequence. The missing number is usually found by deciphering the logical pattern that governs the sequence. The pattern may be based on almost any of the abovementioned concepts. It may be an arithmetic sequence, a sequence based on exponents, or even based on an algebraic structure.

**How to Pass Math Aptitude Tests?**

The simple answer to this question is “know math.” Nonetheless, it is not that simple. Many people know basic math, and yet years have passed since the last time they dealt with mathematical expressions and needed to solve problems, especially in a timed testing context.

Therefore, the best advice is to refresh your knowledge with a focused course that includes short lessons about the specific knowledge required to pass the test, sample math aptitude test questions to familiarize yourself with the format, and practice tests to simulate the testing environment.

**Free Math Aptitude practice test: **Get to know what a Math Aptitude Test will be like by practicing with these sample questions:

###### Question 1 of 6

Convert the decimal to fraction form:

13.375 =

- $$$ 13\dfrac{3}{8} $$$
- $$$ 13\dfrac{7}{8} $$$
- $$$ 13\dfrac{5}{8} $$$
- $$$ 13\dfrac{8}{13} $$$

**The correct answer is A ($$$ 13\dfrac{3}{8} $$$**)**.**

13.375 | (Separate whole number from the decimal) |

= 13 + 0.375 | (Multiply and divide the fraction by 1000). |

= 13 + 0.375 x 1000/1000 | (Rearrange terms in the fraction) |

= 13 + (0.375 × 1000)/1000 | (Multiply the terms in the numerator) |

= 13 + 375/1000 | (Simplify the fraction by dividing the numerator and denominator by ‘125’). |

= 13 + (375÷125)/(1000÷125) | |

= 13 + 3/8 | |

= 13 3/8 |

###### Question 2 of 6

The average number of students in each of the five classes is 20. If two classes consist of 17 students, a third consists of 19 students, and a fourth of 20 students, how many students are in the fifth class?

- 19
- 20
- 21
- 24
- 27

**The correct answer is 27.**

**Explanation:** The average (arithmetic mean) is the sum of all values divided by the number of values. You can use this formula in order to get to the correct answer, but there is a faster way:

Using the formula of the average:

**Average = (sum of elements)/(number of elements)**

20 = (17+17+19+20+X)/5

20*5 = 17+17+19+20+X

100 = 73 + X

X = 100-73**X = 27**

###### Question 3 of 6

Consider the following formula:

**A = B +3 (C – 3)**

If A = 10 and B = 1, what is the value of C?

- 3
- 9
- 4
- 6

**The correct answer is 6.**

In order to solve this question correctly, you need to remember the order of operations (PEMDAS):

- Parentheses
- Exponents
- Multiplication/Division
- Addition/Subtraction

In addition, you should remember that if you see a number which is written to the left of the parentheses with no sign between the number and the left bracket, then this number is a factor of the parentheses, which means it multiplies everything within the parentheses.

In order to find a solution, we need to isolate C.

**First step** – placing the values of A and B:

A = B +3(C – 3) Remember A = 10; B = 1

10 = 1 + 3(C – 3)

**Second step** – removing the parentheses:

10 = 1 + 3(C – 3) 3 is a factor of both C and -3

10 = 1 + 3C – 3*3 Simplify and collect like terms

10 = 3C + 1 – 9

**Third step** – isolating C and finding the solution:

10 = 3C – 8 Adding 8 to both sides

10 + 8 = 3C

18 = 3C Divide by 3**6 = C**

###### Question 4 of 6

In this problem, the ratios are directly proportional. Find the missing variable.

**If x _{1} = 13, x_{2} = 20, y_{2} = 25. What is the value of y_{1}?**

- $$$ 16\dfrac{1}{20} $$$
- $$$ 16\dfrac{1}{4} $$$
- $$$ 15\dfrac{4}{5} $$$
- $$$ 15\dfrac{3}{4} $$$

**The correct answer is B. ($$$ 16\frac{1}{4} $$$).**

Here’s a detailed video walk-through of the explanation:

y_{1} ∶ x_{1} = y_{2} ∶ x_{2} | |

(The above is one of the valid ways to write ratios. There are additional valid ways, e.g. x_{1} ∶ x_{2} = y_{1} ∶ y_{2}). | |

y_{1}/x_{1} = y_{2}/x_{2} | (Converting ratios into fractions and then cross multiply). |

y_{1} = (x_{1} * y_{2})/x_{2} | (Substitute values of x_{1}, x_{2} & y_{2} from the question). |

y_{1} = (13 * 25)/20 | (Multiply both terms in the numerator). |

y_{1} = 325/20 | (Converting Improper fraction to a mixed fraction). |

y_{1} = 320/20 + 5/20 | |

y_{1} = 16 + 1/4 | |

y_{1} = 16 1/4 |

###### Question 5 of 6

Factor the polynomial:

**x ^{5}y^{2}z^{6} – x^{3}y^{2}z^{7}**

- x
^{3}yz^{6}(x^{2}y – z) - x
^{5}y^{2}z^{5}(y – z^{2}) - x
^{5}y^{2}z^{7}(x^{-2}– z) - x
^{3}y^{2}z^{6}(x^{2}– z)

**The correct answer is x ^{3}y^{2}z^{6}(x^{2} – z).**

**Here’s a detailed video walk-through of the explanation:**

We need to find the greatest common divisor of each of the terms (x,y,z) to factor the expression.

We should remember that if the bases of exponent numbers are the same, the multiplication of two terms is found by summing the powers and writing them on the same base.

Similarly; when dividing, the power of the divisor is subtracted from the power of the dividend.

Both x^{5}y^{2}z^{6} and x^{3}y^{2}z^{7} contain x^{3}, y^{2} and ,z^{6}. So;

x^{5}y^{2}z^{6} – x^{3}y^{2}z^{7 }=

x^{3}y^{2}z^{6}(x^{2}*1*1) – x^{3}y^{2}z^{6}(1*1*z^{1}) =

x^{3}y^{2}z^{6}(x^{2}) – x^{3}y^{2}z^{6}(z) =

We can carry x^{3}y^{2}z^{6} out as the factor:

**= x ^{3}y^{2}z^{6}(x^{2} – z)**

###### Question 6 of 6

What is the next number in the following series of numbers?

-1 2 1 3 4

- 5
- 7
- 1
- 6

**The correct answer is 7.**

**Explanation:**

Look at the differences between the numbers:

-1 2 1 3 4

**+3 -1 +2 +1**

While there is no simple pattern to the differences, you do get a hint: all the elements of the series of the differences, except the first one, appear in the same order as the numbers of the original series. You can assume that the next difference will be +3 as it is the number that follows 1 in the original series.

Therefore, the next number of the series is 4 + 3 = **7**

The complete logic of the series is that every term in the series equals the sum of the previous two terms.

It can be formally written as follows: **an+2 = an + an+1**

For learning purposes, here is the series, had it continued for several more steps:

-1 2 1 3 4 7 11 18 29 47

**+3 -1 +2 +1 +3 +4 +7 +11 +18**

And for general knowledge: Did you know that any series of numbers in which each number (third in sequence and above) is the sum of the two preceding numbers is known as the **Fibonacci sequence**, named after Italian mathematician Leonardo of Pisa, known as Fibonacci?

## Well done!

##### You have completed the Sample Questions section.

The complete iPrep course includes full test simulations with detailed explanations and study guides.

#### ‘…TESTS THAT ACTUALLY HELP’

*In the first 30 minutes of use I have learned so much more than skipping along the internet looking for free content. Don’t waste you time, pay and get tests that actually help.*

Richard Rodgers

January 28, 2020 at 7:49 PM

## About the course

Welcome to iPrep’s Math Aptitude Test Course.

This course will help you boost your skills and with it your confidence towards your upcoming aptitude test. The course provides you with the following tools and benefits:

- Refreshment lessons of all the important mathematical concepts that appear in aptitude tests.
- An abundance of practice questions to make sure that you practice any type of questions you may encounter on your test.
- Step-by-step and timed practice drills for you to experience the questions in various formats and to familiarize you with the expected time constriants.
- A great variety of helpful tips for the different types of questions. Some of the tips are in the introductory sections while most are in the detailed explanations that follow each question.

## 8

Learning hours

## 22

Practice tests

## 250

Questions

## 30

Day access

By the end of this course, you will be more knowledgeable and comfortable towards your math aptitude test – Knowledge and familiarity with the test are the two most significant factors that can help you maximize your score and improve your chances of success.

Wishing you an enjoyable learning experience!

### Skills you will learn

Basic Arithmetic

Pre-Algebra & Algebra 1

Math Word Problems

### Curriculum

- Course Introduction
- Basic Arithmetic Operations
- Fractions and Decimals
- Percents
- Exponents and Radicals
- The Order of Operations
- Basic Algebra and Functions
- Math Word Problems
- Number Series/Sequences
- Basic Math – Multiple-Choice Solving Tips
- Course Conclusion

### About the author

### M.A. Tamir Rubin

**Psychology and Cognitive Sciences Expert**

Tamir Rubin has been working in the field of Psychology and Cognitive Sciences for over ten years. His experience includes the development of tens of assessment test preparations in subjects such as Abstract Reasoning, Cognitive Ability, Critical Thinking, Deductive Reasoning, Inductive Reasoning, Numerical Reasoning, Verbal Reasoning, and more.

Rubin has been the Head Of Products for TestPrep, a global leader in assessment test preparation, and holds a Master’s degree from the Bar-Ilan University and a Bachelor’s degree from the Hebrew University.

#### Customer Testimonial

*I highly recommend iPREP. I had to take a test as part of a job interview. I was very out of practice and used iPREP’s Math course to prepare. It helped me with shortcuts, tips for certain types of questions, and quick mental math. I tried out of a few different prep courses and this was the best by far.*

**Andrew Daren**

December 24, 2019 at 4:09 PM

## Reviews

###### Lia L**************

September 23, 2021 at 1:05 PM

Very good explanations, great course, I enjoyed refreshing my math skills and I will go back to the test sections again as it is a very good brain exercise. Thank you Tamir.

###### Ivo P****

May 30, 2020 at 8:41 PM

Excelent! I was kind of rusty in these kind of tests. It helped me recover speed and center my test strategy.

###### Doug A***

March 16, 2020 at 9:05 AM

I found the quizes to be excellent preparation. Really worthwhile and thoughly set me up for success in the assessment. I could not have done without it

###### arlan b*****

December 28, 2019 at 1:59 AM

I believe this is a fundamental tool to pass your test. Best study guide i've seen online, very helpful and broken down well!

###### Andrew D*****

December 24, 2019 at 4:09 PM

I highly recommend iPREP. I had to take the CCAT as part of a job interview. I was very out of practice and used iPREP's curriculum to prepare. It helped me with shortcuts, tips for certain types of questions, and quick mental math. I tried out of a few different prep courses and this was the best by far.

###### Eddie T*****

December 14, 2019 at 9:53 PM

iprep is the best testing tool there is I would refer it to all of my co workers who has to take the test also

###### charles d******

December 12, 2019 at 4:06 PM

Definitely helping me, I've been out of school for quite a while. The step by step explanation is just what I needed!