# Best SHSAT Math Practice Questions - Free and Official

/No matter whether you’re doing self-study, a test prep class, or working with a private tutor, it is best to work with real SHSAT math practice materials.

The SHSAT math test will likely differ from most other math tests you’ve faced. Working with the real material allows you to get used to pacing and style of this unique exam.

In this article, we will provide you with links to the official SHSAT practice tests from the Department of Education (DOE) handbook on the Specialized High Schools.

These tests are the gold standard for SHSAT practice tests as the DOE creates the actual SHSAT tests and uses questions from real SHSAT exams. They are also free.

To help improve your math scores on the SHSAT, we recommend using several key strategies. If you would like to benefit from these strategies, please download the SHSAT free online practice tests by clicking the button below, and we will also send you our SHSAT math practice test checklist on "**4 Tips to Use the DOE’s SHSAT Math Practice Tests Effectively**."

These strategies are culled from 14 years of working with hundreds of students on test preparation for the SHSAT, and can help you excel on this challenging test.

## Other SHSAT Math Materials

Of course there are other SHSAT math practice questions that can you use to help prepare for the math section of the SHSAT.

However, in general, we don’t recommend taking SHSATpractice tests that were not written by the DOE as it won’t be realistic practice. It’s best to use real practice materials so that you ensure you’re taking tests that reflect the actual content and difficulty of the real SHSAT. But since there are only two full practice tests in the DOE handbook (there are additional questions in previous handbooks), you may want to take practices tests made by other companies. Just keep in mind that they may be more difficult or easier and may not include all or the same content on the real SHSAT math section.

So what are unofficial tests good for? They can be very useful for practicing math skills so you can get better and more confident with answering actual SHSAT questions.

So, we recommend using the actual DOE tests as your main practice tests, and use the math material and practice questions from test prep companies to improve the different math skills that the SHSAT assesses.

## SHSAT Math Topics

There are fifty multiple choice math questions on the SHSAT, and these problems test students on many topics. Most questions cover algebra, geometry, basic number theory, and similar topics that students should have practiced in class. There are also questions that require students to use their problem-solving skills or brainstorm clever solutions, instead of wasting time on complicated answers.

## Examples of SHSAT Math Questions

So what kind of questions will you see on the SHSAT? Below we have included some examples, with answer explanations.

**1.Carlos is picking colored pencils from a large bin that contains only 480 red pencils, 240 green pencils, and 160 blue pencils. Without looking, Carlos pulls out 22 pencils. If the pencils were distributed randomly in the bin, how many pencils of each color is it most likely that he picked?**

- A. 8 red, 7 green, 7 blue
- B. 10 red, 7 green, 5 blue
- C. 10 red, 8 green, 4 blue
- D. 11 red, 6 green, 5 blue
- E. 12 red, 6 green, 4 blue

**The correct answer is E**. First, you need to find the ratio of red to green to blue pencils. Then you need to reduce it to its lowest form by dividing by the greatest common divisor: 480:240:160 = 6:3:2.

Since 6 + 3 + 2 = 11, multiply each value by 2 (because 2 x 11 = 22) to get the number of each color pencil in a set of 22 randomly chosen pencils: 12 red, 6 green, 4 blue

**2. How many ways can the letters in the word RAIN be arranged horizontally so that the vowels (A and I) are always immediately next to each other (either AI or IA)**?

- A. 6
- B. 8
- C. 12
- D. 16
- E. 24

**The correct answer is C**. There are three positions for the letters AI in this four-letter combination:

AI , *AI*, and AI

For each of these positions of A and I, there are two combinations of the letters R and N: AIRN, AINR, RAIN, NAIR, RNAI, NRAI. Thus, for the letters AI (in that order), there is a total of 6 combinations. The question indicates that IA is also possible, so there are also 6 combinations with the letters in the order IA. The total number of combinations is 6 + 6 = 12.

**2.What is the greatest common factor of 2,205 and 3,675?**

- A. 147
- B. 245
- C. 441
- D. 735
- E. 1,225

**The correct answer is D**. First, find the prime factorization of each number:

2,205 = 3 • 3 • 5 • 7 • 7

3,675 = 3 • 5 • 5 • 7 • 7

Now, determine what each prime factorization has in common, and multiply those:

2,205 = 3 • (3 • 5 • 7 • 7) = 3 • 735

3,675 = 5 • (3 • 5 • 7 • 7) = 5 • 735

The greatest common factor is 735