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What are the SHSAT Math topics, and how to improve your Math score?

By Bobby-Tariq Tutoring Center | Updated on January 18, 2020

The Specialized High School Admissions Test (SHSAT) is an examination that eighth and ninth grade students in New York City take each year in order to gain admittance to one of the city’s nine elite specialized high schools. Every exam season, about 30,000 students take the test in order to have a chance at admission. The test is made up of two sections, the ELA section and the math section. This blog is your personal guide to the most important concepts on the SHSAT math section, such as Consecutive Integers, Proportions, Percentages and Ratios, and Geometry. In this guide, we’ll provide you with the tips, tricks, and resources needed to ace this exam.

What is the SHSAT Math section?

The SHSAT has a very long and comprehensive math section in order to test students on their knowledge of math up to that year, with some advanced concepts that you may not be familiar with yet. You will not be allowed to use a calculator on the math section, so your job is to become familiar with as many mathematical concepts and rules as you can. There are many shortcuts, tips, and tricks out there to help you with this mission, and we will go over these shortly.

The math section of the exam has 57 questions. 52 of them are multiple choice while 5 of them are grid in questions. The suggested time is 90 minutes, or about half of the exam, but again, it’s up to you how long you want to take. If you are speedy at math, that gives you more time to check your answers and go back to the verbal section if necessary.

Some things are important to note – formulas and definitions are not provided on the exam, diagrams are not necessarily drawn to scale, and fractions should be reduced to the lowest terms possible. Of course, you’ve become a master of mathematics over the years, so you must be ready to answer these more difficult questions in a limited amount of time. If you’re not quite there yet, no worries – that’s where we come in.
Some tips for the math section: ⦁ The math section isn’t going to be checked over with a fine-toothed comb. No one will check if you are using unconventional methods or not showing your work. So be sure that you are using the methods that work for you and you alone, as long as you are sure that they work.
  • Make sure you read every part of the problem. The test writers are trying to trick you and trap you at every turn. Don’t let them get you. Don’t make careless mistakes because you didn’t take one extra second to read the problem carefully.
  • If you are taking too much time to answer a question, skip it and come back to it later. Perhaps the other problems will take less time to solve and you will have a decent amount of time to answer it later.
  • If you’re down to your last minute of the exam and you still haven’t figured out one of the difficult problems, your best bet is to make an educated guess. There’s no use in leaving problems blank. There isn’t a penalty for wrong answers, so be sure to answer absolutely everything, even if you aren’t 100 percent sure. After all, you still have a 25% chance of getting the question correct.

Consecutive Integers

Consecutive integers are a huge topic on the SHSAT. You’ve seen them throughout your middle school years and now they are also featured on the exam. Here’s an example problem:

In a set of consecutive integers from 12 to 30, inclusive, there are four integers that are multiples of both 2 and 3. How many integers in this set are multiples of neither 2 nor 3?

The answer is 6. Why? The question asks for integers from 12 to 30 that aren’t divisible by 2 or 3. That set includes {12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30}. We can remove all even numbers since they’re multiples of 2, and we are left with {13, 15, 17, 19, 21, 23, 25, 27, 29}. Then, after eliminating the multiples of 3, we are left with {13, 17, 19, 23, 25, 29}. That makes six numbers!

Proportions

Proportions are another topic that are quite prevalent on the SHSAT. Here’s an example problem: In a scale diagram, 0.125 inch represents 125 feet. How many inches represent 1 foot?

The answer is A. Let x be the number of inches that represents 1 foot. Then, set up a proportion to solve for x.

, so x = 0.001 inches.

Percentages and Ratios

Percentages and ratios are another very important concept on the exam. This is yet another basic topic, but problems on the exam will take it to the next level with more advanced problems. Here’s an example:

A paste is made by mixing the following ingredients by weight: 4 parts powder, 3 parts water, 2 parts resin, and 1 part hardener. One billboard requires 30 pounds of this paste. How many total pounds of resin are required for 4 billboards?
The answer is 24 lbs. Why? The ratio is 4:3:2:1, so the sum of all of the parts is 10. Since two of those parts are resin, 2/10 or 1/5 are resin. So, for 30 lbs of paste, there will be 6 lbs of resin. For four boards, that makes a total of 24 lbs of resin.

Geometry

While you won’t be officially taking a geometry class until tenth grade, you have been learning about geometry for many years. That’s why the SHSAT focuses on geometry so heavily. Here’s an example problem:
R, S, and T are midpoints of the sides of square MNPQ, as shown above. What is the sum of the areas of the shaded triangles?

The answer is 6 cm. Why? Since R, S, and T are midpoints, TM, MR, RN, and NS are equal to half of 6, or 3 cm. Both TMR and RNS are right triangles, so the area of one of the triangles is ½ bh or ½ x 3 x 3, totaling 9/2. Since the triangles are congruent, the sum of the areas is 9 sq cm, or 9/2 + 9/2.

Resources

At Bobby-Tariq tutoring center, we hope that you use us as your greatest resource to help ace the math section of the SHSAT! We have many great tools that you can use to become a beast. We recommend that you study at home and practice meticulously, but also that you use top-notch preparatory books, attend our SHSAT classes, and even search for private tutors. Learn more about the exam and the math section specifically in our SHSAT guide.
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