The Math section consists of word problems and computational questions in either a grid-in or multiple-choice format. There are five grid-in questions and 52 multiple-choice questions. The Math questions involve application of mathematical skills, mathematical terms, and general concepts from the New York State Learning Standards for Mathematics. However, as one of the purposes of this test is to identify students who will benefit from an education at a Specialized High School, the SHSAT Math items will require you to apply familiar Math skills to complex, multi-step problems.
Math questions on the Grade 8 test forms are based on the New York State Learning Standards through Grade 7. Math questions on the Grade 9 test forms are based on material through Grade 8.
The tips and sample questions below will help you prepare for taking the Math section on the SHSAT. They include the following:
- Tips to Improve your Math Skills
- Things to Keep in Mind While Preparing for the Math Section
- Tips for Solving Math Problems
- Sample Math Items
- Sample Explanations
- Tips for Math Multiple-choice Questions
- How to Complete the Math Grid-In Questions
Tips to Improve Your Math Skills
Review Math Resources:
Use your Math textbook, seek out other Math resources at school or at your local library, or ask your teacher to recommend resources for you to use.
Practice solving Math questions every day. Solve both basic and challenging Questions:
- Basic questions reinforce Math skills such as simplifying fractions and applying the concept of statistics.
- More challenging questions require setting up complex equations with multiple steps. They may also require using various types of Math skills. For example, you may use fractions, solve for equations, and apply your knowledge of statistics to answer one question.
- If you are unsure of how to answer a question, skip it and return to it after answering the other questions. You may have a better idea of how to solve a problem after completing other questions.
Things to Keep in Mind While Preparing for the Math Section
Memorize mathematical terms, symbols, and formulas that you use in your Math class
- You must know the meanings of mathematical terms that are appropriate for your grade level, such as “parallel” and “perpendicular,” as well as the symbols that represent those terms.
- You can find mathematical terms, symbols, and formulas, such as those for perimeter and area of different figures, in the materials for your Math classes and online in the Grade 7 and 8 New York State Learning Standards.
- Definitions and explanations for terms, symbols, and formulas will NOT be given in the test booklet. Practice using them to solve questions until you have memorized them and can use them with ease.
Do not use a calculator when solving questions: The use of calculators is not permitted while taking the SHSAT.
Timing: Before test day, plan how much time you will spend on the Math section; this will help you to be efficient when answering each question on test day.
Tips for Solving Math Problems
- Read each question carefully.
- Read carefully so that you accurately set up complex problems using all the important information from the question.
- Mark up the question, as in Sample 1, below, to ensure you include all the information when solving the problem.
- Change words from the question into mathematical symbols (as noted in Sample 1 and Sample 2 below).
Sample Math Items
Answers to the sample items can be found in the Sample Explanations section below. Note: the sample test questions on this page have not been translated by the NYCDOE, and the website-provided translations of the sample test items below may not reflect the actual sample items.
The sum of two consecutive integers is –15. If 1 is added to the smaller integer and 2 is subtracted from the larger integer, what is the product of the two resulting integers?
Tip: Mark up the question to prepare for solving the problem.
For example, in sample 1:
- Sum can be written as a “+” sign.
- “Two Consecutive integers” can be written as: “x, x+1”.
- “is –15” can be written as “= –15”
Jenny starts a game with twice as many marbles as Keiko. Jenny gives Keiko 5 marbles, but she still has 10 more than Keiko. How many marbles did Jenny have to start with?
Tip: Change words from the question into mathematical symbols.
For example, in sample 2:
- “Jenny” can be represented as “J”
- “Keiko” can be represented as “K”
- “Twice as many marbles as Keiko” can be written as 2K
- “Jenny gives Keiko 5 marbles” can be written as J-5.
The perimeter of a rectangle is 510 centimeters. The ratio of the length to the width is 3:2. What are the dimensions of this rectangle?
- 150 cm by 105 cm
- 153 cm by 102 cm
- 158 cm by 97 cm
- 165 cm by 90 cm
Tip: Draw figures or diagrams for questions that do not have them. Draw figures or diagrams, like in example 3 below, to help you visualize what the question is describing. Label figures and diagrams.
In this case:
- Draw a rectangle.
- Label each side. The right and left sides (width) can be labeled as 2x, and the top and bottom (length) can be labeled as 3x.
Malik has 140 lorgs and 16 dalts. If he exchanges the lorgs and dalts for dollars according to the rates below, how many dollars will he receive?
1 dollar = 7 lorgs
1 dollar = 0.5 dalt
Tip: To solve problems like this, take one step at a time. Some questions ask you to combine a series of steps. Write out one step at a time, like in the example below, to solve multi-step problems.
Step 1: Covert lorgs to dollars
Set up the equation as follows:
- 140/x = 7/1
- 7x = 140
Step 2: Convert dalts to dollars
Set up the equation as follows:
- 16/x = 0.5/1
- 0.5x = 16
Step 3: Add your conversions of lorgs and dalts together: 20+32 = $52.
Sample 1 Explanation
If x is the smaller consecutive integer, then x +1 is the larger consecutive integer. Use their sum −15 to find x:
x + (x + 1) = –15
2x + 1 = –15
2x = –16
x = –8
The two consecutive integers are −8 and −7.
One is added to the smaller integer: −8 + 1 = −7.
Two is subtracted from the larger integer: −7 – 2 = −9.
Find the product: –7 × –9 = 63.
Sample 2 Explanation
Correct Answer: (D) To solve, set up some equations.
Jenny (J) has twice as many marbles as Keiko (K): J = 2K
Jenny gives Keiko 5 marbles, so now they each have: J – 5 and K + 5 marbles.
Jenny still has 10 more than Keiko:
J – 5 = (K + 5) + 10
To find how many marbles Jenny had to start with, solve J = 2K for K and substitute that into the second equation:
In equation J = 2K, solve for K: K = J/2 .
Substitute J/2 in for K.
J – 5 = (K + 5) + 10
J – 5 = (J/2 + 5) + 10
J – 5 = J /2 + 15
J/2 = 20
J = 40 marbles
Sample 3 Explanation
Correct Answer: (f) Let 2x = the width and 3x = the length.
Draw the rectangle to help visualize.
Label the rectangle. The right and left side (width) can be labeled as 2x, and the top and bottom (length) can be labeled as 3x.
Since 2w +2l =P, we get
2(2x)+2(3X) = 510
10x = 510
X = 51
2x = 102cm and 3x = 152
Sample 4 Explanation
Correct Answer: (B) Use proportions to make the conversions:
Lorgs to dollars:
140/x = 7/1
Dalts to dollars:
16/x = 0.5/1
Total dollars = 20 +32 = $52
Tips for Math Multiple Choice Questions
Most multiple-choice questions should be done by working out the answer.
- Solving the problem before looking at the answer options is more effective than looking first at the answer options and then trying to estimate the accuracy of each one to get to the correct answer.
- It is best to solve problems on paper (rather than just in your head) and to focus on solving rather than selecting.
- When you get an answer, look at the choices listed. If your answer is included among the choices, mark it. If it is not, reread the question and solve it again.
- If your answer is not among the answer options, consider other ways to write your answer. For example: 5/9 (3 + x) is equivalent to all of the following:
- 5(3 + x) /9
- 5/ 3 + (5 /9)x
- 5/ 3 + 5x/ 9
- If your answer is still not among the answer options, make your best guess and/or come back later if you have time.
How to Complete the Math Grid-In Questions
The Math section includes five grid-in questions for which students must solve computational questions and provide the correct numerical answer rather than selecting the answer from multiple-choice options.
- The grid for each question is made up of five columns. When you record your answer in the grid, begin on the left.
- For each grid-in question, write your answer in the boxes at the top of the grid.
- Print only one number or decimal symbol in each box. Use the "." symbol if your response includes a decimal point.
- Fill in the circle under the box that matches the number or symbol that you wrote.
For example, if your answer is 5, fill in the circle under the first 0 on the left. If your answer is 3.2, fill in the circle under the first 0 on the left with 3, then a decimal point in the second column followed by a 2 in the third.
The column on the left of the grid is ONLY for recording a negative sign, as in Example C. If your answer is positive, leave the first column blank and begin recording your answer in the second column.
When your answer includes a decimal, make sure to fill in the circles that match all parts of your answer. For example, if your answer is 0.78, fill in the circles under the 0, ".", 7, and 8 Note that an answer displaying .78 will also be accepted as correct.
Do not leave a box blank in the middle of an answer. If there is a blank in the middle of your answer, it will be scored as incorrect. For example, if your answer is 308 Bubble in 3 in the first column, 0 in the second column, and 8 in the third column. If you skip a column when bubbling, it will be marked incorrect.
Do not fill in a circle under an unused box. For example, if your answer is 308, you must leave the last column empty. If you fill in a 0 in the last column, your answer will be scored as 3,080 even though the intended response is 308.
Important Notes about Grid-Ins
- For your answer to be scored, the circles in the grid must be filled in.
- If you write an answer in the boxes but do not fill in the circles in the grid, your answer will be scored as incorrect.
- If your answer written in the boxes does not match how you have filled in the circles, your score will be based on how you have filled in the circles, like in Example H.
- If there is more than one circle filled in for a column, you answer will be scored as incorrect.
- A complete numerical response that is correct will be scored as correct, even if you accidentally begin recording in the wrong column.
- If you accidentally add a decimal point (with no additional values or zeros) after a whole number, your answer will be scored as that whole number. For example, if your answer is “5”, an answer that is filled in as “5.” or “5.0” will be considered an answer of “5” in scoring.