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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:
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.
Memorize mathematical terms, symbols, and formulas that you use in your Math class
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.
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:
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:
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?
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:
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:
Step 2: Convert dalts to dollars
Set up the equation as follows:
Step 3: Add your conversions of lorgs and dalts together: 20+32 = $52.
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.
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
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
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
Most multiple-choice questions should be done by working out the answer.
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.
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.
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