SHSAT Math Ultimate Guide: A breakdown of the most common math questions tested on the SHSAT Math section.
SHSAT Math: Ultimate Guide — Quick Snapshot
Eight domains, Algebra, Arithmetic, Geometry, Number Properties, Percent, Probability, Ratios & Proportions, Statistics, delivered as multiple-choice and grid-in questions. Apply formula mastery and test-day tactics to maximize speed and accuracy on SHSAT Math practice.
SHSAT Mathematics Directions
IMPORTANT NOTES
- Formulas and definitions of mathematical terms and symbols are not provided.
- Diagrams other than graphs are not necessarily drawn to scale. Do not assume any relationship in a diagram unless it is specifically stated or can be determined from the information given.
- Assume that a diagram is in one plane unless the question specifically states that it is not.
- Graphs are drawn to scale. Unless stated otherwise, you can assume relationships according to appearance. For example, lines on a graph that appear to be parallel can be assumed to be parallel. This is also true for concurrent lines, straight lines, collinear points, right angles, etc.
DIRECTIONS: Solve each problem. Select the answer from the choices given or enter your answer in the space provided. When you are solving problems, you can use the online notepad tool or write on the scrap paper given to you.
SHSAT Math Section: Algebra
What it tests: Solving linear equations and manipulating expressions.
Core fundamentals: Combine like terms, distribute accurately, and maintain equation balance.
Tip: Back-solve answer choices to trap errors quickly.
Sample Question:
If 3pq−p4q=△4q\frac{3p}{q} - \frac{p}{4q} = \frac{\bigtriangleup}{4q} and q≠0q \neq 0, what expression is represented by △?
A. 2p2p
B. 11p11p
C. 4p4p
D. 12p12p
Correct Answer: B
SHSAT Math Section: Arithmetic
What it tests: Order of operations (PEMDAS), mental math, and fraction operations.
Core fundamentals: Simplify early, convert mixed numbers, and estimate to check plausibility.
Tip: Eliminate impossible grid-in lengths before filling digits.
Sample Question:
Alex spends 13\frac{1}{3} of his day at work and 16\frac{1}{6} of his day commuting to and from work. How much of his day does he spend on work and commuting combined?
A. 12\frac{1}{2}
B. 16\frac{1}{6}
C. 12+16\frac{1}{2} + \frac{1}{6}
D. 12×16\frac{1}{2} \times \frac{1}{6}
Correct Answer: A
SHSAT Math Section: Geometry
What it tests: Area, perimeter, volume formulas, angle relationships, and coordinate basics.
Core fundamentals: Memorize key formulas (e.g., A△=12bh, C=2πr) and angle pair properties.
Tip: Draw precise diagrams and label all given measures.
Sample Question:
What is the area, in square units, of the shaded region shown above?
A. 96
B. 84
C. 108
D. 72
Correct Answer: B
SHSAT Math Section: Number Properties
What it tests: Divisibility rules, prime/composite classification, and factors & multiples.
Core fundamentals: Use prime factorization for GCF/LCM, digit-sum tests, and parity checks.
Tip: Parity checks eliminate half the options instantly.
Sample Question:
If aa, bb, and cc are consecutive integers such that a<b<ca < b < c, and if the product of these integers is −60-60, what is the value of bb?
A. -5
B. -3
C. 3
D. -4
Correct Answer: D
SHSAT Math Section: Percent
What it tests: Percent-of calculations, percent change, and conversions among fractions, decimals, and percents.
Core fundamentals: Part = Percent × Whole; know benchmark percents (10%, 25%, 50%).
Tip: Convert a percent to decimal before multiplying.
Sample Question:
A store is having a sale with a 20% discount on all items. If an item originally costs $120, what is the sale price after the discount?
A. 96
B. 100
C. 120
D. 144
Correct Answer: A
SHSAT Math Section: Probability
What it tests: Simple versus compound events, independent vs dependent, and the complement rule.
Core fundamentals: P(A)=favorabletotal; multiply probabilities for independent events; use 1−P for “at least one” scenarios.
Tip: Sketch a quick tree diagram for compound questions.
Sample Question:
A standard six-sided die is rolled once. What is the probability that the result is a prime number?
A. 16\frac{1}{6}
B. 13\frac{1}{3}
C. 12\frac{1}{2}
D. 23\frac{2}{3}
Correct Answer: C
SHSAT Math Section: Ratios & Proportions
What it tests: Equivalent ratios, unit rates, and variation.
Core fundamentals: Cross-multiply to solve proportions, then reduce.
Tip: Convert to a unit rate (per one) for speed.
Sample Question:
A recipe requires 3 cups of flour for every 2 cups of sugar. If a baker wants to use 9 cups of flour, how many cups of sugar will be needed to maintain the same ratio?
A. 4
B. 5
C. 6
D. 9
Correct Answer: C
SHSAT Math Section: Statistics
What it tests: Mean, median, mode, range, and interpreting small data sets.
Core fundamentals: Mean = sum/count; median = middle value; mode = most frequent.
Tip: Quickly sort small lists to find the median.
Sample Question:
Based on the box plot, what percentage of the daily temperatures were below 50°F?
A. 25%
B. 50%
C. 75%
D. 100%
Correct Answer: B
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