SHSAT Math Section: Ultimate Strategy 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.

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 \(\frac{3p}{q} - \frac{p}{4q} = \frac{\bigtriangleup}{4q}\) and \(q \neq 0\), what expression is represented by \(\bigtriangleup\)?

  1. A. \(2p\)
  2. B. \(11p\)
  3. C. \(4p\)
  4. D. \(12p\)

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 \(\frac{1}{3}\) of his day at work and \(\frac{1}{6}\) of his day commuting to and from work. How much of his day does he spend on work and commuting combined?

  1. A. \(\frac{1}{2}\)
  2. B. \(\frac{1}{6}\)
  3. C. \(\frac{1}{2} + \frac{1}{6}\)
  4. D. \(\frac{1}{2} \times \frac{1}{6}\)

Geometry

What it tests: Area, perimeter, volume formulas, angle relationships, and coordinate basics.

Core fundamentals: Memorize key formulas (e.g., \(A_{\triangle}=\tfrac12 bh\), \(C=2\pi r\)) and angle pair properties.

Tip: Draw precise diagrams and label all given measures.

Sample Question:

0 4 8 12 16 x y

What is the area, in square units, of the shaded region shown above?

  1. A. 96
  2. B. 84
  3. C. 108
  4. D. 72

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 \(a\), \(b\), and \(c\) are consecutive integers such that \(a < b < c\), and if the product of these integers is \(-60\), what is the value of \(b\)?

  1. A. -5
  2. B. -3
  3. C. 3
  4. D. -4

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?

  1. A. 96
  2. B. 100
  3. C. 120
  4. D. 144

Probability

What it tests: Simple versus compound events, independent vs dependent, and the complement rule.

Core fundamentals: \(P(A)=\tfrac{favorable}{total}\); 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?

  1. A. \(\frac{1}{6}\)
  2. B. \(\frac{1}{3}\)
  3. C. \(\frac{1}{2}\)
  4. D. \(\frac{2}{3}\)

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?

  1. A. 4
  2. B. 5
  3. C. 6
  4. D. 9

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:

DAILY TEMPERATURES 30 40 50 60 70

Based on the box plot, what percentage of the daily temperatures were below 50°F?

  1. A. 25%
  2. B. 50%
  3. C. 75%
  4. D. 100%

Exam-Day Strategies

  1. Mark & Skip: Flag tough items and return if time allows.
  2. Eliminate First: Cross out impossible choices before solving.
  3. Neat Grid-Ins: Fill digits clearly and right-aligned.
  4. Time Check: Aim for ~1.5 min per question; don't get stuck.

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