SHSAT MathTopics, Formulas & Practice Strategy (2026)
The SHSAT Math section is 57 questions — 47 scored, 10 unscored experimental — and no calculator is allowed. Here's everything you need to know to prepare effectively.
Total questions
57
Scored questions
47
Calculator
Not allowed
Approx. time
~90 min
SHSAT Math topics breakdown
Number Sense & Operations
What's covered
- Fractions, decimals, and mixed numbers
- Percents (percent of, percent change, percent of a percent)
- Ratios and proportions
- Absolute value
- Order of operations (PEMDAS)
- Factors, multiples, and prime factorization
- Exponents and square roots
Strategy note
Percent change and ratio problems are the most commonly tested. Practice writing them as equations rather than relying on mental shortcuts.
Algebra & Functions
What's covered
- Evaluating and simplifying expressions
- Solving linear equations and inequalities
- Systems of two equations
- Translating word problems into equations
- Linear functions and slope
- Sequences (arithmetic and geometric)
- Substitution and backsolving
Strategy note
This is the single largest Math category. Start here. Translating word problems into equations is the most important skill — practice it daily.
Geometry & Measurement
What's covered
- Angle relationships (supplementary, vertical, parallel lines)
- Triangle properties (similar, congruent, Pythagorean theorem)
- Circles (circumference, area, arc length, sector area)
- Quadrilaterals (area, perimeter)
- Volume and surface area of 3D figures
- Coordinate geometry (distance, midpoint, slope)
Strategy note
Circle problems (arc length and sector area) are disproportionately hard and appear often. Know how to set up a proportion using the central angle.
Statistics & Probability
What's covered
- Mean, median, mode, and range
- Weighted averages
- Effect of adding/removing values on mean
- Basic probability (single and compound events)
- Reading charts, tables, and graphs
Strategy note
Weighted average problems and 'what happens to the mean if...' questions appear every year. These are fast to master with targeted practice.
What to study first
Not all topics are worth equal time. This is the order that moves the score the most for most students:
| # | Topic |
|---|---|
| 1 | Percents, ratios & proportions |
| 2 | Algebra: linear equations & word problems |
| 3 | Geometry: circles & triangles |
| 4 | Statistics: weighted averages |
| 5 | Systems of equations & sequences |
SHSAT Math formulas reference
No formula sheet is provided on the SHSAT. These need to be memorized.
Algebra
- →Distance = Rate × Time
- →Percent change = (New − Old) / Old × 100
- →Slope = (y₂ − y₁) / (x₂ − x₁)
- →y = mx + b (slope-intercept form)
Geometry
- →Area of circle = πr²
- →Circumference = 2πr
- →Arc length = (central angle / 360) × 2πr
- →Area of triangle = ½ × base × height
- →Pythagorean theorem: a² + b² = c²
- →Volume of rectangular prism = l × w × h
- →Volume of cylinder = πr²h
Number Sense
- →Percent of a number: multiply by decimal (30% of 80 = 0.30 × 80)
- →Ratio a:b means a/(a+b) and b/(a+b) of the total
- →|x| = x if x ≥ 0, −x if x < 0
Statistics
- →Mean = sum of values / number of values
- →Weighted mean = Σ(value × weight) / Σ(weights)
- →Probability = favorable outcomes / total outcomes
No calculator is permitted. Practice computing all of these by hand under timed conditions.
No-calculator strategy
Most 8th graders rely heavily on calculators for schoolwork. The SHSAT does not allow them. This requires specific preparation.
Rebuild mental math fluency
Practice multiplication tables, fraction arithmetic, and percent conversions by hand every day. Even 10 minutes of daily mental math drills over 4 weeks makes a measurable difference on test day.
Use estimation aggressively
On multiple-choice Math questions, you often don't need an exact answer — you need to eliminate 3 wrong choices. Rounding and estimating to eliminate options saves time without sacrificing accuracy.
Practice the 'two-pass' method
On the first pass through Math, answer everything you know immediately. Skip hard questions and mark them. On the second pass, work the hard ones with your remaining time. Never leave a question blank.
Time yourself during practice
Without a calculator, arithmetic takes longer than you expect. Practice Math sets under timed conditions so the no-calculator constraint becomes normal before test day.
SHSAT Math FAQs
What math level is the SHSAT?
The SHSAT tests pre-algebra and algebra concepts covered in 7th and early 8th grade. There is no trigonometry, calculus, or advanced geometry. However, the questions are structured differently than school tests — multi-step word problems and unfamiliar presentations of familiar concepts are common.
Are calculators allowed on the SHSAT?
No. Calculators are not permitted. All arithmetic must be done by hand. Students who are calculator-dependent in school need specific practice rebuilding mental math and written computation skills before the test.
How many math questions are on the SHSAT?
57 Math questions total. Of those, 10 are unscored experimental questions that look identical to the others — you cannot tell which ones they are. Only 47 are scored. There is no penalty for wrong answers, so answer every question.
What is the hardest math topic on the SHSAT?
Multi-step algebra word problems are the most commonly missed. Circle geometry (arc length, sector area) is also difficult for most students. Both are highly trainable with focused practice — they respond well to repetition.
How much time do I have per math question?
The SHSAT has no mandated time split between ELA and Math — you allocate the 3-hour total however you choose. A common approach is to spend roughly 90 minutes on Math, which works out to about 95 seconds per question. Algebra and word problems typically take longer; number sense questions faster.
See exactly which Math topics are costing points
The free practice test gives you a breakdown across every Math topic — so you know whether to focus on algebra, geometry, or number sense first.