The SSAT does not give you a formula sheet on test day, and calculators are banned across all levels. That means every SSAT math formula you need lives in your head or it does not exist for you during those 30-minute Quantitative sections. This cheat sheet is the complete reference: geometry, algebra, statistics, percent, and conversion formulas, organized by category so you can drill them efficiently in the weeks before your test.
The SSAT is structurally different from the SAT in one critical way: it provides no math reference sheet. Every formula a student needs — from the area of a circle to the quadratic formula on the Upper Level — must already be in the student's head before the test begins. That is why building an SSAT math cheat sheet during prep is not optional; it is the spine of any effective study plan.
The Middle and Upper Level SSAT contains 50 multiple-choice math questions split across two Quantitative sections of 25 questions each, with 30 minutes per section. Calculators are banned at every level: Elementary, Middle, and Upper. The test is intentionally designed so that armed only with paper, pencil, and memorized formulas, a strong student can finish on time.
Quantitative 1 appears near the beginning of the test after the writing sample, while Quantitative 2 comes after the Verbal section. Both sections sample the same content domains, mixing geometry, algebra, percentages, and statistics into single multiple-choice items. A wrong answer costs one-quarter of a point on the Middle and Upper Levels, while skipped questions are neither penalized nor rewarded.
The Middle Level (grades 5–7) emphasizes basic geometry, arithmetic operations, fractions, decimals, percent, and simple algebra. The Upper Level (grades 8–11) keeps everything from the Middle Level and adds the quadratic formula, advanced exponent rules, and special right-triangle ratios (30-60-90 and 45-45-90). Knowing your level prevents you from over-studying or under-studying.
Geometry is the largest single source of formula-dependent points on the SSAT, and almost every geometry question rewards quick formula recall. Because the test provides no formula sheet, you must enter test day already fluent in every 2D shape and 3D solid below — there is no time to derive area or volume formulas under the 30-minute clock. The SSAT geometry formulas listed here cover the full set you are likely to see.
| Shape | Area / Volume | Perimeter / Surface | When to Use |
|---|---|---|---|
| Circle | A = πr² | C = 2πr | Any circular figure or arc problem |
| Rectangle | A = lw | P = 2l + 2w | Standard rectangle word problems |
| Triangle | A = ½bh | P = a + b + c | All triangle area questions |
| Parallelogram | A = bh | P = 2a + 2b | Slanted-side quadrilaterals |
| Trapezoid | A = ½h(b₁ + b₂) | Sum of all 4 sides | Two parallel sides of different lengths |
| Rectangular Prism | V = lwh | SA = 2(lw + lh + wh) | Boxes, rooms, swimming pools |
| Cylinder | V = πr²h | SA = 2πr(r + h) | Cans, tubes, tanks |
| Sphere | V = (4/3)πr³ | SA = 4πr² | Balls, planets, spherical tanks |
| Cone | V = (1/3)πr²h | SA = πr(r + s) | Funnels, ice cream cones |
For circles, remember that area uses r² and circumference uses just r — confusing the two is the single most common SSAT geometry mistake. For triangles, the ½ in A = ½bh is non-negotiable. For trapezoids, the formula averages the two parallel bases (b₁ and b₂) and multiplies by the height between them.
Volume formulas for the rectangular prism (V = lwh) and the cylinder (V = πr²h) cover the bulk of SSAT 3D questions. Sphere and cone formulas appear less often but show up more frequently on the Upper Level. Memorize the surface area formulas as a separate group — they are not derivable from the volume formulas.
The sum of the interior angles of any n-sided polygon equals (n − 2) × 180°. A triangle has 180°, a quadrilateral has 360°, a pentagon has 540°, and so on. When a polygon problem feels stuck, write out (n − 2) × 180° in the margin and the rest usually unlocks.
Worked Example
Setup: A cylindrical water tank has a radius of 4 feet and a height of 10 feet. What is its volume in cubic feet? (Use π ≈ 3.14)
The Pythagorean theorem appears in nearly every SSAT math section, often disguised inside word problems involving distance, ladders, or shadows. Knowing the formula is half the battle — the other half is recognizing common Pythagorean triples so you can skip the calculation entirely.
The formula a² + b² = c² applies only to right triangles, where c is always the hypotenuse (the longest side, opposite the right angle). Misapplying it to non-right triangles is one of the most common SSAT mistakes. If a problem does not specify or imply a right angle, the Pythagorean theorem does not work.
The four triples below appear repeatedly on the SSAT. When you see two sides that match one of these patterns (or a multiple of it), the third side is instant — no calculation needed. This is one of the highest-value memorizations on the entire test.
| Triple / Ratio | Pattern | Recognition Tip |
|---|---|---|
| 3-4-5 | 3² + 4² = 5² | Watch for any multiples like 6-8-10 or 9-12-15 |
| 5-12-13 | 5² + 12² = 13² | Common in word problems with longer sides |
| 8-15-17 | 8² + 15² = 17² | Less common but appears on Upper Level |
| 7-24-25 | 7² + 24² = 25² | Hardest to spot — drill it during prep |
| 45-45-90 | 1 : 1 : √2 | Isosceles right triangle (square's diagonal) |
| 30-60-90 | 1 : √3 : 2 | Half of an equilateral triangle |
The two special right triangles appear primarily on the Upper Level SSAT. In a 45-45-90 triangle, the legs are equal and the hypotenuse is leg × √2. In a 30-60-90 triangle, the side opposite 30° is the shortest, the side opposite 60° is that short side × √3, and the hypotenuse is twice the short side. These ratios let you solve without the Pythagorean calculation.
Worked Example
Setup: A right triangle has legs of 9 and 12. What is the length of the hypotenuse?
Pick a leg pair to see if it matches a common Pythagorean triple — and the hypotenuse you should know.
The Upper Level SSAT tests slope, distance, and midpoint formulas plus quadratic formula recall. Without a calculator, fluency with these SSAT algebra formulas separates high scorers from average students. The table below distinguishes which formulas show up at each test level so you do not waste study time.
| Formula Name | Equation | Required Inputs | Test Level |
|---|---|---|---|
| Slope | m = (y₂ − y₁)/(x₂ − x₁) | Two points on a line | Middle and Upper |
| Distance | d = √((x₂ − x₁)² + (y₂ − y₁)²) | Two coordinate points | Middle and Upper |
| Midpoint | M = ((x₁ + x₂)/2, (y₁ + y₂)/2) | Two coordinate points | Middle and Upper |
| Slope-Intercept | y = mx + b | Slope and y-intercept | Middle and Upper |
| Point-Slope | y − y₁ = m(x − x₁) | Slope and one point | Upper |
| Quadratic Formula | x = (−b ± √(b² − 4ac))/2a | Coefficients a, b, c | Upper only |
| Simple Interest | I = prt | Principal, rate, time | Middle and Upper |
| Percent Change | (New − Old)/Old × 100 | Original and new values | Middle and Upper |
| Average Speed | Total distance ÷ total time | Distances and times | Middle and Upper |
Slope is rise over run — change in y divided by change in x. The numerator and denominator order matters: subtract y-values first, then x-values. The distance formula derives directly from the Pythagorean theorem; in fact, if you forget it, you can rebuild it by treating the horizontal and vertical gaps between points as legs of a right triangle.
The slope-intercept form y = mx + b is the workhorse for graphing lines and identifying their equations. The point-slope form y − y₁ = m(x − x₁) is most useful when you know one point and the slope but not the y-intercept. Upper Level test-takers should be fluent in both.
The quadratic formula x = (−b ± √(b² − 4ac))/2a solves any quadratic equation written as ax² + bx + c = 0. On the SSAT Upper Level, factoring will solve most quadratic problems faster, but the formula is your safety net when factoring fails. Middle Level students do not need this formula.
Worked Example
Setup: Find the slope of the line that passes through the points (2, 5) and (8, 17).
Percent and rate problems are some of the most heavily tested categories on the SSAT. They blend arithmetic with word-problem reasoning, and a small mistake in formula application can flip your answer. Memorize the four formulas in this section cold.
Percent change is calculated as (New − Old) divided by Old, then multiplied by 100. Always divide by the original value, not the new value — this is the single most common percent-change mistake. To find a percent of a number, convert the percent to a decimal (15% becomes 0.15) and multiply.
The d = rt formula is the foundation of every motion word problem on the SSAT. Average speed equals total distance divided by total time — never the average of two speeds, even when the problem feels like it should be that simple. When two trips happen at different speeds, sum the distances and divide by the sum of the times.
Simple interest follows I = prt, where p is the principal, r is the rate as a decimal, and t is the time in years. Unlike compound interest (which is rare on the SSAT), simple interest does not accumulate on previous interest — only on the original principal.
Worked Example
Setup: A jacket originally cost $80 and is now on sale for $60. What is the percent decrease?
Statistics and probability questions are easy points if the four key formulas are committed to memory. Exponent rules show up in algebra and arithmetic combined — knowing them prevents you from converting expressions by hand under time pressure. These are SSAT formulas to memorize early in your prep cycle.
| Concept | Formula | Quick Example |
|---|---|---|
| Mean | Sum ÷ count | Mean of 4, 6, 10 is 20/3 ≈ 6.67 |
| Median | Middle value when sorted | Median of 3, 5, 9 is 5 |
| Mode | Most frequent value | Mode of 2, 5, 5, 8 is 5 |
| Range | Largest − smallest | Range of 4, 9, 12 is 8 |
| Probability | Desired ÷ total outcomes | P(red) on 3R/2B die = 3/5 |
| Independent events | P(A and B) = P(A) × P(B) | P(heads twice) = ½ × ½ = ¼ |
| Product Rule | x^a · x^b = x^(a+b) | 2³ · 2² = 2⁵ = 32 |
| Quotient Rule | x^a ÷ x^b = x^(a−b) | 5⁵ ÷ 5² = 5³ = 125 |
| Power Rule | (x^a)^b = x^(ab) | (3²)³ = 3⁶ = 729 |
| Zero Exponent | x⁰ = 1 | 100⁰ = 1 |
| Negative Exponent | x^(−a) = 1/x^a | 2^(−3) = 1/8 |
Mean is the arithmetic average — sum of values divided by count. Median is the middle value when the data set is sorted from smallest to largest; for an even-numbered set, take the mean of the two middle values. Mode is whichever value appears most often, and range is the largest minus the smallest. Confusing mean with median is a high-frequency error.
The probability of a single event is the count of desired outcomes divided by the count of total possible outcomes. For two independent events occurring together (like rolling a die and flipping a coin), multiply the individual probabilities: P(A and B) = P(A) × P(B).
The five exponent rules — product, quotient, power, zero, and negative — together solve almost every exponent problem on the SSAT. The product rule adds exponents when multiplying like bases. The quotient rule subtracts. The power rule multiplies. Any nonzero base raised to the zero power equals 1. Negative exponents flip the base into the denominator.
Worked Example
Setup: What is the probability of rolling a 3 on a fair six-sided die and then flipping heads on a fair coin?
Unit-conversion errors are among the top sources of careless SSAT mistakes. Word problems frequently change units mid-question — feet to yards, square inches to square feet, ounces to pounds — and getting that conversion wrong wipes out an otherwise correct calculation. The same goes for PEMDAS: order-of-operations errors derail multi-step expressions on a regular basis. This SSAT math reference sheet section keeps both topics in one place.
PEMDAS stands for Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. Multiplication and division have equal priority and are performed left to right, as do addition and subtraction. Always work from inside parentheses outward, and resolve exponents before any multiplication.
When linear units convert (12 inches = 1 foot), area conversions square the factor (144 sq in = 1 sq ft), and volume conversions cube it (1,728 cu in = 1 cu ft). This is a frequent stumbling block: a student who knows 12 inches = 1 foot may incorrectly assume 12 sq in = 1 sq ft. Memorize the squared and cubed versions explicitly.
For weight, 16 ounces equal 1 pound. For capacity, 8 ounces equal 1 cup, 4 cups equal 1 quart, and 4 quarts equal 1 gallon. Do not confuse fluid ounces (volume) with weight ounces — the SSAT occasionally tests this distinction in word problems involving recipes or shipping.
| Type | Conversion | Notes |
|---|---|---|
| Length | 12 inches = 1 foot | Foundation of every length problem |
| Length | 3 feet = 1 yard | Useful for backyard or fabric problems |
| Length | 5,280 feet = 1 mile | Common in distance-rate-time questions |
| Area | 144 square inches = 1 square foot | Square the linear conversion (12² = 144) |
| Volume | 1,728 cubic inches = 1 cubic foot | Cube the linear conversion (12³ = 1,728) |
| Weight | 16 ounces = 1 pound | Watch for fluid ounces vs weight ounces |
| Capacity | 8 ounces = 1 cup, 4 cups = 1 quart | Liquid measurements only |
| Capacity | 4 quarts = 1 gallon | Common in mixing and dilution problems |
These three tools let you quickly verify formula application, recognize Pythagorean triples on sight, and track which formulas you have committed to memory. Bookmark this page and revisit them throughout your SSAT prep.
Enter the base and height of any triangle to instantly check your formula application.
Try these five formula-driven questions modeled on real SSAT items. Each one targets a different formula category from the cheat sheet above. Reveal the explanation only after committing to your answer.
The questions below come up most often when students start preparing for the SSAT math sections. Answers are short enough to act as quick references in the final review week.