Quick answer: Yes, you should memorize a core set of GRE math formulas. You do not need to memorize every obscure identity, but you should reliably know high-yield formulas from arithmetic, algebra, geometry, basic statistics, and combinatorics. More important than rote memorization is being able to recognize when to apply a formula and to derive simple variants quickly during the test.
Why this matters for your GRE Quantitative score
Quantitative Reasoning questions test your problem solving, numerical reasoning, and ability to choose efficient methods under time pressure. The test does not give you a comprehensive formula cheat sheet while you work, so not knowing standard formulas slows you down. Time lost trying to re-derive or look up a formula is time you cannot recover during a section. In contrast, knowing the most frequently used formulas will let you focus on strategy, estimation, and question setup rather than low-level recall.
What the GRE provides and what it does not
Important: assume you will not be given a formula sheet during the test. The computer-delivered GRE includes an on-screen basic calculator. Do not rely on a supplied list of formulas. ETS publishes a GRE Math Review and practice materials you can use while studying, but those resources are not available on test day.
What that means for study
- Memorize high-frequency formulas so you can use them without hesitation.
- Practice deriving a few formulas quickly from first principles so you can reconstruct them when needed.
- Practice under timed conditions with only the tools you’ll have on test day: scratch paper and the on-screen calculator.
High-yield formulas to memorize
The list below targets formulas that appear often or simplify common problem types. Learn these thoroughly and be able to apply them without pausing.
| Category | Formulas to memorize | Why it matters |
|---|---|---|
| Arithmetic & algebra |
– Percent change: new = original × (1 + r) or percent change = (new – original)/original. – Ratio and proportion basics. – Properties of exponents: a^m × a^n = a^(m+n), (a^m)^n = a^(mn), a^0 = 1. – Simple polynomial factor patterns: (a – b)(a + b) = a^2 – b^2. |
Used in many word problems, percent and ratio questions. |
| Quadratics |
– Quadratic formula: x = (-b ± sqrt(b^2 – 4ac)) / (2a). – Vertex form and axis: vertex at (-b/(2a), f(vertex)). |
Solves many algebra problems and equation-based quant questions. |
| Geometry |
– Area: triangle = (1/2) × base × height; rectangle = base × height; parallelogram = base × height. – Circle: circumference = 2πr; area = πr^2. – Pythagorean theorem: a^2 + b^2 = c^2. – Volume: rectangular solid = l × w × h; cylinder = πr^2h; cone = (1/3)πr^2h; sphere = (4/3)πr^3. |
Geometry and coordinate geometry problems rely on these. |
| Coordinate geometry |
– Slope = (y2 – y1)/(x2 – x1). – Midpoint = ((x1 + x2)/2, (y1 + y2)/2). – Distance = sqrt((x2 – x1)^2 + (y2 – y1)^2). |
Used on line, distance, and geometry questions. |
| Probability and counting |
– Permutations: nPr = n!/(n – r)!. – Combinations: nCr = n!/(r!(n – r)!). – Probability of independent events: P(A and B) = P(A) × P(B). – Complement rule: P(not A) = 1 – P(A). |
Key for probability and counting problems. |
| Statistics |
– Mean = (sum of values)/n. – Median and mode definitions. – Basic idea of standard deviation; formulas for standard deviation are rarely needed in full form. |
Data interpretation questions require these concepts. |
Which formulas you must memorize, which to understand, and which are optional
Memorization without understanding is less effective than selective memorization plus conceptual fluency. Use the table below to prioritize.
| Priority | Examples | Study focus |
|---|---|---|
| Must memorize | Percent change, area formulas, Pythagorean theorem, quadratic formula, slope, distance, combinations/permutations | Recall quickly and apply without re-deriving. |
| Understand and practice | Exponents/log laws, circle formulas, volume formulas, basic probability rules | Be able to reconstruct or adapt in unusual forms. |
| Optional | Long algebraic identities, full standard deviation formula, advanced trig identities | Useful if you have extra study time or targeting very high quant scores. |
Common challenges students face
- Trying to memorize everything. That wastes short-term memory capacity and increases stress. Focus on a compact, high-yield list.
- Memorizing without practicing applications. Students who only memorize often freeze when a formula appears in a disguised form.
- Forgetting small constants or factors. For example, mixing up area formulas or forgetting the 1/2 in triangle area causes simple arithmetic errors.
- Relying on calculators to “do the math.” Calculators do arithmetic but do not tell you which formula to use or how to set up the problem.
- Time management. Even if you recall a formula, slow setup and calculation cost you points on other questions.
Step-by-step strategy to memorize and use formulas effectively
- Create a compact formula sheet for study only. Write 10 to 20 core formulas on one 8.5 by 11 sheet. Limit the sheet to items you will not reliably reconstruct under pressure.
- Understand derivations for 3 to 5 key formulas. For example, derive the area of a triangle from rectangle area or derive distance formula from Pythagorean theorem. Derivation boosts retention and lets you reconstruct variants.
- Use spaced repetition flashcards. Put a formula prompt on one side and a simple application on the other. Review daily at first, then space to every few days and weekly.
- Practice targeted problem sets. For each formula, do 10 to 20 practice questions that require applying it in different contexts. Mix in questions that disguise the need for the formula so you learn to recognize patterns.
- Time yourself on practice sets. Simulate section timing and include scratch paper only. Build the habit of immediate formula recall under timed pressure.
- Log errors and confusion points. When you make a mistake, note whether it was recall, algebraic manipulation, or arithmetic. Review the underlying formula and do a small correction drill.
- Practice quick derivation techniques. Train to reconstruct formulas in 30 to 60 seconds when possible. For example, derive area of a trapezoid from average of bases times height.
- Do full-length practice tests. The combination of endurance and recall under fatigue is essential.
Common mistakes to avoid
- Relying on rote memorization only. Without practice, you may not recognize when a formula applies.
- Overloading your memory. Trying to memorize dozens of rarely used formulas reduces retention of the high-yield items.
- Ignoring units and constraints. Not checking units or domain restrictions can produce nonsense answers.
- Misapplying formulas in rounded form. Using 3.14 for π prematurely can change multiple choice options; use exact form until final numeric comparison or when the problem specifically uses 3.14.
- Failing to estimate. Not using estimation to check if a computed answer is reasonable often allows calculation errors to pass undetected.
Practice and implementation: worked examples
Example 1. Geometry and area recognition
Question: A circular garden has diameter 10 meters. A rectangular path 2 meters wide surrounds the garden. What is the area of the path?
Solution steps:
- Compute radius of garden: r = 10/2 = 5 m. Area of garden = πr^2 = π × 25 = 25π m^2.
- Outer radius including path: r_outer = 5 + 2 = 7 m. Area of outer circle = π × 7^2 = 49π m^2.
- Area of path = outer area – garden area = 49π – 25π = 24π m^2.
- If numeric approximation is needed, 24π ≈ 24 × 3.14159 ≈ 75.398. But retain exact form when possible.
Key formula use: area of a circle and subtracting areas. Memorize circle area; practice subtraction of shapes.
Example 2. Quadratic formula in an algebra question
Question: Solve x^2 – 6x + 5 = 0.
Solution steps:
- Recognize a quadratic. Either factor quickly: (x – 1)(x – 5) = 0, so x = 1 or 5. If factoring was not obvious, use quadratic formula x = [6 ± sqrt(36 – 20)]/2 = [6 ± sqrt(16)]/2 = [6 ± 4]/2 leading to same results.
Key point: memorize quadratic formula but also practice factoring so you can choose fastest method in test conditions.
Example 3. Counting and combinations
Question: From 6 books, how many ways to choose 3 to take on a trip?
Solution steps:
- This is a combination problem: nCr = 6C3 = 6!/(3!3!) = (6 × 5 × 4)/(3 × 2 × 1) = 20.
Key point: memorize combinations formula and practice quick factorial simplification.
Four-week focused formula study plan (example)
This plan assumes you study 5 to 7 hours per week. Adjust intensity if you have more or less time.
- Week 1: Core arithmetic and algebra
- Memorize percent, ratio, exponent rules, factor patterns.
- Do 30 practice problems combining percent, ratio, and exponent manipulation.
- Daily flashcard review for 15 minutes.
- Week 2: Geometry and coordinate geometry
- Memorize area, circumference, Pythagorean theorem, slope, distance.
- Do targeted geometry sets (triangles, circles, coordinate questions).
- Practice quick diagram-sketching and labeling on scratch paper.
- Week 3: Probability, counting, and statistics
- Memorize nCr/nPr and basic probability rules; review mean/median definitions.
- Do 30 counting and probability problems, with varying contexts.
- Flashcards and error log review.
- Week 4: Integration and timed practice
- Take two timed quantitative sections. Review every mistake to identify formula recall gaps.
- Focus drills on any weak formulas and derivation practice.
- Do a final sweep of the compact formula sheet and test yourself by writing formulas from memory.
Frequently asked questions
Do I need to memorize the quadratic formula?
Yes. The quadratic formula is a high-value formula that appears in algebra problems. Memorize it and practice both factoring and using the formula so you can pick the fastest route.
Will ETS give me a formula sheet on test day?
No. Do not expect a comprehensive formula sheet during the test. ETS provides practice materials and guides during study, but on test day you should be prepared to recall the formulas you need.
Should I memorize standard deviation and variance formulas?
Understand the concept of standard deviation and mean. Full formulas for population or sample standard deviation are rarely required in raw algebraic form. If you are weak on statistics questions, focus on concept and practice problems rather than memorizing a long formula.
Is it enough to memorize formulas, or should I learn derivations too?
Both. Memorize the highest priority formulas so recall is immediate. Learn derivations for a few key formulas. Derivations let you reconstruct variants and deepen understanding, which is particularly helpful if a question disguises the formula requirement.
How do I remember formulas under time pressure?
Use spaced repetition, write formulas daily on a single sheet from memory, and practice timed sets so recall becomes automatic. Building a small habit of writing the formulas before each practice section can speed retrieval during an actual test.
Final thoughts
Memorizing a targeted set of GRE formulas is a high-return use of study time. Prioritize a compact list of arithmetic, algebra, geometry, coordinate geometry, counting, and basic statistics formulas. Pair memorization with practice problems, derivations for a few core formulas, and timed drills so recall and application become automatic. Track errors to find weak spots, and simulate test conditions often. With focused, practiced recall you will reduce time wasted on low-level recall and increase time available for strategy and careful checking.
