Top 30 SAT Math Formulas You Must Memorise Before Test Day
- Edu Shaale
- Apr 30
- 27 min read
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Master the top 30 SAT Math formulas you must memorize before test day.
The SAT reference sheet only covers basic geometry, meaning over 70% of the math section — including algebra, quadratics, and data analysis — requires memorization.
This guide breaks down all essential formulas by domain so you can solve faster and score higher.
4 Domains · What's on the Reference Sheet · What You Must Memorise · Desmos Tips · CBSE Guide
Published: April 2026 | Updated: April 2026 | ~14 min read
30 Essential formulas covered in this guide | 0 Algebra formulas on the reference sheet | 12 Geometry formulas on reference sheet | 70% Exam questions from Algebra + Advanced Math |
ALG Algebra — largest exam domain (~35%) | ADV Advanced Math — hardest domain (~35%) | PS&DA Problem-Solving & Data Analysis (~15%) | GEO Geometry & Trigonometry (~15%) |
Table of Contents
Introduction: The Reference Sheet Covers Only Geometry — Everything Else Is Yours to Memorise
Every SAT Math section begins with a reference sheet — a list of formulas you can access anytime during the test. Students who discover this for the first time feel relieved. Then they read it and realise it only covers basic geometry: areas, volumes, Pythagorean theorem, and special right triangles. The vast majority of SAT Math — the 70% of questions from Algebra and Advanced Math — is not on the reference sheet at all.
This means that every linear equation property, every quadratic formula, every exponential growth formula, every percentage calculation — the formulas that appear on more than half of all SAT Math questions — must come from memory. Students who do not memorise these formulas are, in effect, going into the most-tested portion of the SAT unarmed.
This guide covers the 30 most important SAT Math formulas across all four domains. For each formula, you get the formula itself, what it means in plain language, when it appears on the SAT, and how to use Desmos as a backup when the formula is needed but the calculation is complex. By test day, all 30 should be as automatic as the multiplication table.
1. The SAT Math Reference Sheet — What Is and Is Not Provided
The official SAT Math reference sheet is available in Bluebook throughout the entire Math section. Knowing its contents precisely — and its limits — is the first step in knowing what to memorise.
✅ ON THE REFERENCE SHEET | ❌ NOT ON REFERENCE SHEET — MUST MEMORISE |
Area of circle: A = πr² Circumference: C = 2πr Area of rectangle: A = lw Area of triangle: A = ½bh Pythagorean Theorem: a² + b² = c² 30-60-90 triangle ratios: 1 : √3 : 2 45-45-90 triangle ratios: 1 : 1 : √2 Volume of box: V = lwh Volume of cylinder: V = πr²h Volume of sphere: V = (4/3)πr³ Volume of cone: V = (1/3)πr²h Volume of pyramid: V = (1/3)lwh | Slope formula: m = (y₂-y₁)/(x₂-x₁) Slope-intercept: y = mx + b Quadratic formula: x = (-b ± √(b²-4ac))/2a Vertex of parabola: x = -b/2a Distance formula: d = √((x₂-x₁)²+(y₂-y₁)²) Midpoint: ((x₁+x₂)/2, (y₁+y₂)/2) Percent change: (new-old)/old × 100 Exponential growth: y = a(1+r)ᵗ Circle equation: (x-h)² + (y-k)² = r² SOH-CAH-TOA: sin, cos, tan definitions Mean: sum ÷ count Probability: favourable ÷ total |
Critical Truth: Zero algebra formulas are on the reference sheet. Zero trigonometry definitions. Zero percentage formulas. Zero statistical formulas. The reference sheet covers only geometry — the smallest domain at ~15% of the exam. The 70% of questions from Algebra and Advanced Math requires formulas from memory alone.
2. Why Memorisation Is Non-Negotiable
Reason | Why It Matters for Your Score |
No Algebra formulas provided | Slope formula, slope-intercept form, point-slope form, distance, midpoint — none of these are given. They appear on multiple questions in every SAT. |
No quadratic formula provided | The quadratic formula is the most important Advanced Math formula — tested directly and used to justify Desmos-found answers. Not on the sheet. |
No trig definitions | SOH-CAH-TOA is not provided. Every trigonometry question requires it from memory. |
Time cost of looking up vs recalling | Accessing the reference sheet takes 3–5 seconds per use. Over 44 questions, even if you use it only 8 times, that's 40 seconds wasted. Students who have formulas automatic save this time for harder questions. |
Confidence and accuracy | Students who hesitate on formulas make more errors under exam pressure. Automatic recall eliminates the 'what was that formula again?' pause that causes careless mistakes. |
Desmos is not a formula replacement | Desmos graphing calculator helps APPLY formulas (find intersections, graph quadratics) but does not replace knowing what to type. You still need to know the formula structure. |
3. Quick Reference: All 30 Formulas at a Glance
This table is your master study checklist. Use it for daily quick-review drilling. Check off each formula as you achieve automatic recall.
# | Formula Name | Formula | Domain |
ALGEBRA (Formulas 1–8) — NOT on reference sheet — must memorise | |||
1 | Slope | m = (y₂ - y₁) / (x₂ - x₁) | Algebra |
2 | Slope-Intercept Form | y = mx + b | Algebra |
3 | Point-Slope Form | y - y₁ = m(x - x₁) | Algebra |
4 | Standard Form of Line | ax + by = c → slope = -a/b | Algebra |
5 | Midpoint Formula | M = ((x₁+x₂)/2, (y₁+y₂)/2) | Algebra |
6 | Distance Formula | d = √((x₂-x₁)² + (y₂-y₁)²) | Algebra |
7 | Parallel Lines | Same slope: m₁ = m₂ | Algebra |
8 | Perpendicular Lines | Slopes negative reciprocal: m₁ × m₂ = -1 | Algebra |
ADVANCED MATH (Formulas 9–16) — NOT on reference sheet — must memorise | |||
9 | Quadratic Formula | x = (-b ± √(b²-4ac)) / 2a | Advanced Math |
10 | Vertex x-coordinate | x_v = -b / (2a) | Advanced Math |
11 | Vertex Form | f(x) = a(x - h)² + k; vertex: (h, k) | Advanced Math |
12 | Discriminant | D = b² - 4ac; D>0: two roots; D=0: one; D<0: none | Advanced Math |
13 | Factored Form | f(x) = a(x - r)(x - s); roots: r and s | Advanced Math |
14 | Exponential Growth/Decay | y = a·bˣ; b > 1: growth; 0 < b < 1: decay | Advanced Math |
15 | Difference of Squares | a² - b² = (a+b)(a-b) | Advanced Math |
16 | Perfect Square Identities | (a+b)² = a²+2ab+b²; (a-b)² = a²-2ab+b² | Advanced Math |
PROBLEM-SOLVING & DATA ANALYSIS (Formulas 17–22) — NOT on reference sheet — must memorise | |||
17 | Percentage | % = (part / whole) × 100 | PS & Data Analysis |
18 | Percent Change | % change = (new - old) / old × 100 | PS & Data Analysis |
19 | Percent Increase/Decrease | New = old × (1 + r/100) or (1 - r/100) | PS & Data Analysis |
20 | Mean (Average) | Mean = sum of values / count of values | PS & Data Analysis |
21 | Probability | P = favourable outcomes / total outcomes | PS & Data Analysis |
22 | Compound Interest | A = P(1 + r/n)^(nt) | PS & Data Analysis |
GEOMETRY & TRIGONOMETRY (Formulas 23–30) — Geometry ON sheet; Trig must memorise | |||
23 | Circle Equation | (x - h)² + (y - k)² = r²; centre (h, k), radius r | Geometry |
24 | Arc Length | Arc = (θ/360) × 2πr | Geometry |
25 | Sector Area | Sector = (θ/360) × πr² | Geometry |
26 | Sum of Interior Angles | Sum = (n - 2) × 180° where n = sides | Geometry |
27 | SOH-CAH-TOA | sin = opp/hyp; cos = adj/hyp; tan = opp/adj | Geometry — Trig |
28 | Co-function Identity | sin(x) = cos(90° - x); cos(x) = sin(90° - x) | Geometry — Trig |
29 | Equilateral Triangle Area | A = (√3/4)s² where s = side length | Geometry |
30 | Surface Area of Cylinder | SA = 2πr² + 2πrh | Geometry |
4. Domain 1: Algebra — Formulas 1–8
Algebra accounts for approximately 35% of SAT Math — the largest domain. These 8 formulas are the backbone of every linear equation, linear function, and coordinate geometry question. None are on the reference sheet.
#1 Slope Formula
Formula: m = (y₂ - y₁) / (x₂ - x₁)What it means: Slope is the rate of change of a linear function — how much y changes for every 1 unit change in x. A positive slope means the line rises left-to-right; negative means it falls; zero means horizontal; undefined means vertical.
When to use: Use when: given two points on a line and asked for the slope, rate of change, or gradient. Also used when asked to find the equation of a line through two known points.
Desmos tip: Graph both points in Desmos → draw the line → click the line to see the slope. Or type y = m(x-x₁)+y₁ and adjust m until it passes through both points.
#2 Slope-Intercept Form
Formula: y = mx + b
What it means: m = slope (rate of change); b = y-intercept (value when x = 0). Every linear equation can be written in this form. The y-intercept is the 'starting value' in real-world word problems; the slope is the 'rate.'
When to use: Use when: the question gives a linear equation or asks for one; interpreting slope as rate of change or y-intercept as initial value in context problems. Most SAT linear equation questions reduce to identifying m and b.
Desmos tip: `Type y = mx + b in Desmos. Adjust m to change steepness; adjust b to shift the line up/down. Intersection of two lines gives the solution to a system.
#3 Point-Slope Form
Formula: y - y₁ = m(x - x₁)
What it means: Gives the equation of a line passing through point (x₁, y₁) with slope m. Identical to slope-intercept after simplification, but faster when you have a point and a slope rather than the y-intercept.
When to use: Use when: given a point on a line and its slope, and asked to find the equation. Frequently appears in harder SAT linear equation problems.
Desmos tip: `Enter the point in Desmos and type the slope form — verify the line passes through the correct point.
#4 Standard Form of a Line
Formula: ax + by = c → slope = -a/bWhat it means: Standard form hides slope in a/b ratio. When SAT gives an equation like 3x + 4y = 12, the slope is -3/4 and y-intercept is c/b = 3. Parallel lines have the same a:b ratio; perpendicular lines have slopes that are negative reciprocals.
When to use: Use when: a linear equation is given in standard form (not slope-intercept) and you need slope or y-intercept without rearranging.
Desmos tip: Type the standard form equation directly into Desmos — it graphs the line. Click the line or use the expression to find slope and intercepts.
#5 Midpoint Formula
Formula: M = ((x₁+x₂)/2, (y₁+y₂)/2)
What it means: The midpoint of a line segment is found by averaging the x-coordinates and averaging the y-coordinates of the two endpoints. Works in any two points.
When to use: Use when: finding the midpoint of a segment, the centre of a segment, or the coordinates of an unknown endpoint given the midpoint and the other endpoint (reverse: solve for one coordinate).
Desmos tip: Plot both points in Desmos → draw the segment → the midpoint is visually halfway; verify by averaging.
#6 Distance Formula
Formula: d = √((x₂-x₁)² + (y₂-y₁)²)
What it means: The distance between two points in a coordinate plane — derived directly from the Pythagorean theorem. The horizontal and vertical distances between points form the legs; the distance is the hypotenuse.
When to use: Use when: finding the length of a segment between two known points, or the radius of a circle given centre and a point on it.
Desmos tip: Plot both points in Desmos → draw the segment → use a right triangle to visualise the Pythagorean theorem beneath the formula.
#7 Parallel Lines
Formula: m₁ = m₂ (same slope, different y-intercepts)
What it means: Two lines are parallel if and only if they have the same slope. Parallel lines never intersect — a system of parallel linear equations has no solution.
When to use: Use when: asked if two lines are parallel, when asked to write a line parallel to a given line through a new point, or when a system of equations has 'no solution.'
Desmos tip: Enter both equations in Desmos → if lines are parallel they never cross (no intersection point).
#8 Perpendicular Lines
Formula: m₁ × m₂ = -1 (negative reciprocal slopes)
What it means: Two lines are perpendicular if their slopes are negative reciprocals: if one has slope 2/3, the perpendicular slope is -3/2. Perpendicular lines meet at a 90° angle.
When to use: Use when: finding a line perpendicular to a given line through a specific point; identifying whether two lines are perpendicular from their slopes.
Desmos tip: Enter both lines in Desmos → if perpendicular, they form a right angle (visually obvious at the intersection).
5. Domain 2: Advanced Math — Formulas 9–16
Advanced Math is the second-largest domain (~35%) and the hardest on the SAT. These formulas are the most common source of lost points — because students who know Algebra often underestimate the need to memorise the quadratic family of formulas.
#9 The Quadratic Formula
Formula: x = (-b ± √(b² - 4ac)) / 2a
What it means: Finds the exact x-intercepts (roots/zeros) of any quadratic equation ax² + bx + c = 0. The ± gives two solutions, one, or none depending on the discriminant. This is the most important Advanced Math formula on the entire SAT.
When to use: Use when: factoring is difficult or impossible; when asked for the exact roots of a quadratic; when the discriminant question asks about the number of solutions.
Desmos tip: Type the quadratic into Desmos → click where it crosses the x-axis → coordinates shown. But always verify with the formula when asked for exact (non-decimal) answers.
#10 Vertex x-coordinate
Formula: x_vertex = -b / (2a)
What it means: For any quadratic f(x) = ax² + bx + c, the vertex (turning point) is at x = -b/2a. This gives the axis of symmetry and the x-value at which the max/min occurs. Substitute back into f(x) to find the y-coordinate of the vertex.
When to use: Use when: asked for the maximum/minimum value of a quadratic; asked for the axis of symmetry; asked when a quadratic model reaches its peak or minimum.
Desmos tip: Type the quadratic in Desmos → click the vertex (peak or valley) → coordinates shown instantly. No formula needed in Desmos.
#11 Vertex Form of a Quadratic
Formula: f(x) = a(x - h)² + k; vertex at (h, k)
What it means: When a quadratic is in vertex form, the vertex is (h, k) — readable directly. If a > 0, opens upward (minimum at k). If a < 0, opens downward (maximum at k). h is the x-shift; k is the vertical shift.
When to use: Use when: the SAT gives a quadratic in vertex form and asks for vertex, axis of symmetry, max/min value, or the direction the parabola opens.
Desmos tip: Type f(x) = a(x-h)² + k in Desmos with sliders for a, h, k → see how each parameter transforms the parabola in real-time.
#12 Discriminant
Formula: D = b² - 4ac
What it means: The discriminant (the part under the radical in the quadratic formula) tells you how many real solutions exist: D > 0 → two distinct real solutions; D = 0 → exactly one solution (a perfect square); D < 0 → no real solutions (complex roots only).
When to use: Use when: asked how many real solutions a quadratic has; asked for what value of a constant makes the equation have one solution; asked about the nature of roots.
Desmos tip: Graph the quadratic in Desmos → count x-intercepts: two crossings = D > 0; one touch = D = 0; no crossing = D < 0.
#13 Factored Form of a Quadratic
Formula: f(x) = a(x - r)(x - s); roots at x = r and x = s
What it means: When a quadratic is in factored form, the roots (x-intercepts) are r and s. The vertex x-coordinate is the average: (r+s)/2. If the SAT gives a factored form, the roots and vertex are immediately readable.
When to use: Use when: a quadratic is given in factored form and asked for roots, vertex, or y-intercept (set x = 0 to get a·r·s... wait, evaluate f(0) = a(0-r)(0-s) = ars).
Desmos tip: Enter f(x) = a(x-r)(x-s) in Desmos → x-intercepts appear at r and s automatically.
#14 Exponential Growth and Decay
Formula: y = a·bˣ (b > 1: growth; 0 < b < 1: decay)
What it means: a = initial value (y when x = 0); b = growth/decay factor per period. For percentage growth: b = 1 + (rate/100). For percentage decay: b = 1 - (rate/100). Common SAT form: y = a(1+r)ᵗ.
When to use: Use when: a SAT question describes something that grows or shrinks by a constant percentage per period — population, bacteria, investment, radioactive decay.
Desmos tip: Type y = a·bˣ in Desmos → use sliders for a and b → observe growth or decay. Click the y-intercept to verify a.
#15 Difference of Squares
Formula: a² - b² = (a + b)(a - b)
What it means: Any expression that looks like a perfect square minus another perfect square factors into the product of a sum and a difference. Recognising this pattern saves significant time on factoring questions.
When to use: Use when: asked to factor an expression of the form x² - 9 (= (x+3)(x-3)), 25 - y² (= (5+y)(5-y)), or any difference of two perfect square terms.
Desmos tip: Enter both forms in Desmos to verify they produce the same graph — they should overlay perfectly.
#16 Perfect Square Identities
Formula: (a+b)² = a²+2ab+b² and (a-b)² = a²-2ab+b²
What it means: Expanding a perfect square binomial always produces three terms. The middle term is twice the product of the two parts. SAT questions often give the expanded form and ask to identify the original binomial, or vice versa.
When to use: Use when: completing the square; expanding squared binomials; identifying vertex form from standard form; solving SAT questions about polynomial identities.
Desmos tip: Expand both sides in Desmos by defining both expressions as functions and checking they are identical.
6. Domain 3: Problem-Solving and Data Analysis — Formulas 17–22
PS&DA accounts for approximately 15% of SAT Math — more applied, less formula-heavy. But the formulas that do appear are specific and non-negotiable. None are on the reference sheet.
#17 Percentage Formula
Formula: % = (part / whole) × 100
What it means: The fundamental percentage relationship. To find the part: Part = (% / 100) × whole. To find the whole: Whole = Part / (% / 100). To find the percent: (Part/Whole) × 100.
When to use: Use when: any SAT question involving a percentage — 'what percent of 80 is 20?' (answer: 25%), 'what is 35% of 140?', or 'if 45 is 60% of a number, what is the number?'
Desmos tip: Calculate directly; Desmos not needed for basic percentage arithmetic.
#18 Percent Change Formula
Formula: % change = (new - old) / old × 100
What it means: Measures relative change from an original value. Positive result = increase; negative = decrease. Common SAT trap: students use the new value in the denominator instead of the original.
When to use: Use when: asked for the percentage increase or decrease between two values; asked how much something grew or shrank relative to its starting point.
Desmos tip: The new-old/old formula is the only correct approach — always divide by the original value, not the new one.
#19 Percent Increase/Decrease (multiplier method)
Formula: New = old × (1 + r/100) or (1 - r/100)
What it means: After a percentage increase of r%, multiply by (1 + r/100). After a decrease, multiply by (1 - r/100). For multiple successive changes: apply multipliers in sequence. Most efficient for multi-step percentage questions.
When to use: Use when: applying a percentage change to a value; calculating final price after a discount and tax; finding a value after successive percentage changes.
Desmos tip: For successive changes: 20% increase then 15% decrease → multiply by 1.20 × 0.85 = 1.02 → 2% net increase.
#20 Mean (Arithmetic Average)
Formula: Mean = (sum of all values) / (number of values)
What it means: The arithmetic average. Rearranges to: Sum = Mean × Count — this form is essential for solving SAT problems that give the mean and count, and ask for the total or a missing value.
When to use: Use when: finding an unknown value in a dataset given the mean; finding a new mean after adding/removing values; interpreting mean in a word problem context.
Desmos tip: Sum = Mean × Count is the most-used rearrangement. If mean of 5 numbers is 12, their sum is 60.
#21 Probability Formula
Formula: P(event) = favourable outcomes / total outcomes
What it means: Basic probability. Ranges from 0 (impossible) to 1 (certain). Conditional probability from a two-way table: P(A|B) = (A and B cells) / (B row total). Complement rule: P(not A) = 1 - P(A).
When to use: Use when: any probability question — selecting from a group, drawing from a deck, or reading probability from a two-way frequency table.
Desmos tip: Two-way table problems: always identify the specific row or column total as the denominator for conditional probability.
#22 Compound Interest Formula
Formula: A = P(1 + r/n)^(nt)
What it means: A = final amount; P = principal (initial amount); r = annual interest rate (as decimal); n = compounding periods per year; t = time in years. For annual compounding: n = 1, simplifies to A = P(1+r)ᵗ.
When to use: Use when: SAT questions about money growing with compound interest over time — explicitly using the compound interest setup rather than simple interest.
Desmos tip: Type the full formula into Desmos with known values substituted — use a slider for t to see growth over time.
7. Domain 4: Geometry and Trigonometry — Formulas 23–30
Geometry accounts for ~15% of SAT Math. Most area and volume formulas ARE on the reference sheet — but circle equations, arc length, sector area, polygon angles, and all trigonometry are NOT. The 8 formulas below are what you must add to what the sheet provides.
#23 Circle Equation (Standard Form)
Formula: (x - h)² + (y - k)² = r²
What it means: A circle with centre (h, k) and radius r. Given an equation in this form, read off h, k, r directly. If the equation is in general form (x²+y²+Dx+Ey+F=0), complete the square to convert to standard form — or use Desmos.
When to use: Use when: any SAT circle question involving coordinates — finding centre, radius, or whether a point is inside/outside/on the circle.
Desmos tip: Enter the circle equation directly in Desmos — it graphs the circle immediately. Click the centre to read coordinates. Measure radius from centre to edge.
#24 Arc Length Formula
Formula: Arc Length = (θ / 360°) × 2πr
What it means: The arc length is a fraction of the full circumference (2πr). The fraction is the central angle θ divided by 360°. For radians: Arc Length = θ × r (where θ is in radians).
When to use: Use when: finding the length of an arc (a portion of a circle's circumference) given the radius and central angle.
Desmos tip: Arc length is always a fraction of 2πr — the central angle fraction tells you exactly what fraction.
#25 Sector Area Formula
Formula: Sector Area = (θ / 360°) × πr²
What it means: The area of a sector (pie slice) is a fraction of the full circle area (πr²). The fraction is the same central angle fraction as in arc length.
When to use: Use when: finding the area of a portion of a circle (a sector) given the radius and central angle.
Desmos tip: Arc Length: fraction × circumference. Sector Area: fraction × circle area. Same fraction, different base — memorise the parallel structure.
#26 Sum of Interior Angles
Formula: Sum = (n - 2) × 180° where n = number of sides
What it means: The sum of all interior angles of any polygon equals (n-2) times 180°. Triangle: 180°. Quadrilateral: 360°. Pentagon: 540°. Hexagon: 720°. For a regular polygon, each angle = sum/n.
When to use: Use when: any SAT question involving the interior angles of a polygon — finding a missing angle, identifying a polygon type from its angle sum.
Desmos tip: Parallelogram property: opposite angles equal; consecutive angles supplementary. These are tested independently.
#27 SOH-CAH-TOA
Formula: sin = opp/hyp · cos = adj/hyp · tan = opp/adj
What it means: The three primary trigonometric ratios for right triangles. SOH: Sine = Opposite over Hypotenuse. CAH: Cosine = Adjacent over Hypotenuse. TOA: Tangent = Opposite over Adjacent. These are the foundation of all SAT trigonometry.
When to use: Use when: any SAT question involving right triangle side lengths and angles — finding a missing side, identifying an angle, or using trig in a real-world context.
Desmos tip: Desmos can evaluate trig functions numerically. Type sin(30°) or cos(45°) etc. — Desmos handles degrees. Verify trig answers instantly.
#28 Co-function Identity
Formula: sin(x) = cos(90° - x) and cos(x) = sin(90° - x)
What it means: In a right triangle with angles x and (90°-x), the sine of one equals the cosine of the other. This identity appears directly on SAT — For what value of x does sin(x) = cos(40)? Answer: x = 50.
When to use: Use when: SAT asks for angle x where sin(x) = cos(something) or vice versa.
Desmos tip: Use Desmos: verify sin(50) equals cos(40).
#29 Area of Equilateral Triangle
Formula: A = (√3/4) × s² where s = side length
What it means: An equilateral triangle has all sides equal and all angles 60°. Derived from the standard triangle area formula combined with the height of an equilateral triangle (h = (√3/2)s). This formula saves deriving from scratch.
When to use: Use when: an SAT geometry question gives the side length of an equilateral triangle and asks for its area.
Desmos tip: Alternatively: draw the equilateral triangle in Desmos, drop the height, and calculate area = ½ × base × height using the √3/2 height ratio.
#30 Surface Area of Cylinder
Formula: SA = 2πr² + 2πrh
What it means: Two circular bases (2πr²) plus the lateral surface (2πrh, which is a rectangle rolled around the cylinder with width = circumference and height = h). The volume formula (πr²h) IS on the reference sheet; the surface area is NOT.
When to use: Use when: SAT asks for the surface area or the total material needed to make a cylindrical object — distinct from volume questions.
Desmos tip: Volume vs Surface Area: Volume = πr²h (on reference sheet). Surface Area = 2πr² + 2πrh (NOT on reference sheet). Know the difference.
8. Desmos: When to Use It Instead of a Formula
The Desmos graphing calculator is built into Bluebook and available for all 44 SAT Math questions. It does not replace formula knowledge — but it can bypass lengthy formula application in specific situations:
When Desmos Replaces Manual Formula Application | How | Time Saved |
Finding roots of a quadratic | Enter the quadratic → click x-intercepts | 45–90 seconds vs using quadratic formula |
Finding vertex of a parabola | Enter the quadratic → click the peak/valley | 30–60 seconds vs calculating -b/2a and substituting |
Finding circle centre from general form | Enter the circle equation → Desmos graphs and shows centre | 60–90 seconds vs completing the square twice |
Solving any equation with one variable | Enter left side as y= and right side as y= → click intersection | 30–60 seconds vs algebraic solving |
Finding intersection of two lines (system of equations) | Enter both equations → click intersection | 20–30 seconds vs elimination/substitution |
Evaluating exponential function at a point | Enter the function → evaluate at specific x | 10–15 seconds vs manual calculation |
⚠️ Desmos Does NOT Replace Formula Memorisation: To use Desmos effectively, you still need to know what the formula looks like so you can type it correctly. Students who do not know the quadratic formula structure cannot type it into Desmos. Students who do not know the circle equation form cannot enter it. Formula knowledge and Desmos fluency work together — not as substitutes.
9. How to Memorise SAT Math Formulas — Proven Methods
Categorise by Domain First
Group formulas into 4 domains (Algebra, Advanced Math, PS&DA, Geometry+Trig). Study one domain at a time — never mix all formulas together in early study sessions. Domain grouping mirrors how the SAT itself organises questions.
Write Each Formula From Memory Daily
Every morning for 2 weeks: write all 30 formulas from memory on a blank sheet. Do not check until you have attempted every formula. Circle any you could not recall. The next morning, start with those.
Apply Each Formula Immediately After Memorising
A formula you can write but cannot apply is not yet learned. After memorising each formula, immediately solve 3 SAT-style questions using that specific formula. This builds the 'when to use it' instinct alongside the 'what it is' recall.
Use Flashcard Sets With Formula + ApplicationFront: formula name. Back: the formula AND one example application. Do not just test recall of the formula — test recall of an application. 'Vertex x-coordinate: x = -b/2a' → 'For x² + 6x + 5, vertex at x = -6/2(1) = -3.'
The Quick 5-Minute Daily Review
Every day in the final 2 weeks before the SAT: write all 30 formulas in under 5 minutes. If any takes more than 10 seconds, put it on a priority review list. The goal is automatic recall — the same way the multiplication table is automatic.
10. CBSE Students: Which Formulas You Already Know
Formula # | Formula | CBSE Status | Notes |
1–2 | Slope and slope-intercept form | ✅ CBSE Class 10 and 11 | Covered in linear equations and coordinate geometry; CBSE students typically strong here |
3–4 | Point-slope, standard form | ✅ CBSE Class 10 and 11 | Covered; CBSE terminology may differ (intercept form, slope-intercept form) |
5–6 | Midpoint and distance formula | ✅ CBSE Class 10 | Explicitly taught in coordinate geometry chapters |
7–8 | Parallel and perpendicular slopes | ✅ CBSE Class 10–11 | Covered in lines and angles; slope relationships explicitly tested in CBSE |
9 | Quadratic formula | ✅ CBSE Class 10 (Ch 4) | Directly taught in CBSE — one of the core Class 10 formulas |
10–11 | Vertex formulas | ⚠️ CBSE partial | CBSE covers completing the square; vertex formula -b/2a is implicit but not always explicitly memorised in CBSE context |
12 | Discriminant | ✅ CBSE Class 10 (Ch 4) | Explicitly covered in CBSE — nature of roots |
13 | Factored form | ✅ CBSE Class 10 | Factoring quadratics is a core CBSE topic |
14 | Exponential growth/decay | ✅ CBSE Class 12 (partial) | CBSE covers exponential functions; SAT's specific y = a·bˣ form needs explicit practice in SAT context |
15–16 | Difference of squares, perfect squares | ✅ CBSE Class 9–10 | Standard algebraic identities — explicitly taught and drilled in CBSE |
17–19 | Percentage formulas | ✅ CBSE Class 7–10 | Extensively covered; CBSE students typically strong in percentage calculations |
20 | Mean formula | ✅ CBSE Class 9–10 | Basic statistics — well-covered |
21 | Probability | ✅ CBSE Class 10 and 12 | Covered in both Class 10 and 12; SAT probability is less complex than CBSE Class 12 advanced probability |
22 | Compound interest | ✅ CBSE Class 8–10 | Explicitly taught; formula memorised in CBSE context |
23 | Circle equation | ⚠️ CBSE Class 11 (partial) | CBSE Class 11 covers coordinate geometry of circles but completing-the-square to standard form needs SAT-specific practice |
24–25 | Arc length, sector area | ✅ CBSE Class 10 | Directly taught in areas related to circles; same formulas |
26 | Interior angles polygon | ✅ CBSE Class 8–9 | Sum of angles in polygons — explicitly covered in CBSE geometry |
27 | SOH-CAH-TOA | ✅ CBSE Class 10 | Trigonometry chapter — explicitly taught; CBSE students should be strong here |
28 | Co-function identity | ⚠️ Partial | CBSE covers this but in different notation; needs SAT-specific practice |
29–30 | Equilateral triangle area, cylinder SA | ⚠️ Partial | CBSE covers areas and volumes broadly; these specific derived formulas may need explicit memorisation |
CBSE Advantage: CBSE students have genuine preparation for approximately 75–80% of these 30 SAT Math formulas through Classes 9–12 Mathematics. The primary areas needing additional SAT-specific preparation: vertex formula application, circle equation from general form, co-function identity, and SAT-specific context problems that use CBSE-familiar formulas in unfamiliar framing.
11. Formula Memorisation Study Plan
Week | Focus | Daily Time | Goal by End of Week |
Week 1 | Algebra Formulas 1–8 | 10–15 min formula drill + 20 min practice questions | Write all 8 Algebra formulas from memory with no hesitation |
Week 2 | Advanced Math Formulas 9–16 | 10–15 min formula drill + 25 min practice questions | Write all 8 Advanced Math formulas from memory with no hesitation |
Week 3 | PS&DA (17–22) and Geometry+Trig (23–30) | 10–15 min formula drill + 20 min practice questions | Write all 14 remaining formulas from memory |
Week 4 | All 30 formulas — full recall drill + integrated practice | 5–10 min daily formula recall + 30 min mixed practice tests | Write all 30 formulas in under 5 minutes; apply correctly in timed practice |
Final Week | Quick recall maintenance | 5 min daily — write all 30 formulas from memory | Zero hesitation on any formula; Desmos backup fluent for complex applications |
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12. Frequently Asked Questions (10 FAQs)
Based on official College Board Digital SAT specifications.
What formulas are on the SAT Math reference sheet?
The SAT Math reference sheet (available in Bluebook on all 44 Math questions) contains 12 geometry formulas: area and circumference of a circle, area of a rectangle and triangle, Pythagorean theorem, special right triangle ratios (30-60-90 and 45-45-90), and volumes of rectangular prisms, cylinders, spheres, cones, and pyramids. It does NOT contain any algebra formulas, any trigonometry definitions (SOH-CAH-TOA), any percentage formulas, or any statistical formulas. All of these must be memorised.
What SAT Math formulas must I memorise?
The 30 most essential formulas to memorise are: Algebra (slope, slope-intercept, point-slope, standard form, midpoint, distance, parallel slopes, perpendicular slopes), Advanced Math (quadratic formula, vertex x-coordinate, vertex form, discriminant, factored form, exponential growth/decay, difference of squares, perfect square identities), Problem-Solving & Data Analysis (percentage, percent change, percent multiplier, mean, probability, compound interest), Geometry/Trig (circle equation, arc length, sector area, polygon angle sum, SOH-CAH-TOA, co-function identity, equilateral triangle area, cylinder surface area).
Is the quadratic formula on the SAT reference sheet?
No — the quadratic formula (x = (-b ± √(b²-4ac)) / 2a) is not on the SAT Math reference sheet. It must be memorised. This is one of the most important facts about SAT Math preparation, because the quadratic formula is one of the most frequently tested formulas in the Advanced Math domain (~35% of the exam). Students who do not know the quadratic formula from memory will struggle on a significant portion of the test.
Do I need to memorise geometry formulas if they're on the sheet?
You need to know what the geometry formulas on the sheet mean and how to apply them — not necessarily memorise them exactly. However, several important geometry formulas are NOT on the sheet: the circle equation (x-h)²+(y-k)²=r², arc length, sector area, sum of interior angles of a polygon, and all trigonometry (SOH-CAH-TOA, co-function identity). These must be memorised. Additionally, even formulas on the sheet are faster to use when you know them automatically than when you look them up — for time-pressed questions, automatic recall is an advantage.
Which SAT Math formula is most important?
If forced to choose one, the quadratic formula is the most strategically important formula not on the reference sheet — because it applies to Advanced Math questions (~35% of the exam), it appears directly in many questions, and it cannot be avoided on hard questions. However, slope-intercept form (y = mx + b) is the most-applied formula overall, because linear equation questions appear throughout both modules of SAT Math. Both should be memorised with equal automaticity.
How many SAT Math formulas should I memorise?
Students should memorise approximately 25–40 core formulas before test day. This guide covers 30 of the highest-frequency formulas. College Board guidance, PrepScholar, and UWorld all recommend a similar range of 25–50 formulas depending on difficulty target. For a score of 650+, the 30 formulas in this guide cover the majority of tested content. For a score of 750+, additional harder formulas (law of sines/cosines for very hard geometry, more advanced function properties) may be worth adding.
Can Desmos replace formula memorisation on the SAT?
No — Desmos assists formula application but cannot replace formula knowledge. To use Desmos effectively, you must know what to type. To find the roots of a quadratic, you must know to enter the quadratic equation. To graph a circle, you must know the circle equation format. Desmos helps with computation (finding exact intersection coordinates, evaluating at specific points, graphing complex functions) — but it requires formula knowledge as the input. Students who try to use Desmos without knowing formulas waste time and miss the specific SAT questions that require algebraic (non-graphical) answers.
What is the best way to memorise SAT Math formulas?
The most effective methods are: (1) Daily recall — write all 30 formulas from memory each morning for 2 weeks; circle any hesitations. (2) Application immediately after memorisation — solve 3 SAT questions using each new formula the same day you memorise it. (3) Formula flashcards with one application example on the back — not just the formula but a sample usage. (4) 5-minute daily quick-review sprints in the final 2 weeks — write all 30 in under 5 minutes. (5) Group formulas by domain, not randomly — domain grouping mirrors how SAT organises questions.
Which SAT Math domain is most tested?
Algebra and Advanced Math together account for approximately 70% of all SAT Math questions — roughly 30 of the 44 questions. Algebra alone (~35%) is the most tested single domain, covering linear equations, systems, inequalities, and linear functions. Advanced Math (~35%) covers quadratics, exponentials, polynomials, and functions. Problem-Solving & Data Analysis and Geometry & Trigonometry each account for approximately 15%. This means the 16 formulas from Algebra and Advanced Math (Formulas 1–16 in this guide) should receive the most preparation time.
Are CBSE students at an advantage in SAT Math formulas?
Yes — significantly. CBSE Classes 9–12 Mathematics covers approximately 75–80% of the 30 formulas in this guide through standard curriculum. CBSE Class 10 covers the quadratic formula, discriminant, distance formula, midpoint formula, coordinate geometry of lines, areas related to circles, and trigonometry (SOH-CAH-TOA). CBSE Class 11–12 adds exponential functions, compound interest, and statistics. The primary gaps for CBSE students are: SAT-specific vertex formula application, circle equation from general form, co-function identity, and SAT-style contextual problem framing — rather than formula knowledge itself.
13. EduShaale — Expert SAT Math Coaching
EduShaale helps students across India master the exact formula inventory the Digital SAT requires — and build the Desmos fluency that turns those formulas into fast, accurate answers.
Formula Mastery Programme: We take every student through all 30 formulas using the daily recall + immediate application method — building automatic recall before the first full-length practice test, not after.
CBSE Gap Analysis: We identify which of the 30 SAT Math formulas CBSE preparation already covers and which require targeted memorisation — ensuring students don't waste time on formulas they already know while precisely targeting the genuine gaps.
Desmos Integration: We teach the 7 core Desmos techniques (intersection, vertex click, circle graphing, slider, regression, function evaluation, equation solving) as a fluency module — so students use Desmos to verify and accelerate formula application, not as a substitute for it.
Domain-Weighted Preparation: With Algebra and Advanced Math at 70% of the exam, we weight formula drilling and practice time accordingly — spending 70% of Math preparation time on Formulas 1–16 and 30% on Formulas 17–30.
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EduShaale's rule: Every formula in this guide should take under 3 seconds to recall. If any of the 30 takes longer, it is not yet memorised — it is only partially learned. Partial learning costs points on test day. We drill until every formula is automatic, not just familiar.
14. References & Resources
Official Resources
SAT Math Formula Guides
EduShaale SAT Resources
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SAT® and Bluebook™ are registered trademarks of the College Board. All formula content based on official Digital SAT specifications as of April 2026. Verify at satsuite.collegeboard.org. This guide is for educational purposes only.
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