All 39 formulas you need on test day. The official SAT provides 10 formulas on its reference sheet — the remaining 29 must be memorized. Each card shows the formula, a plain-English explanation, a worked example, and a common mistake to avoid.
No formulas match your search. Try a shorter term.
Slope equals rise over run between two points.
Subtracting x values in the wrong order (x1 − x2 instead of x2 − x1).
Memory hook: Rise over Run — go up before you go across.
m is the slope; b is the y-intercept.
Confusing m (slope) with b (intercept).
Memory hook: y = mx + b: m is the mover, b is the base.
Used when you know a point and the slope.
Forgetting to negate x₁ and y₁ signs.
Memory hook: You have a point and a slope — plug straight in.
Finds the roots of ax² + bx + c = 0.
Forgetting the ±, or dividing only the numerator by 2a.
Memory hook: "x equals negative b, plus or minus the square root of b squared minus 4ac, all over 2a."
Vertex is at (h, k); a determines direction and width.
Reading vertex as (−h, k) instead of (h, k).
Memory hook: h and k are the coordinates of the vertex — watch the sign of h.
Δ > 0: two real roots. Δ = 0: one root. Δ < 0: no real roots.
Forgetting to multiply 4 × a × c before subtracting.
Memory hook: Discriminant discriminates between root types.
a = initial value, r = rate, t = time. Use + for growth, − for decay.
Using the decimal rate as a percentage (e.g., entering 5 instead of 0.05).
Memory hook: Start × (1 ± rate) raised to time.
If f(r) = 0, then (x − r) is a factor of f(x).
Confusing roots and factors — a root r gives a factor (x − r).
Memory hook: Zero output → zero factor.
A squared minus B squared factors as (A+B)(A−B).
Trying to factor a sum of squares a² + b² — it does not factor over the reals.
Memory hook: Difference factors, sum does not.
Squaring a binomial gives three terms with the middle term 2ab.
Writing (a + b)² = a² + b² — the 2ab middle term is always present.
Memory hook: Square the first, twice the product, square the last.
First, Outer, Inner, Last — multiply each term pair.
Missing the Outer or Inner cross-products.
Memory hook: F-O-I-L: First, Outer, Inner, Last.
Sum all values, then divide by the count.
Forgetting to include all values when summing.
Memory hook: Mean = total ÷ count.
Sort the data; the median is the middle value (or average of the two middle values).
Forgetting to sort the data before finding the middle.
Memory hook: Median is the middle of the road.
IQR is the range of the middle 50% of data.
Confusing Q1 and Q3 positions when the dataset has an even count.
Memory hook: IQR spans the middle half — Q3 minus Q1.
Larger sample size shrinks the margin of error.
Dividing by n instead of √n.
Memory hook: Bigger n → smaller spread.
A regression line minimising the sum of squared residuals.
Using the line to predict far outside the data range (extrapolation).
Memory hook: Same slope-intercept form — applied to scatter plots.
Probability = favorable ÷ total.
Counting an outcome twice when events overlap.
Memory hook: Favorable over total.
Probability of A given B has already occurred.
Swapping P(A|B) and P(B|A) — order matters.
Memory hook: Condition restricts the sample space to B.
Positive = increase; negative = decrease.
Dividing by the new value instead of the old value.
Memory hook: Change over original × 100.
Convert the percent to a decimal and multiply by the whole.
Forgetting to convert percent to decimal.
Memory hook: Percent → decimal → multiply.
Cross-multiply to solve for an unknown in a proportion.
Adding instead of cross-multiplying.
Memory hook: Cross-multiply to clear fractions.
Express a ratio as a single unit (e.g., miles per hour).
Inverting the ratio — always check units.
Memory hook: Per = divide.
In a right triangle, the sum of the squares of the legs equals the square of the hypotenuse.
Adding legs then taking one square root, instead of squaring each leg first.
Memory hook: Legs squared, hypotenuse squared — a² + b² = c².
30-60-90 sides ratio 1:√3:2; 45-45-90 sides ratio 1:1:√2.
Mixing up the 30-60-90 and 45-45-90 ratios.
Memory hook: Half-equilateral = 30-60-90; diagonal of square = 45-45-90.
The three interior angles of any triangle sum to 180°.
Using 360° instead of 180°.
Memory hook: Triangle = 180°, straight line = 180°.
Half base times height (height must be perpendicular to base).
Using a slant side as the height instead of the perpendicular height.
Memory hook: Half of rectangle: ½ × base × height.
Area uses radius squared; circumference uses radius (or diameter).
Using diameter instead of radius in the area formula.
Memory hook: Area: π r² — "pie are square." Circumference: 2πr.
Arc length is the fraction of the circumference determined by the central angle.
Using θ in radians when the formula requires degrees, or vice versa.
Memory hook: Fraction of the full circle × full circumference.
Sector area is the fraction of the circle area determined by the central angle.
Forgetting to use the fraction θ/360.
Memory hook: Fraction of circle × full area.
Center is at (h, k), radius is r.
Reading center as (−h, −k) — the signs inside are subtracted.
Memory hook: Center (h, k), radius r — watch the signs.
Volume of a cylinder = base area × height.
Using diameter instead of radius.
Memory hook: Circle base area × height.
A cone holds one-third the volume of a cylinder with the same base and height.
Forgetting the 1/3 factor.
Memory hook: Cone = 1/3 of cylinder.
Volume scales with the cube of the radius.
Confusing sphere surface area (4πr²) with sphere volume.
Memory hook: 4/3 π r-cubed.
Distance between two points using the Pythagorean theorem.
Forgetting to take the square root at the end.
Memory hook: It's just Pythagorean theorem in disguise.
Average the x-coordinates and average the y-coordinates.
Subtracting instead of adding the coordinates.
Memory hook: Midpoint = average of each coordinate.
Sine = Opposite/Hypotenuse; Cosine = Adjacent/Hypotenuse; Tangent = Opposite/Adjacent.
Swapping opposite and adjacent sides.
Memory hook: SOH-CAH-TOA: Some Old Horses Can Always Hear Their Owners Approaching.
Multiply degrees by π/180 to get radians; multiply radians by 180/π for degrees.
Inverting the conversion factor.
Memory hook: Degrees × (π/180) = radians. Think "divide by 180, multiply by π."
Sine and cosine are cofunctions — sin of an angle equals cos of its complement.
Forgetting that complementary angles sum to 90°, not 180°.
Memory hook: Co-sine means complement's sine.
Powers of i cycle every 4: i, −1, −i, 1.
Not reducing the exponent modulo 4 first.
Memory hook: Cycle of 4: i → −1 → −i → 1 → repeat.
The official SAT provides 11 formulas: circle area/circumference, rectangle area, triangle area, Pythagorean theorem, special right triangles (30-60-90 and 45-45-90), and volume formulas for box, cylinder, sphere, cone, and pyramid.
The SAT provides a reference sheet, but you must memorize formulas NOT on the sheet, including the quadratic formula, slope formula, percent change formula, and probability rules. Shrutam marks which formulas you must memorize.
The quadratic formula is x = (-b ± √(b²-4ac)) / 2a. It solves any quadratic equation ax² + bx + c = 0. It is NOT on the SAT reference sheet — you must memorize it.
Apply these formulas with SAT Math practice problems by domain, or check your projected score.