SAT Formulas Cheatsheet: Essential Reference Guide for Test Day Success
Master every formula you need for SAT Math success. This comprehensive cheatsheet from SATHELP24x7.com organizes all essential SAT formulas into an easy-to-reference format designed for efficient studying and quick review. Whether you're in active preparation or doing last-minute review, this guide ensures you have instant access to every critical mathematical relationship.
How to use this cheatsheet: Print it for offline study, bookmark it for quick reference, or review it daily during preparation. The formulas are organized by topic area with memory aids for complex equations. Focus especially on formulas NOT provided on the test reference sheet—these must be memorized for test day.
CRITICAL: Formulas marked with ⚠️ are NOT provided on the SAT reference sheet and MUST be memorized. Formulas marked with ✓ ARE provided but should still be memorized for speed.
Algebra Formulas (35% of SAT Math)
Linear Equations & Functions
⚠️ Slope
\( m = \frac{y_2 - y_1}{x_2 - x_1} \)
Rise over run between two points
⚠️ Slope-Intercept Form
\( y = mx + b \)
m = slope, b = y-intercept
⚠️ Point-Slope Form
\( y - y_1 = m(x - x_1) \)
Given slope and one point
⚠️ Standard Form
\( Ax + By = C \)
General linear equation form
⚠️ Parallel Lines
\( m_1 = m_2 \)
Equal slopes
⚠️ Perpendicular Lines
\( m_1 \cdot m_2 = -1 \)
Negative reciprocal slopes
Quadratic Equations
⚠️ MUST MEMORIZE: Quadratic Formula
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Solves \( ax^2 + bx + c = 0 \)
Memory Trick: "Negative boy couldn't decide (±) whether to go to the radical party or the square dance (b²), but he missed 4 awesome chicks (4ac), all over 2 awesome guys (2a)"
⚠️ Discriminant
\( \Delta = b^2 - 4ac \)
Δ > 0: two solutions
Δ = 0: one solution
Δ < 0: no real solutions
Δ = 0: one solution
Δ < 0: no real solutions
⚠️ Vertex Form
\( y = a(x - h)^2 + k \)
Vertex at (h, k)
⚠️ Standard Quadratic Form
\( y = ax^2 + bx + c \)
Vertex x-coordinate: \( x = -\frac{b}{2a} \)
⚠️ Factored Form
\( y = a(x - r_1)(x - r_2) \)
r₁, r₂ are roots/x-intercepts
⚠️ Difference of Squares
\( a^2 - b^2 = (a+b)(a-b) \)
High-frequency pattern
⚠️ Perfect Square Trinomial
\( a^2 \pm 2ab + b^2 = (a \pm b)^2 \)
Exponents & Exponentials
⚠️ Product Rule
\( x^a \cdot x^b = x^{a+b} \)
⚠️ Quotient Rule
\( \frac{x^a}{x^b} = x^{a-b} \)
⚠️ Power Rule
\( (x^a)^b = x^{ab} \)
⚠️ Negative Exponent
\( x^{-a} = \frac{1}{x^a} \)
⚠️ Zero Exponent
\( x^0 = 1 \) (x ≠ 0)
⚠️ Fractional Exponent
\( x^{\frac{m}{n}} = \sqrt[n]{x^m} \)
⚠️ Exponential Growth
\( y = a(1 + r)^t \)
a = initial amount
r = growth rate
t = time
r = growth rate
t = time
⚠️ Exponential Decay
\( y = a(1 - r)^t \)
a = initial amount
r = decay rate
t = time
r = decay rate
t = time
⚠️ Compound Interest
\( A = P\left(1 + \frac{r}{n}\right)^{nt} \)
P = principal, r = rate, n = times/year, t = years
⚠️ Simple Interest
\( I = Prt \)
Principal × rate × time
Coordinate Geometry
⚠️ Distance Formula
\( d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \)
Distance between two points
⚠️ Midpoint Formula
\( M = \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right) \)
Midpoint between two points
Advanced Math Formulas (35% of SAT Math)
Function Transformations
⚠️ Transformation Rules (Must Know)
Vertical Shift
\( f(x) + k \)
UP k units
Horizontal Shift
\( f(x + k) \)
LEFT k units (opposite!)
Vertical Stretch
\( kf(x) \) (k > 1)
Stretches vertically
Reflection over x-axis
\( -f(x) \)
Flips upside down
Reflection over y-axis
\( f(-x) \)
Flips left-right
Horizontal Shift Trick: For f(x+3), think "What x-value gives me zero inside?" Need x = -3, so graph moves LEFT 3. Do the opposite!
Polynomials
⚠️ Sum of Cubes
\( a^3 + b^3 = (a+b)(a^2-ab+b^2) \)
⚠️ Difference of Cubes
\( a^3 - b^3 = (a-b)(a^2+ab+b^2) \)
Geometry & Trigonometry Formulas (15% of SAT Math)
Triangles
✓ Triangle Area
\( A = \frac{1}{2}bh \)
Provided on reference sheet
✓ Pythagorean Theorem
\( a^2 + b^2 = c^2 \)
Right triangles only; provided
⚠️ Triangle Angle Sum
Sum = 180°
Interior angles
✓ Special Right Triangles (Memorize for Speed)
45-45-90 Triangle
\( x : x : x\sqrt{2} \)
Legs equal; hypotenuse = leg√2
30-60-90 Triangle
\( x : x\sqrt{3} : 2x \)
Short : Medium : Hypotenuse
45-45-90: "Square root 2 for the hypotenuse"
30-60-90: "1, 2, root 3" — short leg (1), hypotenuse (2), medium leg (√3)
30-60-90: "1, 2, root 3" — short leg (1), hypotenuse (2), medium leg (√3)
Common Pythagorean Triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25 (and all their multiples like 6-8-10, 9-12-15)
Circles
✓ Circle Area
\( A = \pi r^2 \)
Provided on reference sheet
✓ Circumference
\( C = 2\pi r = \pi d \)
Provided on reference sheet
⚠️ Arc Length
\( L = \frac{\theta}{360°} \times 2\pi r \)
θ = central angle in degrees
⚠️ Sector Area
\( A = \frac{\theta}{360°} \times \pi r^2 \)
"Pizza slice" area
⚠️ Circle Equation
\( (x-h)^2 + (y-k)^2 = r^2 \)
Center at (h, k), radius r
Polygons
✓ Rectangle Area
\( A = lw \)
Provided on reference sheet
⚠️ Parallelogram Area
\( A = bh \)
Base × height
⚠️ Trapezoid Area
\( A = \frac{1}{2}(b_1 + b_2)h \)
Average of bases × height
⚠️ Polygon Angle Sum
\( S = (n-2) \times 180° \)
n = number of sides
3D Geometry
✓ Rectangular Solid Volume
\( V = lwh \)
Provided on reference sheet
✓ Cylinder Volume
\( V = \pi r^2 h \)
Provided on reference sheet
✓ Sphere Volume
\( V = \frac{4}{3}\pi r^3 \)
Provided on reference sheet
✓ Sphere Surface Area
\( SA = 4\pi r^2 \)
Provided on reference sheet
✓ Cone Volume
\( V = \frac{1}{3}\pi r^2 h \)
Provided on reference sheet
✓ Pyramid Volume
\( V = \frac{1}{3}Bh \)
B = base area; provided
Trigonometry
⚠️ SOHCAHTOA (Right Triangle Trig)
Sine
\( \sin\theta = \frac{\text{opposite}}{\text{hypotenuse}} \)
Cosine
\( \cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}} \)
Tangent
\( \tan\theta = \frac{\text{opposite}}{\text{adjacent}} \)
SOHCAHTOA Memory: "Some Old Hippie Caught Another Hippie Trippin' On Acid" or "Silly Old Harry Caught A Herring Trawling Off America"
⚠️ Pythagorean Identity
\( \sin^2\theta + \cos^2\theta = 1 \)
⚠️ Complementary Angles
\( \sin(90° - \theta) = \cos\theta \)
Statistics & Data Analysis (15% of SAT Math)
Central Tendency & Spread
⚠️ Mean (Average)
\( \bar{x} = \frac{\sum x}{n} \)
Sum of values ÷ count
⚠️ Median
Middle value when ordered (or average of two middle values)
⚠️ Mode
Most frequently occurring value
⚠️ Range
Max − Min
Spread of data
Ratios, Proportions & Percentages
⚠️ Proportion
\( \frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc \)
Cross-multiply to solve
⚠️ Percent
\( \frac{\text{part}}{\text{whole}} \times 100\% \)
⚠️ Percent Change
\( \frac{\text{new} - \text{old}}{\text{old}} \times 100\% \)
⚠️ Percent of Number
\( n\% \text{ of } x = \frac{n}{100} \times x \)
Example: 15% of 80 = 0.15 × 80
Rate & Distance
⚠️ Distance Formula
\( d = rt \)
Distance = rate × time
⚠️ Average Speed
\( \text{Avg Speed} = \frac{\text{total distance}}{\text{total time}} \)
Probability
⚠️ Basic Probability
\( P(E) = \frac{\text{favorable}}{\text{total}} \)
⚠️ Independent Events
\( P(A \text{ and } B) = P(A) \times P(B) \)
⚠️ Complement Rule
\( P(\text{not } A) = 1 - P(A) \)
Quick Reference: Values to Memorize
Perfect Squares (1-15)
1²=1, 2²=4, 3²=9, 4²=16, 5²=25
6²=36, 7²=49, 8²=64, 9²=81
10²=100, 11²=121, 12²=144
13²=169, 14²=196, 15²=225
6²=36, 7²=49, 8²=64, 9²=81
10²=100, 11²=121, 12²=144
13²=169, 14²=196, 15²=225
Perfect Cubes
1³=1, 2³=8, 3³=27
4³=64, 5³=125
6³=216, 10³=1000
4³=64, 5³=125
6³=216, 10³=1000
Common Fractions to Decimals
½ = 0.5, ¼ = 0.25, ¾ = 0.75
⅓ ≈ 0.333, ⅔ ≈ 0.667
⅕ = 0.2, ⅖ = 0.4, ⅗ = 0.6
⅓ ≈ 0.333, ⅔ ≈ 0.667
⅕ = 0.2, ⅖ = 0.4, ⅗ = 0.6
Common Square Roots
√2 ≈ 1.414
√3 ≈ 1.732
√5 ≈ 2.236
√3 ≈ 1.732
√5 ≈ 2.236
Memorization Strategy
Effective Formula Memorization:
- Write: Copy each formula 5 times by hand (motor memory)
- Apply: Solve 10-15 problems using each formula (application memory)
- Test: Quiz yourself daily without looking (retrieval practice)
- Visual: Create color-coded cheatsheet to post where you study
- Spaced: Review formulas daily, not in marathon cramming sessions
Test Day Morning: Review this cheatsheet once during breakfast. Don't try to memorize new formulas the day of the test. Trust your preparation and focus on staying calm and confident.
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