№ 01SAT + ACT
Algebra
Slopes, lines, quadratics, exponent rules — the workhorse of every SAT and ACT math section.
- Slope·Two points on a line
- m = (y₂ − y₁) / (x₂ − x₁)
- Slope-Intercept
- y = mx + b
- Point-Slope
- y − y₁ = m(x − x₁)
- Standard Form
- Ax + By = C
- Quadratic Formula
- x = (−b ± √(b² − 4ac)) / 2a
- Discriminant
- D = b² − 4ac
- Vertex (Standard)
- x = −b / (2a)
- Vertex Form
- y = a(x − h)² + k
- Difference of Squares
- a² − b² = (a + b)(a − b)
- Exponent Product
- xᵃ · xᵇ = xᵃ⁺ᵇ
- Exponent Quotient
- xᵃ / xᵇ = xᵃ⁻ᵇ
- Power Rule
- (xᵃ)ᵇ = xᵃᵇ
Chapter I
№ 02SAT + ACT
Geometry
Distance, circles, triangles. The SAT prints some of these on the test — the ACT prints none.
- Distance
- d = √((x₂ − x₁)² + (y₂ − y₁)²)
- Midpoint
- M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
- Triangle Area
- A = ½ b h
- Circle Area
- A = π r²
- Circumference
- C = 2 π r
- Circle Equation
- (x − h)² + (y − k)² = r²
- Arc Length
- s = (θ / 360) × 2 π r
- Sector Area
- A = (θ / 360) × π r²
- 30-60-90 Triangle
- x : x√3 : 2x
- 45-45-90 Triangle
- x : x : x√2
- Pythagorean Theorem
- a² + b² = c²
Chapter II
№ 03SAT + ACT
Trigonometry
SOH-CAH-TOA plus the identities you actually need. The Law of Sines and Cosines are ACT-only.
- Sine
- sin θ = opposite / hypotenuse
- Cosine
- cos θ = adjacent / hypotenuse
- Tangent
- tan θ = opposite / adjacent
- Pythagorean Identity
- sin² θ + cos² θ = 1
- Complementary
- sin(x) = cos(90° − x)
- Radians Conversion
- θ(rad) = θ(deg) × π / 180
- Law of Sines·ACT only
- a / sin A = b / sin B = c / sin C
- Law of Cosines·ACT only
- c² = a² + b² − 2ab cos C
Chapter III
№ 04SAT + ACT
Statistics & Probability
Means, percent change, simple interest, exponential growth. Money problems hide here.
- Mean
- x̄ = Σx / n
- Probability
- P(E) = favorable / total
- Percent Change
- ((new − old) / old) × 100
- Simple Interest
- I = P r t
- Compound Interest
- A = P (1 + r/n)^(nt)
- Exponential Growth
- y = a (1 + r)ᵗ
- Exponential Decay
- y = a (1 − r)ᵗ
Chapter IV
№ 05ACT only
3D Geometry
Volumes and surface areas of every solid the ACT throws at you. The SAT rarely tests these.
- Rectangular Prism V
- V = l w h
- Cylinder Volume
- V = π r² h
- Cone Volume
- V = ⅓ π r² h
- Sphere Volume
- V = (4/3) π r³
- Sphere Surface Area
- SA = 4 π r²
- Pyramid Volume
- V = ⅓ B h
Chapter V