Master these key concepts and memorize critical formulas
TOPIC 01 · PRE-ALGEBRA
Number Properties & Ratios
Integers include positive, negative, and zero. A prime number has exactly two distinct factors: 1 and itself. A composite number has more than two factors. Ratios compare two quantities, and proportions state two ratios are equal.
Solve linear equations by isolating the variable. For systems of equations, use substitution or elimination. Quadratics can be solved by factoring, completing the square, or using the quadratic formula.
Quadratic: ax² + bx + c = 0
x = (−b ± √(b²−4ac)) / 2a
Discriminant: D = b²−4ac
D > 0: two real rootsD = 0: one rootD < 0: no real rootsFOIL
TOPIC 03 · FUNCTIONS
Function Notation & Transformations
f(x) represents the output when input is x. Domain is all valid inputs; range is all possible outputs. Composite functions: (f∘g)(x) = f(g(x)). Inverse function f⁻¹(x) reverses the operation.
Slope: m = (y₂ − y₁) / (x₂ − x₁)
Slope-intercept: y = mx + b
Point-slope: y − y₁ = m(x − x₁)
Vertical line testf(g(x)) compositionParallel: same slopePerpendicular: m₁×m₂ = −1
TOPIC 04 · GEOMETRY
Area, Volume & Angle Theorems
Know formulas for all 2D and 3D shapes. Triangles: angles sum to 180°. Exterior angle = sum of two non-adjacent interior angles. Similar triangles have proportional sides. The Pythagorean theorem applies to right triangles.
Sine, cosine, and tangent relate angles to side ratios in a right triangle. Remember SOH-CAH-TOA. Know key angles: 0°, 30°, 45°, 60°, 90°. The Law of Sines and Law of Cosines extend trig to non-right triangles.
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent = sin θ/cos θ
sin²θ + cos²θ = 1
sin 30° = 1/2cos 60° = 1/2tan 45° = 1sin 90° = 1
TOPIC 06 · COORDINATE GEOMETRY
Distance, Midpoint & Circles
The coordinate plane uses (x, y) pairs. Distance formula derives from the Pythagorean theorem. Midpoint finds the center of a segment. The standard equation of a circle centered at (h, k) with radius r.
Distance: d = √[(x₂−x₁)² + (y₂−y₁)²]
Midpoint: ((x₁+x₂)/2 , (y₁+y₂)/2)
Circle: (x−h)² + (y−k)² = r²
Standard form ax+by=cQuadrants I-IVParabola: y=ax²+bx+c
TOPIC 07 · STATISTICS & PROBABILITY
Mean, Median, Mode & Probability
Mean is the arithmetic average. Median is the middle value when sorted. Mode is the most frequent value. Range = max − min. Probability of an event = favorable outcomes / total outcomes. Independent events: P(A and B) = P(A) × P(B).
Mean = Σx / n
P(A or B) = P(A) + P(B) − P(A∩B)
Combinations: C(n,r) = n! / (r!(n−r)!)
Ordered data for medianStandard deviationBox plotComplement: P(not A) = 1−P(A)