SAT Math Master Practice — 20 Essential Questions

1

Linear Equations & Inequalities

~4 Qs

Core Concept

A linear equation has degree 1. Solve by isolating the variable using inverse operations. For inequalities, flip the sign when multiplying/dividing by a negative number.

Key Formulas

Slope-intercept: y = mx + b
Point-slope: y − y₁ = m(x − x₁)
Standard form: Ax + By = C
Slope: m = (y₂ − y₁) / (x₂ − x₁)

Quick Example

If 3x − 7 = 14, find x.

→ 3x = 21 → x = 7

2

Systems of Linear Equations

~2 Qs

Core Concept

Substitution: Solve one equation for a variable, substitute into the other.
Elimination: Add/subtract equations to cancel a variable.
No solution: parallel lines (same slope, different intercepts).
Infinite solutions: same line (identical equations).

Quick Example

Solve: 2x + y = 10 and x − y = 2.

→ Add: 3x = 12 → x = 4, y = 2

3

Quadratic Equations & Parabolas

~3 Qs

Key Formulas

Standard: ax² + bx + c = 0
Quadratic Formula: x = (−b ± √(b²−4ac)) / 2a
Discriminant: Δ = b²−4ac
Δ>0: 2 real roots | Δ=0: 1 root | Δ<0: no real roots
Vertex: x = −b/(2a), y = f(−b/2a)
Vertex form: y = a(x−h)² + k

Quick Example

Solve x² − 5x + 6 = 0.

→ (x−2)(x−3) = 0 → x = 2 or x = 3

4

Functions & Graphs

~3 Qs

Core Concept

f(a) means substitute x = a into f(x).
Composition: (f∘g)(x) = f(g(x)) — apply g first, then f.
Domain = all valid inputs; Range = all possible outputs.
Transformation: f(x−h)+k shifts right h, up k.

Quick Example

If f(x) = 2x + 3 and g(x) = x², find f(g(3)).

→ g(3) = 9 → f(9) = 2(9)+3 = 21

5

Ratios, Rates & Proportions

~2 Qs

Key Formulas

Proportion: a/b = c/d → ad = bc
Percent change: ((New−Old)/Old) × 100
Unit rate: quantity / time
Direct variation: y = kx

Quick Example

If a car travels 150 miles in 3 hours, how far in 5 hours at the same rate?

→ Rate = 50 mph → 50 × 5 = 250 miles

6

Statistics & Data Analysis

~2 Qs

Key Formulas

Mean = sum of values / count
Median = middle value (sorted)
Mode = most frequent value
Standard deviation ↑ = data more spread out

Core Concept

Scatterplot correlation: positive slope = positive correlation. Line of best fit minimizes total distance to points. Outliers pull the mean but not the median.

7

Geometry & Trigonometry

~2 Qs

Key Formulas

Circle: A = πr², C = 2πr
Arc length: (θ/360°) × 2πr
Triangle: A = (1/2)bh
Pythagorean: a² + b² = c²
SOH-CAH-TOA:
sin θ = opp/hyp
cos θ = adj/hyp
tan θ = opp/adj

8

Exponentials, Radicals & Polynomials

~2 Qs

Key Formulas

Exponential growth: y = a(1+r)^t
Exponential decay: y = a(1−r)^t
Power rules: x^a · x^b = x^(a+b)
(x^a)^b = x^(ab)
x^(−n) = 1/x^n
FOIL: (a+b)(c+d) = ac+ad+bc+bd

Quick Example

Simplify: (x³)(x⁻²)

→ x^(3+(−2)) = x¹ = x

Concept Review & Key Formulas

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