★ SAT Math Master Series

SAT
Math
실전 20제

High-Yield Problems · Instant Explanations · Score Tracker

Quadratics Linear Systems Geometry Statistics Functions Ratios Inequalities Percent

📖 개념 → 예제 → 실전문제 → 해설 순서로 진행됩니다

핵심 개념 & 암기 공식

오답률 높은 8개 단원 핵심 정리

1
Quadratic Functions & Equations

🔑 Must-Know Formulas

Standard form: ax² + bx + c = 0 Quadratic formula: x = (−b ± √(b²−4ac)) / 2a Vertex: x = −b/(2a) Discriminant: D = b²−4ac D > 0 → 2 real roots D = 0 → 1 real root (repeated) D < 0 → no real roots Vertex form: y = a(x−h)² + k → vertex at (h,k) Factored form: y = a(x−r₁)(x−r₂) Sum of roots: r₁+r₂ = −b/a Product of roots: r₁·r₂ = c/a

✏️ Example

Example

If x² − 5x + 6 = 0, what are the values of x?

Factor: (x−2)(x−3) = 0

✓ Answer: x = 2 or x = 3
2
Linear Equations & Systems

🔑 Must-Know Formulas

Slope: m = (y₂−y₁)/(x₂−x₁) Slope-intercept: y = mx + b Point-slope: y−y₁ = m(x−x₁) Parallel lines: same slope (m₁ = m₂) Perpendicular lines: m₁ · m₂ = −1 System solutions: Substitution or Elimination method No solution → parallel lines (same m, diff b) Infinitely many → same line (identical equations)

✏️ Example

Example

Line through (1,3) and (3,9): find slope.

m = (9−3)/(3−1) = 6/2 = 3 → y = 3x

✓ Answer: slope = 3, equation y = 3x
3
Geometry: Circles & Triangles

🔑 Must-Know Formulas

Circle: Area = πr², Circumference = 2πr Arc length = (θ/360°)·2πr Sector area = (θ/360°)·πr² Circle equation: (x−h)² + (y−k)² = r² Triangle area = ½·base·height Pythagorean: a² + b² = c² Special triangles: 30-60-90: sides 1 : √3 : 2 45-45-90: sides 1 : 1 : √2 Similar triangles: ratios of sides are equal

✏️ Example

Example

A circle has radius 6. What is the arc length of a 60° sector?

Arc = (60/360)·2π·6 = (1/6)·12π = 2π

✓ Answer: 2π ≈ 6.28
4
Statistics & Data Analysis

🔑 Must-Know Concepts

Mean = sum of values / number of values Median = middle value (sorted list) Mode = most frequent value Range = max − min Standard deviation: spread of data from mean Higher SD → data more spread out Margin of error: affects confidence interval Correlation ≠ Causation (key SAT trap!) Outlier: pulls mean but not median

✏️ Example

Example

Data: {2, 4, 4, 6, 8, 100}. Mean vs Median?

Mean = (2+4+4+6+8+100)/6 = 124/6 ≈ 20.7; Median = (4+6)/2 = 5

✓ Outlier (100) pulls mean far above median
5
Functions: Domain, Range & Composition

🔑 Must-Know Concepts

f(g(x)): substitute g(x) into f Domain: all valid x inputs Avoid: division by 0, √(negative) Range: all possible y outputs f(x+k): horizontal shift LEFT by k f(x)+k: vertical shift UP by k −f(x): reflection over x-axis f(−x): reflection over y-axis Even function: f(−x) = f(x) (symmetric about y-axis) Odd function: f(−x) = −f(x) (symmetric about origin)

✏️ Example

Example

If f(x) = 2x+1 and g(x) = x², find f(g(3)).

g(3) = 9, then f(9) = 2(9)+1 = 19

✓ Answer: 19
6
Ratios, Rates & Proportions

🔑 Must-Know Concepts

Proportion: a/b = c/d → ad = bc (cross multiply) Unit rate: quantity per 1 unit Percent change = (new−old)/old × 100% Speed = Distance / Time Concentration problems: C₁V₁ = C₂V₂ Scale factor: if sides ratio = k, area ratio = k² Direct variation: y = kx Inverse variation: y = k/x

✏️ Example

Example

If 3 workers complete a job in 12 days, how many days for 9 workers? (inverse variation)

3×12 = 9×d → d = 36/9 = 4

✓ Answer: 4 days
7
Inequalities & Absolute Value

🔑 Must-Know Rules

Flip inequality sign when multiplying/dividing by NEGATIVE number |x| < a → −a < x < a |x| > a → x < −a OR x > a Linear inequality → shaded half-plane on graph System of inequalities → overlapping region Absolute value: distance from 0 on number line

✏️ Example

Example

Solve: |2x − 3| ≤ 7

−7 ≤ 2x−3 ≤ 7 → −4 ≤ 2x ≤ 10 → −2 ≤ x ≤ 5

✓ Answer: −2 ≤ x ≤ 5
8
Exponential Functions & Percent

🔑 Must-Know Formulas

Growth: y = a(1+r)^t Decay: y = a(1−r)^t a = initial value, r = rate, t = time Compound interest: A = P(1+r/n)^(nt) Exponential vs Linear: Linear: constant DIFFERENCE Exponential: constant RATIO Percent: part/whole × 100 New = Original × (1 ± percent/100)

✏️ Example

Example

A population of 500 grows at 20% per year. Population after 3 years?

y = 500 × (1.2)³ = 500 × 1.728 = 864

✓ Answer: 864
35:00
Question 1 of 20 Score: 0

Quiz Complete!

Here's your performance summary

—
OUT OF 20
—
Correct
—
Incorrect
—
Accuracy
—
Time Used