SSAT Math Mastery

1

Number Theory & Properties

📌 Key Concepts

Prime numbers have exactly two factors: 1 and themselves. Composite numbers have more than two factors. The number 1 is neither prime nor composite.

🧠 Memorize

LCM(a, b) × GCF(a, b) = a × b

Even ± Even = Even | Odd ± Odd = Even

Even × anything = Even

📝 Example

Q: What is the LCM of 12 and 18?

Solution: 12 = 2²×3, 18 = 2×3². LCM = 2²×3² = 36

Divisibility Prime Factorization LCM/GCF

2

Algebra & Equations

📌 Key Concepts

To solve linear equations, isolate the variable by performing the same operation on both sides. For quadratics, use factoring or the quadratic formula.

🧠 Memorize

Quadratic Formula: $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$(a+b)^2 = a^2 + 2ab + b^2$

$(a-b)(a+b) = a^2 - b^2$

📝 Example

Q: If $3x + 7 = 22$, what is $x$?

Solution: $3x = 15 \Rightarrow x = 5$

Linear Equations Quadratics Factoring

3

Geometry

📌 Key Concepts

Angles in a triangle sum to 180°. A right angle = 90°. Similar triangles have proportional sides. The Pythagorean theorem applies only to right triangles.

🧠 Memorize

Pythagorean Theorem: $a^2 + b^2 = c^2$

Area of Triangle: $A = \frac{1}{2} \times base \times height$

Area of Circle: $A = \pi r^2$ | Circumference: $C = 2\pi r$

Special triangles: 3-4-5 · 5-12-13 · 30-60-90

📝 Example

Q: A right triangle has legs 6 and 8. What is the hypotenuse?

Solution: $\sqrt{6^2 + 8^2} = \sqrt{36+64} = \sqrt{100} = \mathbf{10}$

Triangles Circles Area & Perimeter Pythagorean

4

Ratios, Proportions & Percents

📌 Key Concepts

A ratio compares two quantities. Proportions set two ratios equal. Percent means "per hundred." Percent change = (new − old) / old × 100%.

🧠 Memorize

Percent Change = $\dfrac{\text{new} - \text{old}}{\text{old}} \times 100\%$

Cross-multiply: $\dfrac{a}{b} = \dfrac{c}{d} \Rightarrow ad = bc$

Part = Percent × Whole (convert % to decimal)

📝 Example

Q: A price increases from $40 to $50. What is the percent increase?

Solution: $\frac{50-40}{40} \times 100 = 25\%$

Ratios Proportions Percent Change

5

Word Problems & Applied Math

📌 Key Concepts

Assign variables to unknowns, translate keywords: "sum" = +, "difference" = −, "product" = ×, "quotient" = ÷, "is/was/equals" = =.

🧠 Memorize

Distance = Rate × Time (D = rt)

Work = Rate × Time (combined rates add)

Simple Interest: $I = P \times r \times t$

📝 Example

Q: A train travels 180 miles in 3 hours. What is its average speed?

Solution: Speed = $\frac{180}{3} = \mathbf{60}$ mph

Distance-Rate-Time Work Problems Consecutive Integers

6

Data, Statistics & Probability

📌 Key Concepts

Mean = average. Median = middle value (when ordered). Mode = most frequent value. Range = max − min. Probability = favorable outcomes / total outcomes.

🧠 Memorize

Mean: $\bar{x} = \dfrac{\sum x_i}{n}$

Probability: $P(A) = \dfrac{\text{favorable}}{\text{total}}$

$P(A \text{ and } B) = P(A) \times P(B)$ (independent events)

$P(A \text{ or } B) = P(A) + P(B) - P(A \cap B)$

📝 Example

Q: Data: 3, 7, 7, 9, 14. Find mean and median.

Solution: Mean = $\frac{40}{5} = 8$. Median = 7 (middle value)

Mean/Median/Mode Probability Counting

Core Concepts & Key Formulas

20 Practice Problems

Answer Key & Full Explanations

Answer Key & Explanations