Chapter 1
Integers & Operations
Integer Sign Multiplication Rules
(+) × (+) = (+) | (-) × (-) = (+) | (+) × (-) = (-) | (-) × (+) = (-)
Rules apply identically to division: (-a) ÷ (-b) = +(a/b).
Variables: Product of an even count of negative integers is positive; odd count is negative.
Exam Tip: (-1)^n = 1 when n is even, and -1 when n is odd.
Additive & Multiplicative Identities
a + 0 = a (0 is additive identity) | a × 1 = a (1 is multiplicative identity)
Adding additive inverse yields 0; multiplying reciprocal yields 1.
Variables: Additive inverse of a is -a; Multiplicative inverse of a is 1/a (a ≠ 0)
Exam Tip: 0 has no reciprocal because division by zero is mathematically undefined.
Chapter 2
Rational Numbers & Equations
Rational Number Density Mean
Rational number between a and b = (a + b) / 2
The arithmetic mean always lies strictly between a and b, proving infinitely many rational numbers exist.
Variables: a < b are any two distinct rational numbers
Exam Tip: Another quick method: write both fractions with a large common denominator, e.g. multiply both by 10/10.
Simple Equations Transposition Rule
ax + b = cx + d => (a - c)x = d - b => x = (d - b) / (a - c)
Collect variable terms on LHS and numerical constants on RHS.
Variables: Transposing a term across = changes its sign from + to - and vice-versa.
Exam Tip: Brackets must be expanded first using the distributive law before transposing terms.
Chapter 3
Lines & Angles
Angle Relationships
Complementary: ∠1 + ∠2 = 90° | Supplementary: ∠1 + ∠2 = 180° | Linear Pair = 180°
Formed by intersecting lines and transversals across parallel lines.
Variables: Vertically opposite angles are equal: ∠1 = ∠3, ∠2 = ∠4
Exam Tip: When two parallel lines are cut by a transversal, alternate interior angles (Z-shape) and corresponding angles (F-shape) are equal.
Angle Sum Property of Triangle
∠A + ∠B + ∠C = 180° | Exterior Angle = Sum of opposite interior angles
Fundamental theorem used in solving polygon and geometric proofs.
Variables: Exterior angle ∠ACD = ∠A + ∠B
Exam Tip: Sum of interior angles of an n-sided polygon = (n - 2) × 180°.