Study Guide
Key Concepts & Rules
Master these essential formulas and patterns before tackling the quiz.
CONCEPT 01
Order of Operations (PEMDAS)
Parentheses → Exponents → Multiply/Divide → Add/Subtract
Example: 3 + 4 × 2 = 3 + 8 = 11 (NOT 14)
CONCEPT 02
Integer Operations
Same signs: add & keep sign | Different signs: subtract & take larger sign
Neg × Neg = Positive | Neg × Pos = Negative
Example: (−7) + (−3) = −10 (−4) × (−6) = +24
CONCEPT 03
Fractions
Add/Subtract: find LCD, then add numerators
Multiply: numerator × numerator / denominator × denominator
Example: 2/3 + 1/4 = 8/12 + 3/12 = 11/12
CONCEPT 04
Percent
Part = Percent% × Whole = (Percent/100) × Whole
Example: 30% of 80 = 0.30 × 80 = 24
CONCEPT 05
Ratios & Proportions
a/b = c/d → cross-multiply: a × d = b × c
Example: 3/5 = 12/x → 3x = 60 → x = 20
CONCEPT 06
Absolute Value
|x| = distance from zero; always ≥ 0
Example: |−9| − |4| = 9 − 4 = 5
CONCEPT 07
Exponents
xᴦ × xᴧ = xᴦ⁺ᴧ | (xᴦ)ᴧ = xᴦᴧ | x⁰ = 1
Example: 2³ × 2² = 2⁵ = 32
CONCEPT 08
Square Roots
√(a × b) = √a × √b | Perfect squares: 1,4,9,16,25,36,49,64,81,100,121,144...
Example: √144 = 12 because 12 × 12 = 144
CONCEPT 09
Evaluating Expressions
Substitute the given value, then follow PEMDAS
Example: 3x + 2 when x = 4 → 3(4) + 2 = 12 + 2 = 14
CONCEPT 10
Solving Equations
Undo operations in reverse PEMDAS order; keep equation balanced
Example: 2x + 5 = 13 → 2x = 8 → x = 4
CONCEPT 11
Inequalities
Solve like an equation; FLIP the sign when multiplying/dividing by a negative
Example: 3x − 1 > 11 → 3x > 12 → x > 4
CONCEPT 12
Distributive Property
a(b + c) = ab + ac
Example: 4(x + 3) = 4x + 12
CONCEPT 13
GCF & LCM
GCF: largest factor both share | LCM: smallest multiple both share
Example: GCF(18,24) = 6 | LCM(4,6) = 12
CONCEPT 14
Coordinate Plane
Quadrant I (+,+) | II (−,+) | III (−,−) | IV (+,−)
Example: Point (−3, 2): x<0, y>0 → Quadrant II
CONCEPT 15
Probability
P(event) = favorable outcomes / total outcomes
Example: P(even) rolling a die = 3/6 = 1/2