Core Concepts & Formulas
Review all units before taking the test. Memorize the highlighted formulas.
Order of Operations
PEMDAS: Parentheses → Exponents → Multiply/Divide (L→R) → Add/Subtract (L→R)
Prime Numbers
Divisible only by 1 and itself. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29… Note: 1 is NOT prime.
LCM & GCF
LCM: smallest common multiple. GCF: largest common factor. Use prime factorization.
Fractions & Decimals
a/b ÷ c/d = a/b × d/c. To compare fractions, cross-multiply or convert to decimals.
Must Memorize — Formulas
What is 15% of 240?
✓ 240 × 0.15 = 36
Linear Equations
Isolate the variable. Whatever you do to one side, do to the other side.
Slope
m = (y₂ − y₁) / (x₂ − x₁). Slope-intercept: y = mx + b
Inequalities
Flip the inequality sign when multiplying or dividing by a negative number.
Exponent Rules
aᵐ · aⁿ = aᵐ⁺ⁿ, aᵐ/aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1
Must Memorize — Formulas
If 3x − 7 = 11, what is x?
✓ 3x = 18 → x = 6
Triangle Rules
Angles sum to 180°. Pythagorean theorem: a² + b² = c². Area = ½ × b × h.
Circles
Area = πr². Circumference = 2πr. Diameter = 2r. Arc length = (θ/360°) × 2πr.
Polygons
Sum of interior angles of n-gon = (n−2) × 180°. Each angle of regular n-gon = (n−2)×180/n.
Volume & Surface Area
Cube: V = s³, SA = 6s². Rectangular prism: V = lwh. Cylinder: V = πr²h.
Must Memorize — Formulas
A right triangle has legs 6 and 8. What is the hypotenuse?
✓ 6² + 8² = 36 + 64 = 100 → c = 10
Mean / Median / Mode
Mean = sum ÷ count. Median = middle value (sorted). Mode = most frequent value.
Probability
P(event) = favorable outcomes / total outcomes. P(A and B) = P(A) × P(B) (independent).
Range & Spread
Range = max − min. Know how adding/removing values shifts the mean.
Counting
Permutation: nPr = n!/(n−r)!. Combination: nCr = n!/[r!(n−r)!].
Must Memorize — Formulas
Data set: {3, 7, 7, 9, 14}. Find mean, median, and mode.
✓ Mean = 40/5 = 8, Median = 7, Mode = 7
Ratios & Proportions
a:b = c:d → cross multiply: ad = bc. Scale: if 1 cm = 5 km, then 3 cm = 15 km.
Rate Problems
Distance = Rate × Time. Work done = Rate × Time. Combined rate: add individual rates.
Mixture Problems
Total value = Amount₁ × Price₁ + Amount₂ × Price₂. Set up a table to organize.
Sequences
Arithmetic: aₙ = a₁ + (n−1)d. Geometric: aₙ = a₁ × rⁿ⁻¹. Find pattern first.
Must Memorize — Formulas
A car travels 180 miles in 3 hours. What is its average speed?
✓ Speed = Distance / Time = 180 / 3 = 60 mph