Concept Review & Formula Bank
Master these key concepts before attempting the practice test. Each unit includes the essential formulas you must memorize and a worked example.
Number theory covers the fundamental properties of integers including divisibility, prime factorization, LCM, GCF, and number patterns.
LCM(a, b) = (a × b) ÷ GCF(a, b)
Prime: divisible only by 1 and itself
Even × Odd = Even · Odd ± Odd = Even
Divisibility by 3: digit sum divisible by 3
Divisibility by 9: digit sum divisible by 9
- Primes to 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
- Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
- A number is divisible by 4 if its last two digits are divisible by 4
Converting between fractions, decimals, and percents is essential. Know how to compare, order, and operate on all three forms.
Percent = (Part ÷ Whole) × 100
Part = (Percent ÷ 100) × Whole
% Change = [(New − Old) ÷ Old] × 100
Fraction ÷ Fraction: multiply by reciprocal
- 1/4 = 0.25 = 25% ; 1/3 ≈ 0.333 = 33.3% ; 1/5 = 0.2 = 20%
- 3/4 = 0.75 = 75% ; 2/3 ≈ 0.667 = 66.7%
- To find 15%: find 10%, then add half of that
Ratios compare two quantities. Proportions set two ratios equal. Rates express a ratio with different units (e.g., miles per hour).
Cross multiply: a/b = c/d → ad = bc
Distance = Rate × Time (D = R × T)
Unit rate = total ÷ number of units
Scale: actual = scale × map distance
- If ratio of A:B = m:n, then A = mk and B = nk for some value k
- Combined rate: if A does job in a hours, rate = 1/a per hour
- Average speed = Total Distance ÷ Total Time
Algebra involves using variables to represent unknown quantities. Solve equations by performing inverse operations on both sides.
Distributive: a(b + c) = ab + ac
FOIL: (a+b)(c+d) = ac + ad + bc + bd
Difference of squares: a² − b² = (a+b)(a−b)
Quadratic formula: x = [−b ± √(b²−4ac)] / 2a
- Solve for x: isolate x by adding/subtracting, then multiplying/dividing
- Inequality: flip sign when multiplying/dividing by a negative number
- (a + b)² = a² + 2ab + b² ; (a − b)² = a² − 2ab + b²
Translate English phrases into mathematical expressions. Identify the unknown, write an equation, and solve systematically.
"more than" → add (+)
"less than / fewer" → subtract (−)
"of" (with percent) → multiply (×)
"per" → divide (÷) or rate
"consecutive integers" → n, n+1, n+2, ...
- Simple interest: I = P × r × t
- Mixture problems: quantity × concentration = amount of substance
- Age problems: use a variable, express all ages in terms of it
Know area, perimeter, and volume formulas. Understand properties of triangles, circles, quadrilaterals, and 3-D shapes.
Triangle: A = ½bh ; Pythagorean: a²+b²=c²
Circle: A = πr² ; C = 2πr
Rectangle: A = lw ; P = 2(l+w)
Trapezoid: A = ½(b₁+b₂)h
Cylinder: V = πr²h ; Cube: V = s³
- Triangle angles sum = 180° ; Quadrilateral = 360°
- Common Pythagorean triples: 3-4-5, 5-12-13, 8-15-17
- 30-60-90: sides = x : x√3 : 2x ; 45-45-90: x : x : x√2
Analyze data sets using statistical measures. Interpret graphs, charts, and tables accurately.
Mean = Sum of values ÷ Number of values
Median = middle value when ordered
Mode = most frequently occurring value
Range = Maximum − Minimum
Probability = Favorable ÷ Total outcomes
- For even number of data: median = mean of two middle values
- Outliers affect mean more than median
- Weighted average: (sum of weight × value) ÷ total weight
Identify arithmetic and geometric sequences, find nth terms, and recognize functional relationships.
Arithmetic: aₙ = a₁ + (n−1)d
Arithmetic sum: Sₙ = n(a₁+aₙ)/2
Geometric: aₙ = a₁ × rⁿ⁻¹
Function notation: f(x) = expression
- Common difference (d) in arithmetic sequence is constant
- Common ratio (r) in geometric sequence is constant
- f(x) = 2x + 3 means: substitute x, multiply by 2, add 3
SSAT Mathematics Practice Test
20 questions · 5 choices each · Select your answer — feedback appears immediately