Pre-Algebra Master Quiz

1

Integers & Absolute Value

UNIT 1

|a| = distance from 0 on number line
−(−a) = a |−a| = |a|

Adding integers: same sign → add & keep sign; different sign → subtract & take larger sign

Subtracting: a − b = a + (−b) (add the opposite)

Multiplying/Dividing: same signs → positive; different signs → negative

✏ Example

|−7| = 7 | −3 − (−5) = −3 + 5 = 2 | (−4)(−3) = 12

2

Fractions, Decimals & Percents

UNIT 2

a/b ÷ c/d = a/b × d/c
% = (part ÷ whole) × 100

LCM: find Least Common Multiple to add/subtract fractions

To divide fractions: multiply by the reciprocal (flip the second fraction)

Percent to decimal: divide by 100 | Decimal to percent: multiply by 100

✏ Example

2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6 | 35% = 0.35

3

Ratios, Proportions & Rates

UNIT 3

a/b = c/d → a × d = b × c (Cross-multiply)

Rate: ratio comparing two different units (e.g., miles per hour)

Unit rate: denominator = 1

Scale factor: ratio of similar figure measurements

✏ Example

3/x = 6/10 → 6x = 30 → x = 5

4

Algebraic Expressions

UNIT 4

Distributive: a(b + c) = ab + ac
Combine Like Terms: 3x + 5x = 8x

Term: a number, variable, or product of both

Coefficient: the number in front of a variable (in 4x, coefficient = 4)

Like terms must have the same variable AND same exponent

✏ Example

3(2x − 4) = 6x − 12 | 5x + 3x − 2 = 8x − 2

5

Linear Equations (One Variable)

UNIT 5

Goal: isolate the variable
Do same operation to both sides

Inverse operations: undo addition with subtraction, multiply with divide

Two-step: first undo addition/subtraction, then multiplication/division

Always check your answer by substituting back into the original equation

✏ Example

2x + 5 = 13 → 2x = 8 → x = 4 ✓ (check: 2×4+5=13)

6

Inequalities

UNIT 6

Multiply/Divide by NEGATIVE → FLIP the sign
−2x < 6 → x > −3

Symbols: < (less than), > (greater than), ≤ (≤), ≥ (≥)

Open circle: < or > (not included) | Closed circle: ≤ or ≥ (included)

Solution is a range of values, not just one number

✏ Example

3x − 4 ≥ 8 → 3x ≥ 12 → x ≥ 4 (closed circle at 4)

7

Coordinate Plane & Graphing

UNIT 7

Slope = (y₂ − y₁) / (x₂ − x₁) = rise/run
y = mx + b (slope-intercept form)

Origin (0,0) | Points (x, y) | x = horizontal, y = vertical

m = slope (steepness) | b = y-intercept (where line crosses y-axis)

Positive slope: goes up left to right | Negative: goes down

✏ Example

Slope from (1,2) to (3,8): (8−2)/(3−1) = 6/2 = 3

8

Exponents & Scientific Notation

UNIT 8

aᵐ × aⁿ = aᵐ⁺ⁿ aᵐ ÷ aⁿ = aᵐ⁻ⁿ
(aᵐ)ⁿ = aᵐⁿ a⁰ = 1 a⁻ⁿ = 1/aⁿ

Scientific notation: a × 10ⁿ where 1 ≤ a < 10

Large numbers: positive exponent | Small decimals: negative exponent

Square roots: √(a²) = a (for a ≥ 0)

✏ Example

x³ × x⁴ = x⁷ | 0.0035 = 3.5 × 10⁻³

9

Geometry: Area, Perimeter & Volume

UNIT 9

Rectangle: A = lw, P = 2(l+w)
Triangle: A = ½bh
Circle: A = πr², C = 2πr
Pythagorean: a² + b² = c²

Area = square units | Perimeter/Circumference = linear units

Rectangular prism volume: V = lwh | Cylinder: V = πr²h

Pythagorean theorem: only for RIGHT triangles; c = hypotenuse (longest side)

✏ Example

Right triangle: a=3, b=4 → c² = 9+16 = 25 → c = 5

10

Statistics: Mean, Median, Mode & Probability

UNIT 10

Mean = (sum of all values) / (number of values)
P(event) = favorable outcomes / total outcomes

Median: middle value when data is ordered (if even count, average the two middle)

Mode: value that appears most often (can be more than one or none)

Range = maximum − minimum | Probability: 0 ≤ P ≤ 1

✏ Example

Data: 2,4,4,6,8 → Mean=4.8, Median=4, Mode=4, Range=6

Master QuizAll Units

Integers & Absolute Value

Fractions, Decimals & Percents

Ratios, Proportions & Rates

Algebraic Expressions

Linear Equations (One Variable)

Inequalities

Coordinate Plane & Graphing

Exponents & Scientific Notation

Geometry: Area, Perimeter & Volume

Statistics: Mean, Median, Mode & Probability

Master Quiz
All Units