Read each concept box, memorize the highlighted rule, then check the worked example before starting the test.
🔢Order of Operations
Operations must be performed in a fixed sequence so every person gets the same answer.
Memorize
PEMDAS — Parentheses → Exponents → Multiplication/Division (left to right) → Addition/Subtraction (left to right)
Example
3 + 2 × (4 + 1)² = 3 + 2 × 25 = 3 + 50 = 53
➕➖Integers (Signed Numbers)
Adding/subtracting integers depends on the signs; subtracting a negative is the same as adding a positive.
Memorize
Same signs → add and keep sign. Different signs → subtract smaller from larger, keep sign of bigger number. a − (−b) = a + b
Example
−7 + 12 − (−5) = −7 + 12 + 5 = 10
🍰Fractions
Add/subtract fractions using a common denominator; multiply numerators & denominators directly; divide by multiplying by the reciprocal.
Memorize
÷ fractions = × by the reciprocal (flip the 2nd fraction). Always simplify to lowest terms.
Example
5/6 ÷ 1/3 = 5/6 × 3/1 = 15/6 = 2 1/2
🔟Decimals
Line up decimal points to add/subtract. When multiplying, count total decimal places in both factors.
Memorize
Multiplying decimals: ignore decimals, multiply as whole numbers, then place the decimal point by counting total decimal digits.
Example
0.6 × 0.4 → 6×4=24 → 2 decimal places → 0.24
⚖️Ratios & Proportions
A ratio compares two quantities; a proportion is two equal ratios, solved by cross-multiplying.
Memorize
Simplify ratios by dividing by the GCF. For a/b = c/d, cross-multiply: a×d = b×c.
Example
x/4 = 15/20 → 20x = 60 → x = 3
%Percentages
"Percent" means "out of 100." To increase/decrease by a percent, find that percent of the number and add/subtract it.
Memorize
Part = Percent (as decimal) × Whole. New amount after p% increase = Original × (1 + p/100).
Example
$50 increased by 20% → 50 × 1.2 = $60
^Exponents & Square Roots
Exponents show repeated multiplication; square roots ask "what number times itself gives this?"
Memorize
Same base, multiplying: aᵇ × aᶜ = a^(b+c). √(perfect square): √81 = 9 because 9×9=81.
Example
2³ × 2² = 2⁵ = 32
🔬Scientific Notation
Used to write very large or very small numbers as a number between 1–10 multiplied by a power of 10.
Memorize
Moving decimal point right (small numbers) → negative exponent. Moving left (large numbers) → positive exponent.
Example
0.00045 → move decimal 4 places right → 4.5 × 10⁻⁴
xExpressions, Equations & Inequalities
Evaluate expressions by substituting values. Solve equations/inequalities by undoing operations with inverse operations (keep both sides balanced).
Memorize
Two-step equation: undo addition/subtraction first, then multiplication/division. For inequalities, flip the sign only when multiplying/dividing by a negative.
Example
3x + 5 = 20 → 3x = 15 → x = 5
📐GCF, LCM & Geometry
GCF is the largest shared factor; LCM is the smallest shared multiple. Triangle area uses base and height.
Memorize
Area of a triangle = 1/2 × base × height. LCM of 8 and 12: list multiples until they match → 24.
Example
Triangle: base 10, height 6 → 1/2 × 10 × 6 = 30 cm²
Tap an answer for each question. Correct answers trigger instant feedback — explanations appear right away. A full answer key is also collected at the end.