Grade 9 Math Exam Cheat Sheet: Algebra, Linear Relations, and Geometry Formulas
The rules and formulas most grade 9 math courses cover — organized for quick final exam review.
Before you start: Grade 9 math courses vary by school and country. This grade 9 math exam cheat sheet covers common topics: number sense, exponent laws, algebra, linear relations, and measurement. Check your course outline and only bring a formula sheet into the exam if your teacher allows it.
Grade 9 math builds the foundation for everything after it. This grade 9 math exam cheat sheet gathers the rules and formulas you’ll use most.
Number Sense and Percent
- Order of operations: Brackets, exponents, division and multiplication (left to right), addition and subtraction (left to right).
- Integer signs: Same signs multiply to positive; different signs multiply to negative.
- Percent of a number: Convert to decimal and multiply (15% of 80 = 0.15 × 80 = 12).
- Percent change: (New − original) ÷ original × 100.
- Ratios and proportions: Cross-multiply to solve a ÷ b = c ÷ d.
Grade 9 Math Exam Cheat Sheet: Exponent Laws
| Law | Rule | Example |
|---|---|---|
| Product | aᵐ × aⁿ = aᵐ⁺ⁿ | x³ × x² = x⁵ |
| Quotient | aᵐ ÷ aⁿ = aᵐ⁻ⁿ | x⁵ ÷ x² = x³ |
| Power of a power | (aᵐ)ⁿ = aᵐⁿ | (x²)³ = x⁶ |
| Zero exponent | a⁰ = 1 | 7⁰ = 1 |
| Negative exponent | a⁻ⁿ = 1 ÷ aⁿ | 2⁻³ = 1/8 |
Algebra and Equations
- Like terms: Only combine terms with the same variable and exponent (3x + 2x = 5x, but 3x + 2x² stays as is).
- Distributive property: a(b + c) = ab + ac.
- Solving equations: Do the same operation to both sides to isolate the variable.
- Check your answer: Substitute it back into the original equation.
Linear Relations
- Slope-intercept form: y = mx + b.
- Slope: m = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁).
- Direct variation: Passes through the origin (y = mx).
- Partial variation: Has a starting value (y = mx + b, with b ≠ 0).
- Horizontal line: y = b (slope 0). Vertical line: x = a (undefined slope).
Measurement Formulas
| Shape | Formula |
|---|---|
| Rectangle area | A = l × w |
| Triangle area | A = ½ × b × h |
| Circle area / circumference | A = πr²; C = 2πr |
| Rectangular prism volume | V = l × w × h |
| Cylinder volume | V = πr²h |
| Cone volume | V = ⅓πr²h |
| Sphere volume | V = ⁴⁄₃πr³ |
| Pythagorean theorem | a² + b² = c² |
Key Takeaways
- Know the order of operations and percent calculations.
- Memorize the five exponent laws with examples.
- Solve equations by doing the same thing to both sides, then check.
- Understand slope, y = mx + b, and direct vs. partial variation.
- Learn area, volume, and Pythagorean formulas — and always include units.
Frequently Asked Questions
What topics are on a grade 9 math exam?
Many grade 9 math courses cover number sense, exponent laws, algebra, linear relations, and measurement such as area and volume. Check your course outline for specifics.
What are the exponent laws?
The main exponent laws are the product rule (add exponents), the quotient rule (subtract exponents), the power of a power (multiply exponents), the zero exponent (equals 1), and negative exponents (take the reciprocal).
What is the difference between direct and partial variation?
Direct variation passes through the origin (y = mx), while partial variation has a starting value (y = mx + b, where b isn’t zero).
Can I bring a formula sheet to my grade 9 math exam?
Only if your teacher allows it. Making one is still a great way to study.
The Bottom Line
This grade 9 math exam cheat sheet covers the foundations you’ll keep using for years. Practice each type of problem, check your work, and you’ll be ready for exam day.
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