Grade 10 Math Exam Cheat Sheet: Quadratics, Linear Systems, Analytic Geometry, and Trig
The formulas and methods most grade 10 math courses test — with quick examples.
Before you start: Grade 10 math courses differ by school and country. This grade 10 math exam cheat sheet covers topics many courses include: linear systems, quadratics, analytic geometry, and trigonometry. Check your course outline, and only bring a formula sheet into the exam if your teacher allows it.
Grade 10 math introduces big ideas like quadratics and trigonometry. This grade 10 math exam cheat sheet puts the formulas and methods side by side for fast review.
Linear Systems
- Slope-intercept form: y = mx + b (m = slope, b = y-intercept).
- Slope: m = (y₂ − y₁) ÷ (x₂ − x₁).
- Solving systems: Graphing, substitution, or elimination.
- Number of solutions: One (lines cross), none (parallel lines), infinitely many (same line).
Grade 10 Math Exam Cheat Sheet: Quadratics
| Form | Equation | Tells you |
|---|---|---|
| Standard | y = ax² + bx + c | y-intercept is c; opens up if a > 0 |
| Vertex | y = a(x − h)² + k | Vertex at (h, k); axis of symmetry x = h |
| Factored | y = a(x − r)(x − s) | x-intercepts (zeros) at r and s |
- Quadratic formula: x = [−b ± √(b² − 4ac)] ÷ 2a.
- Discriminant (b² − 4ac): Positive → 2 real roots; zero → 1 root; negative → no real roots.
- Factoring patterns: Difference of squares a² − b² = (a − b)(a + b); perfect square a² + 2ab + b² = (a + b)².
- Completing the square: Converts standard form to vertex form.
Analytic Geometry
| Formula | Expression |
|---|---|
| Distance | d = √[(x₂ − x₁)² + (y₂ − y₁)²] |
| Midpoint | M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2) |
| Circle centered at origin | x² + y² = r² |
| Parallel lines | Same slope |
| Perpendicular lines | Slopes are negative reciprocals (m₁ × m₂ = −1) |
Trigonometry
- SOH CAH TOA: sin = opposite ÷ hypotenuse; cos = adjacent ÷ hypotenuse; tan = opposite ÷ adjacent.
- Pythagorean theorem: a² + b² = c² (right triangles).
- Sine law: a ÷ sin A = b ÷ sin B = c ÷ sin C.
- Cosine law: c² = a² + b² − 2ab cos C.
- Calculator check: Make sure it’s in degree mode.
Exam Tips
- Show every step — partial marks add up.
- Check answers by substituting them back into the original equation.
- Sketch graphs to check whether your answers make sense.
- Practice mixed problems: See our tips on preparing for math exams.
Key Takeaways
- Know slope, y = mx + b, and the three ways to solve linear systems.
- Master the three quadratic forms, the quadratic formula, and the discriminant.
- Memorize distance, midpoint, and perpendicular-slope rules.
- Use SOH CAH TOA for right triangles and the sine and cosine laws for others.
Frequently Asked Questions
What topics are on a grade 10 math exam?
Many grade 10 math courses cover linear systems, quadratics, analytic geometry, and trigonometry. Topics vary by school, so check your course outline.
What is the quadratic formula?
The quadratic formula is x = [−b ± √(b² − 4ac)] ÷ 2a, used to solve equations in the form ax² + bx + c = 0.
What does the discriminant tell you?
The discriminant, b² − 4ac, tells you the number of real roots: positive means two, zero means one, and negative means none.
Can I bring a formula sheet to my grade 10 math exam?
Only if your teacher allows it. If not, making one is still a great way to memorize the formulas.
The Bottom Line
This grade 10 math exam cheat sheet covers the formulas that matter most. Pair it with plenty of practice problems, and you’ll walk into your exam ready.
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