High School Mathematics Mastery
Notes (Grades 9–12)
These comprehensive, straight-to-the-point notes are tailored to help students from Grade 9 to
Grade 12 not only understand key mathematical concepts but also excel in assessments. These
notes are well-structured, contain formulas, tricks, diagrams, and practice questions—perfect
for students or tutors aiming to boost performance and confidence.
📒 Grade 9 Mathematics
✅ Algebra Basics
Concepts Covered:
- Variables, constants, expressions
- Expanding and factorising
- Simplifying algebraic expressions
Key Rules:
- Distributive Law: a(b + c) = ab + ac
- (a + b)^2 = a^2 + 2ab + b^2
- a^2 - b^2 = (a - b)(a + b)
Tips:
- Collect like terms
- Factorisation is the reverse of expanding
Practice:
1. Expand: (x + 5)^2
2. Factorise: x^2 - 9
3. Simplify: 3a + 2b - 4a + 6b
📐 Diagrams and Formula Sheets will be inserted here in the full version.
Grade 9 – Formula Sheet
- Distributive Law: a(b + c) = ab + ac
- Perfect Square: (a + b)^2 = a^2 + 2ab + b^2
- Difference of Squares: a^2 - b^2 = (a - b)(a + b)
- Linear Equation: y = mx + c
- Triangle angle sum: 180°
, Grade 9 – Exam-Style Mock Questions
1. 1. Expand and simplify: (x + 2)(x - 5)
2. 2. Solve for x: 3x - 7 = 2x + 8
3. 3. A triangle has angles 40° and 60°. Find the third angle.
4. 4. Plot the graph of y = -x + 3 using at least 2 points.
Grade 10 – Formula Sheet
- Quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)
- Discriminant D = b² - 4ac
- Trig Ratios: SOH-CAH-TOA
- Pythagoras: a² + b² = c²
Grade 10 – Exam-Style Mock Questions
5. 1. Solve using the quadratic formula: x² - 4x - 5 = 0
6. 2. Factorise: x² - 6x + 9
7. 3. A ladder leans against a wall. The ladder is 10m long and touches the wall at 8m height.
Find the distance from the wall.
8. 4. Solve the system: 2x + y = 10 and x - y = 1
Grade 11 – Formula Sheet
- Laws of Indices: a^m * a^n = a^(m+n), (a^m)^n = a^(mn)
- Surd Rules: √a * √b = √(ab), Rationalise: 1/√a = √a/a
- Circle Theorems (angles in semicircle = 90°, tangent perpendicular to radius)
- Statistics: Mean = Σx/n, SD = √(Σ(x - mean)²/n)
Grade 11 – Exam-Style Mock Questions
9. 1. Simplify: (2x^3 * x^2) / x^4
10. 2. Rationalise: 5 / √3
11. 3. A circle has a chord that subtends an angle of 60° at the circumference. What is the angle
at the centre?
12. 4. Find mean and standard deviation of the following set: 4, 6, 8, 6, 10
Grade 12 – Formula Sheet
- Derivative of x^n = nx^(n-1)
- ∫ x^n dx = (x^(n+1))/(n+1) + C
- Sine Rule: a/sin A = b/sin B = c/sin C
- Cosine Rule: c² = a² + b² - 2ab cos C
- Matrix Multiplication, Determinant of 2x2: ad - bc
- Log Laws: log(ab) = log a + log b
Grade 12 – Exam-Style Mock Questions
13. 1. Differentiate: f(x) = 5x³ - 2x² + 4x - 7
Notes (Grades 9–12)
These comprehensive, straight-to-the-point notes are tailored to help students from Grade 9 to
Grade 12 not only understand key mathematical concepts but also excel in assessments. These
notes are well-structured, contain formulas, tricks, diagrams, and practice questions—perfect
for students or tutors aiming to boost performance and confidence.
📒 Grade 9 Mathematics
✅ Algebra Basics
Concepts Covered:
- Variables, constants, expressions
- Expanding and factorising
- Simplifying algebraic expressions
Key Rules:
- Distributive Law: a(b + c) = ab + ac
- (a + b)^2 = a^2 + 2ab + b^2
- a^2 - b^2 = (a - b)(a + b)
Tips:
- Collect like terms
- Factorisation is the reverse of expanding
Practice:
1. Expand: (x + 5)^2
2. Factorise: x^2 - 9
3. Simplify: 3a + 2b - 4a + 6b
📐 Diagrams and Formula Sheets will be inserted here in the full version.
Grade 9 – Formula Sheet
- Distributive Law: a(b + c) = ab + ac
- Perfect Square: (a + b)^2 = a^2 + 2ab + b^2
- Difference of Squares: a^2 - b^2 = (a - b)(a + b)
- Linear Equation: y = mx + c
- Triangle angle sum: 180°
, Grade 9 – Exam-Style Mock Questions
1. 1. Expand and simplify: (x + 2)(x - 5)
2. 2. Solve for x: 3x - 7 = 2x + 8
3. 3. A triangle has angles 40° and 60°. Find the third angle.
4. 4. Plot the graph of y = -x + 3 using at least 2 points.
Grade 10 – Formula Sheet
- Quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)
- Discriminant D = b² - 4ac
- Trig Ratios: SOH-CAH-TOA
- Pythagoras: a² + b² = c²
Grade 10 – Exam-Style Mock Questions
5. 1. Solve using the quadratic formula: x² - 4x - 5 = 0
6. 2. Factorise: x² - 6x + 9
7. 3. A ladder leans against a wall. The ladder is 10m long and touches the wall at 8m height.
Find the distance from the wall.
8. 4. Solve the system: 2x + y = 10 and x - y = 1
Grade 11 – Formula Sheet
- Laws of Indices: a^m * a^n = a^(m+n), (a^m)^n = a^(mn)
- Surd Rules: √a * √b = √(ab), Rationalise: 1/√a = √a/a
- Circle Theorems (angles in semicircle = 90°, tangent perpendicular to radius)
- Statistics: Mean = Σx/n, SD = √(Σ(x - mean)²/n)
Grade 11 – Exam-Style Mock Questions
9. 1. Simplify: (2x^3 * x^2) / x^4
10. 2. Rationalise: 5 / √3
11. 3. A circle has a chord that subtends an angle of 60° at the circumference. What is the angle
at the centre?
12. 4. Find mean and standard deviation of the following set: 4, 6, 8, 6, 10
Grade 12 – Formula Sheet
- Derivative of x^n = nx^(n-1)
- ∫ x^n dx = (x^(n+1))/(n+1) + C
- Sine Rule: a/sin A = b/sin B = c/sin C
- Cosine Rule: c² = a² + b² - 2ab cos C
- Matrix Multiplication, Determinant of 2x2: ad - bc
- Log Laws: log(ab) = log a + log b
Grade 12 – Exam-Style Mock Questions
13. 1. Differentiate: f(x) = 5x³ - 2x² + 4x - 7
