Study notes

Grade 10 Mathematics Notes
1. Number System
 • Real Numbers: Rational and Irrational Numbers
 • Integers, Whole Numbers, Natural Numbers
 • Properties: Commutative, Associative, Distributive
 • Exponents and Powers: a^m × a^n = a^(m+n); (a^m)^n = a^(mn); a^0 = 1


2. Algebraic Expressions
 • Simplifying expressions using laws of exponents
 • Multiplying binomials using FOIL method
 • Factorisation: Common factor, Difference of squares, Trinomials
 • Algebraic Fractions: Simplify and perform operations (add, subtract, multiply, divide)


3. Equations and Inequalities
 • Linear Equations: ax + b = 0
 • Quadratic Equations: ax² + bx + c = 0 (Solve by factorising or using the quadratic
formula)
 • Inequalities: Solve and represent on a number line


4. Functions and Graphs
 • Linear Functions: y = mx + c
 • Quadratic Functions: y = ax² + bx + c
 • Exponential Functions: y = a^x
 • Interpret and sketch graphs


5. Number Patterns
 • Arithmetic Sequences: Tn = a + (n−1)d
 • Geometric Sequences: Tn = ar^(n−1)
 • Finding general term (Tn)
 • Recognising patterns from tables


6. Trigonometry
 • Definitions: sin(θ), cos(θ), tan(θ) = opposite/adjacent/hypotenuse
 • Right-angled triangle ratios
 • Trigonometric values for 0°, 30°, 45°, 60°, 90°