Grade 9 Mathematics is the final year of the Senior Phase and must lay a complete foundation for FET Mathematics or Mathematical Literacy. The CAPS curriculum consolidates algebra, functions, geometry and data handling at the highest Senior Phase level. Learners work with quadratic expressions and equations, more complex functions, formal geometry proofs and trigonometry. Grade 9 Maths is the most important year before the FET split — the concepts covered here appear directly in Grade 10.
- Products: (a + b)² = a² + 2ab + b², (a - b)² = a² - 2ab + b², (a + b)(a - b) = a² - b²
- Factorise: common factor, difference of squares, perfect squares, trinomials ax² + bx + c
- Algebraic fractions: simplify, add, subtract with polynomial denominators
- Solve quadratic equations: by factorisation
- Solve simultaneous equations: substitution and elimination methods
- Exponential equations: solve equations with same base
- Number patterns: quadratic sequences — first and second difference
- Word problems: set up and solve equations from context
- Functions: definition, domain, range, notation f(x)
- Linear functions: y = mx + c — gradient, intercepts, parallel and perpendicular lines
- Quadratic functions: y = ax² + q — shape, turning point, axis of symmetry, roots
- Hyperbolic functions: y = a/x + q — asymptotes, shape, domain and range
- Exponential functions: y = ab^x — growth and decay, shape
- Draw and interpret all four function types on the same set of axes
- Determine equations of functions from graphs
- Financial mathematics: simple and compound interest — growth and decay applications
- Congruent triangles: full proof using all four conditions (SSS, SAS, AAS, RHS)
- Similar triangles: proof using AA condition and proportionality
- Theorem of Pythagoras: proof and converse application
- Properties of quadrilaterals: formal proofs — parallelogram, rectangle, rhombus, square
- Circle geometry: introduction — parts of a circle, chord, arc, tangent
- Trigonometry: sin, cos, tan in right-angled triangles — calculate sides and angles
- Trig ratios: sin²θ + cos²θ = 1 — application
- Solve 2D problems using trigonometry
- Volume and surface area: cone, pyramid, sphere — formulae and calculation
- Enlargement and reduction: effect on area and volume
- Data: measures of central tendency and spread from grouped data
- Cumulative frequency: ogive — draw and use to find median, quartiles
- Box-and-whisker plots: draw and interpret
- Scatter plots: correlation coefficient — positive, negative, none
- Revision of all algebra, functions and geometry for FET readiness
- Examination strategy: time allocation, showing working, checking answers
Factorise completely before solving. Always take out a common factor first. Then check for difference of squares. Then trinomial. Never skip steps.
Geometry proofs need reasons. Every statement must have a reason in brackets: (opp. sides of parallelogram are equal), (SSS), (Pythagoras). No reason = no mark.
For graphs: calculate the key points. x-intercepts (let y = 0), y-intercept (let x = 0), turning point. Plot these first, then sketch the curve.
Trig ratios: SOH-CAH-TOA. Sin = Opp/Hyp. Cos = Adj/Hyp. Tan = Opp/Adj. Learn it once, use it for life.
Grade 9 Maths determines Grade 10 placement. If you are aiming for Pure Maths in Grade 10, you need consistent 60%+ in Grade 9. Start building that habit now.