Grade 11 Mathematics is the most demanding year of the FET Phase and the direct preparation for the Grade 12 NSC examination. The CAPS curriculum extends algebra, functions, trigonometry, Euclidean geometry, analytical geometry, statistics and probability to a level where formal proof and multi-step reasoning are central. Every topic in Grade 11 recurs in Grade 12 — mastery here is non-negotiable.
- Quadratic equations: completing the square (full), quadratic formula x = (−b ± √(b²−4ac)) / 2a
- Quadratic inequalities: solve and represent on number line
- Nature of roots: discriminant Δ = b² − 4ac — determine and interpret
- Quadratic equations with rational expressions: algebraic fractions
- Surds: simplify, rationalise the denominator, solve surd equations
- Exponential equations: with different bases — use logs (introduction) or inspection
- Simultaneous equations: one linear, one quadratic — full solution
- Word problems: quadratic models in real contexts
- Quadratic function y = a(x−p)² + q: transformations — shift, reflect, stretch
- Cubic function: y = ax³ — basic shape, turning points, roots
- Exponential function y = ab^(x+p) + q: transformations
- Logarithmic function: y = log_a x — inverse of exponential, domain, range, graph
- Inverse functions: definition, notation f⁻¹(x), restrict domain for inverse to be a function
- Finance: compound interest, decay, nominal vs effective interest rates
- Annuities: future value of annuity — F = x[(1+i)ⁿ − 1]/i
- Loan repayment: present value of annuity — P = x[1−(1+i)^(−n)]/i
- Trig identities: sin²θ + cos²θ = 1, tanθ = sinθ/cosθ — prove and apply
- Compound angle formulae: sin(A±B), cos(A±B), sin2A, cos2A
- Trig equations: general solution — sin θ = k → θ = arcsin k + 360°n
- 2D and 3D trig problems: apply sine rule, cosine rule, area formula
- Circle geometry theorems: angle at centre = 2 × angle at circumference
- Cyclic quadrilateral: opposite angles supplementary
- Tangent-chord angle: equals inscribed angle in alternate segment
- Write formal proofs using circle geometry theorems
- Analytical geometry: distance, midpoint, gradient revision
- Equation of a circle: (x−a)² + (y−b)² = r² — centre, radius, write equation
- Tangent to circle: perpendicular to radius at point of tangency — find equation
- Statistics: regression — least-squares regression line, correlation coefficient r
- Interpret r: strength and direction of linear relationship
- Probability: counting principles — fundamental counting principle, factorial notation
- Permutations: ⁿPᵣ = n!/(n−r)! — with and without repetition
- Combinations: ⁿCᵣ = n!/[r!(n−r)!] — apply in probability
Quadratic formula: write it out every time. x = (−b ± √(b²−4ac)) / 2a. Do not try to remember the answer — derive it step by step.
Trig identity proofs: work on one side only. Choose the more complex side. Never move terms across the equals sign.
Circle geometry: state the theorem. Every angle calculation needs a reason: 'angle at centre is twice angle at circumference'. No reason = no mark.
Annuity formulae are given — but know what each variable means. F = future value, P = present value, x = payment, i = interest per period, n = number of periods.
Grade 11 Maths is the hardest year. The jump from Grade 10 is steep. Work consistently — weekly practice beats last-minute cramming every time.