Grade 11 Mathematics Past Papers

Quadratic Equations and Inequalities is one of the highest-yield topics in Grade 11 CAPS Mathematics Paper 1. Learners must solve quadratic equations using three methods: factorisation, completing the square, and the quadratic formula (x = [−b ± √(b² − 4ac)] / 2a). The discriminant Δ = b² − 4ac determines the nature of roots: Δ > 0 gives two real unequal roots (rational when Δ is a perfect square, irrational otherwise); Δ = 0 gives two equal real roots; and Δ < 0 means no real roots exist.

Simultaneous equations — one linear and one quadratic — are solved by substitution: the linear equation yields one variable in terms of the other, which is substituted into the quadratic. NSC Paper 1 also tests quadratic inequalities, requiring learners to factorise, identify critical values, and express the solution set using interval notation (e.g., −2 < x < 3) or set-builder notation. Completing the square is also the algebraic gateway to writing a quadratic in vertex form — essential for Functions.

The Functions chapter of Grade 11 CAPS Mathematics requires learners to analyse the effect of parameters a, p, and q on three key graph families. For the parabola y = a(x + p)² + q: a controls direction of opening and vertical stretch; p shifts the axis of symmetry horizontally; q is the vertical shift and determines the minimum or maximum value. For the hyperbola y = a/(x + p) + q: p displaces the vertical asymptote and q displaces the horizontal asymptote. For the exponential graph y = ab^{(x + p)} + q: a governs reflection and stretch while q defines the horizontal asymptote.

NSC Paper 1 CAPS questions require learners to determine the equation of each function from a given graph, identify all key features (intercepts, asymptotes, axes of symmetry, turning point, domain, and range), and describe transformations precisely. Mixed-function questions — reading off coordinates shared between two graphs or solving graphically — are a consistent feature of Grade 11 Paper 1 examinations.

Grade 11 CAPS Trigonometry introduces reduction formulae — systematic rules for rewriting trigonometric ratios of angles in the second, third, and fourth quadrants as equivalent expressions involving a first-quadrant reference angle. Key reductions include sin(180° − θ) = sin θ, cos(180° − θ) = −cos θ, sin(360° − θ) = −sin θ, and their third- and fourth-quadrant equivalents. Learners must know the CAST diagram and apply reductions fluently in simplification and proof problems.

Co-function identities (sin θ = cos(90° − θ)) and negative-angle identities complete the reduction toolkit tested in NSC Paper 2. The Sine Rule, Cosine Rule, and Area Formula (Area = ½ab sin C) are applied in 2D context problems involving non-right-angled triangles — requiring learners to select the correct rule for the given information and interpret answers in the context of the real-world scenario described.

Grade 11 Euclidean Geometry introduces the foundational circle theorems that build directly toward the full Grade 12 CAPS circle geometry syllabus. The core CAPS results at Grade 11 level include: the tangent to a circle is perpendicular to the radius drawn to the point of tangency; the perpendicular from the centre to a chord bisects the chord (and conversely, the line from the centre to the midpoint of a chord is perpendicular to the chord); and the angle in a semicircle equals 90°.

NSC Paper 2 tests these theorems through formal proof questions — where the correct theorem name must be cited as a reason — and multi-step riders. Riders require learners to identify all applicable circle geometry theorems from a diagram, combine them with properties of triangles or parallel lines, and present a structured logical argument. Mastery of Grade 11 Euclidean Geometry is essential preparation for the higher-order Grade 12 CAPS similarity and proportionality proofs.