Grade 10 Mathematics Past Papers 2025

Algebraic Expressions and Factoring is the gateway topic of Grade 10 CAPS Mathematics Paper 1. Learners must factorise trinomials of the form ax² + bx + c using the product-and-sum method, apply the difference of squares identity (a² − b² = (a + b)(a − b)), and use factoring by grouping for four-term expressions. Simplifying algebraic fractions — including multiplying, dividing, and adding expressions with polynomial numerators and denominators — requires complete factorisation before any cancellation, a discipline tested in every NSC Grade 10 Math Paper.

Linear equations and inequalities in one variable are solved algebraically and represented on a number line. Literal equations (changing the subject of a formula) and simultaneous linear equations — solved by substitution or elimination — are core CAPS Paper 1 skills. Fluency with these algebraic techniques is the single most important foundation a Grade 10 learner can build: every subsequent CAPS topic from quadratic equations to financial mathematics relies on confident, accurate algebraic manipulation.

The Functions chapter of Grade 10 CAPS Mathematics introduces three foundational graph families. The linear function y = mx + c: gradient m determines direction and steepness; c is the y-intercept; the x-intercept is found by setting y = 0. The parabola y = ax² + q: a determines whether the parabola opens upward (a > 0) or downward (a < 0) and controls its width; q shifts the turning point vertically. The hyperbola y = a/x + q: q defines the horizontal asymptote, with the vertical asymptote fixed at x = 0 at Grade 10 level.

NSC Grade 10 Math Papers require learners to sketch all three graph types with all intercepts and asymptotes clearly labelled, state the domain and range, and determine the equation of each function from a given graph. Intersection points — where two functions share a common coordinate — are calculated algebraically by equating the two expressions and verified from the sketch, building the graphical problem-solving skills needed for Grade 11 and 12 CAPS examinations.

Trigonometry Basics introduces Grade 10 CAPS learners to the three primary ratios in right-angled triangles: sin θ = opposite / hypotenuse, cos θ = adjacent / hypotenuse, and tan θ = opposite / adjacent — the SOH CAH TOA mnemonic. These ratios are used to calculate unknown sides and angles in 2D right-triangle problems drawn from real-world contexts such as heights of buildings, angles of elevation, and distances across rivers.

Special angles (0°, 30°, 45°, 60°, 90°) and their exact sine, cosine, and tangent values must be recalled without a calculator — these exact values appear in NSC Grade 10 Math Papers and directly underpin Grade 12 CAPS compound angle identities. Basic trigonometric graphs — y = sin θ, y = cos θ, and y = tan θ — are sketched for 0° ≤ θ ≤ 360°, with amplitude, period, and all key intercepts correctly identified and labelled in CAPS Paper 2 questions.

Grade 10 Euclidean Geometry establishes the formal proof conventions and geometric vocabulary used throughout the NSC Mathematics curriculum. Learners master line and angle geometry — vertically opposite angles (equal), angles on a straight line (supplementary), co-interior angles (supplementary for parallel lines), alternate angles (equal), and corresponding angles (equal) — and apply these results to calculate unknown angles with full geometric reasons in multi-step diagrams.

Triangle properties — the sum of interior angles (180°), the exterior angle theorem, and congruence tests (SSS, SAS, AAS, RHS) — are tested through formal proofs and application riders. Grade 10 CAPS quadrilateral properties — parallelogram, rectangle, rhombus, square, kite, and trapezium — are identified by their defining properties of sides, angles, and diagonals, and applied in NSC Grade 10 Math Paper 2 questions requiring angle calculations supported by correct geometric reasons. This formal reasoning foundation is the direct precursor to the circle geometry theorems and similarity proofs examined in Grades 11 and 12.