Grade 10 Mathematics is the first year of FET and dramatically raises the bar from Grade 9. The CAPS curriculum introduces algebraic manipulation, functions, Euclidean geometry, trigonometry, statistics and probability at a formal level. Grade 10 Maths is foundational — every topic introduced here recurs in Grades 11 and 12 at greater depth. Learners who master Grade 10 thoroughly are positioned strongly for the NSC examination.
- Algebraic expressions: products — (a±b)², (a+b)(a-b), (a±b)³
- Factorisation: HCF, difference of squares, sum/difference of cubes, trinomials, grouping
- Algebraic fractions: simplify, add, subtract, multiply, divide with polynomial denominators
- Equations: quadratic equations — factorisation, completing the square (intro)
- Simultaneous equations: linear and quadratic — substitution method
- Inequalities: solve and represent on number line and interval notation
- Nature of roots: discriminant Δ = b² - 4ac — determine number and type of roots
- Word problems: set up and solve quadratic equations from context
- Functions: definition, domain, range, notation, function vs non-function
- Linear function y = mx + c: gradient, intercepts, sketch, interpret
- Quadratic function y = ax² + bx + c: turning point (completing the square), axis, roots, sketch
- Hyperbola y = a/x + q: asymptotes, domain, range, sketch
- Exponential y = ab^x + q: growth/decay, asymptote, sketch
- Trigonometric functions: y = sin x, y = cos x, y = tan x — period, amplitude, sketch
- Determine equations of functions from graphs
- Financial maths: compound interest A = P(1+i)ⁿ, depreciation A = P(1-i)ⁿ
- Revised axioms and theorems: lines, angles, triangles — proofs required
- Circle geometry: parts of a circle, chord, arc, tangent, secant
- Midpoint theorem: proof and application
- Proportion theorem: a line parallel to one side of a triangle
- Trigonometry: sin, cos, tan in right-angled triangles — SOHCAHTOA
- Special angles: 30°, 45°, 60° — exact values without calculator
- Trig equations: solve for θ in [0°; 360°]
- 2D problems: angles of elevation and depression
- Measures of central tendency: mean, median, mode — ungrouped and grouped data
- Measures of spread: range, quartiles, interquartile range, semi-interquartile range
- Five-number summary: min, Q1, median, Q3, max
- Box-and-whisker plots: draw, interpret, compare two data sets
- Scatter plots: draw, identify correlation, line of best fit
- Probability: theoretical and experimental probability
- Probability of compound events: addition rule, complementary events
- Venn diagrams: represent and calculate probability
Factorise in order every time. HCF first → difference of squares → sum/difference of cubes → trinomial → grouping. Never skip the order.
Functions: always find key points first. x-intercepts, y-intercept, turning point, asymptotes. Plot these, then sketch.
Geometry proofs need reasons. Every statement must have a reason. No reason = no mark. Learn the standard phrasing.
Discriminant determines roots before you solve. Δ > 0: two real roots. Δ = 0: one real root. Δ < 0: no real roots. Check this first.
Grade 10 Maths repeats in Grades 11 and 12. Master each topic before moving on. Everything here comes back harder next year.