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Browse Mathematical Literacy📚 Grade 10 lessons(27)
Every lesson is one focused sub-topic, worked in full, with a printable worksheet and an exam paper with its memo.
Term 1
Algebraic Fractions: Simplify, Add & Subtract (Grade 10)Simplifying algebraic fractions by factorising, multiplying and dividing them, and adding or subtracting using a lowest common denominator — including denominators that factorise as cubes.10min read · lesson, worksheet & exam paperFactorising: Grouping in Pairs & the Cubes (Grade 10)A decision guide based on counting the terms, then the two new Grade 10 methods: grouping four terms in pairs, and the sum and difference of two cubes.10min read · lesson, worksheet & exam paperLaws of Exponents & Rational Exponents (Grade 10)The exponent laws extended to negative and fractional powers, converting between roots and rational exponents, simplifying harder expressions, and solving exponential equations by matching bases.11min read · lesson, worksheet & exam paperLinear Inequalities & Interval Notation (Grade 10)Solving linear inequalities, the one rule that catches everybody (dividing by a negative), showing the answer on a number line, and writing it in interval notation.9min read · lesson, worksheet & exam paperLiteral Equations: Changing the Subject of a FormulaRearranging a formula to make a different letter the subject — the same inverse operations as solving an equation, but the answer is an expression instead of a number.8min read · lesson, worksheet & exam paperMultiplying a Binomial by a Trinomial (Grade 10)Expanding products like (2x + 3)(x² − x + 4) reliably using a grid, then collecting like terms — plus the cube identities that come from it.8min read · lesson, worksheet & exam paperReal Numbers, Surds & Rounding (Grade 10)Rational versus irrational numbers, working out which two integers a surd lies between, and rounding to a given number of decimal places or significant figures — the opening skills of the Grade 10 syllabus.8min read · lesson, worksheet & exam paperSimultaneous Linear Equations (Grade 10)Solving two equations in two unknowns by substitution and by elimination, what the solution means graphically, and the word problems that lead to a pair of equations.10min read · lesson, worksheet & exam paperSpecial Angles, Reciprocal Ratios & Trig Equations (Grade 10)The exact values for 0°, 30°, 45°, 60° and 90° without a calculator, the reciprocal ratios cosec, sec and cot, and solving simple trig equations for angles between 0° and 90°.11min read · lesson, worksheet & exam paperTrigonometry: SOH-CAH-TOA and Every Question TypeEvery right-angled trig question in Grade 10 — naming sides, finding a side with sin/cos/tan, finding the hypotenuse, finding an angle with the inverse, special angles, and an angle-of-elevation application — each worked in full, with a diagram and worksheet.15min read · lesson, worksheet & exam paperTrigonometry: Solving Triangles & Angles of ElevationUsing sin, cos and tan to find a missing side or angle in a right-angled triangle, and applying them to angles of elevation and depression in real problems.9min read · lesson, worksheet & exam paper
Term 2
Analytical Geometry: All the Exam Question TypesThe three core formulas — distance, midpoint, gradient — and every way an exam uses them: parallel and perpendicular lines, collinear points, and finding an unknown coordinate, each worked in full with a worksheet.15min read · lesson, worksheet & exam paperCongruent & Similar Triangles (Grade 10)The four conditions for congruency (SSS, SAS, AAS and RHS), what similarity means, and how to set out a proof so that every statement earns its reason.11min read · lesson, worksheet & exam paperProperties of Quadrilaterals & Their Proofs (Grade 10)Definitions and full property lists for the parallelogram, rectangle, rhombus, square, trapezium and kite — sides, angles and diagonals — plus how to prove a shape is a parallelogram.11min read · lesson, worksheet & exam paperSketching the Parabola: The Complete Exam GuideThe full method for sketching any quadratic — plus every exam variation: upward and downward parabolas, no x-intercepts, and finding the equation from a graph — each worked in full, with a diagram and a worksheet.15min read · lesson, worksheet & exam paperSolving Equations by Factorisation (Product = 0)The zero-product rule, solving equations of the form (x + a)(x + b) = 0, factorising first when the equation is not yet in that form, and dividing polynomials by a monomial.9min read · lesson, worksheet & exam paperStraight-Line Graphs: Reading y = mx + cEvery straight line is described by y = mx + c. Once you know what m and c do, you can sketch any line and read any graph.6min read · lesson, worksheet & exam paperThe Hyperbola & Exponential Graph (Grade 10)Sketching y = a/x and y = abᵙ, finding asymptotes and intercepts, and reading the effect of a, b and a vertical shift q — the two curved graphs of Grade 10.10min read · lesson, worksheet & exam paperThe Midpoint Theorem (Grade 10)The line joining the midpoints of two sides of a triangle is parallel to the third side and half its length — the theorem, its converse, and how to use each in a proof.8min read · lesson, worksheet & exam paper
Term 3
Grouped Data, Percentiles & Modal Interval (Grade 10)Estimating the mean of grouped data using midpoints, identifying the modal interval and the interval containing the median, and finding percentiles and the semi-interquartile range.11min read · lesson, worksheet & exam paperHire Purchase, Exchange Rates & Population Growth (Grade 10)Working out a hire-purchase agreement with a deposit and monthly instalments, converting between currencies, and using the compound formula for population growth.11min read · lesson, worksheet & exam paperMeasurement: Surface Area, Volume & Scaling (Grade 10)Surface area and volume of prisms, cylinders, cones, spheres and pyramids, and what happens to area and volume when every dimension is multiplied by a factor k.9min read · lesson, worksheet & exam paperProbability: Venn Diagrams & the Addition Rule (Grade 10)Sample spaces, complementary and mutually exclusive events, the addition rule, and reading a two-set Venn diagram to answer probability questions.9min read · lesson, worksheet & exam paperSimple & Compound Interest: Every Exam TypeBoth interest formulas and every question type an exam sets — finding the final amount, the interest earned, working back to the principal or rate, depreciation, and inflation — each worked in full, with a worksheet.14min read · lesson, worksheet & exam paperStatistics: Five-Number Summary & Box Plots (Grade 10)Mean, median and mode, the five-number summary, quartiles and the interquartile range, drawing and reading a box-and-whisker plot, and describing the spread and skewness of data.10min read · lesson, worksheet & exam paperTrigonometric Graphs (Grade 10)The shapes of y = sin x, y = cos x and y = tan x on [0° ; 360°], and what a and q do in y = a sin x + q — amplitude, vertical shift, range and asymptotes.12min read · lesson, worksheet & exam paper
📖Grade 10 Mathematics: curriculum guide & study tipsRead more ▾Show less ▴
Grade 10 is the start of the FET Phase and the first year of the three-year curriculum that ends in the National Senior Certificate (NSC) examinations. The jump from Grade 9 is significant: functions become a central theme, Euclidean geometry returns with formal proofs, and trigonometry appears for the first time. Everything examined in Grade 12 rests on the Grade 10 foundations, and the paper structure — Paper 1 (algebra and functions) and Paper 2 (geometry, trigonometry and statistics) — mirrors the final NSC format.
Topics by term (CAPS)
Term 1
Algebraic expressions (products, factorisation, algebraic fractions), exponents, equations and inequalities (linear, quadratic, simultaneous), and trigonometry (definitions and special angles).
Term 2
Functions (linear, quadratic, hyperbolic and exponential graphs), trigonometric functions, Euclidean geometry, and the June examination.
Term 3
Analytical geometry (distance, midpoint, gradient), finance and growth (simple and compound interest, exchange rates), statistics, and further trigonometry (solving triangles, 2D problems).
Term 4
Probability (Venn diagrams, mutually exclusive and complementary events), measurement (surface area and volume), revision, and the November examination.
How you'll be assessed
From Grade 10 onward, examinations are written as two papers: Paper 1 covers algebra, equations, functions, finance and probability; Paper 2 covers analytical geometry, trigonometry, Euclidean geometry, statistics and measurement. Both papers on this page follow that split, so practise them as pairs.
Study tips from the classroom
- Learn the shape, intercepts and asymptotes of each function family — sketching questions are guaranteed marks once the patterns are known.
- Trigonometry is new in Grade 10: memorise the definitions (sin, cos, tan) and special angles (30°, 45°, 60°) early in the year.
- For Euclidean geometry, write out theorem statements and their accepted reasons on flashcards.
- Time yourself on full papers from Term 3 onwards — running out of time is the most common complaint in November.