📚 Grade 10 lessons by term & topic(31)
Choose your term, then the topic you have been told to study, and you will see every lesson you need to master for it — each one with a printable worksheet and an exam paper with its memo.
Step 1 · Choose a term
Step 2 · Choose a topic in Term 1
Algebraic Equations
Term 12 lessons to masterSolving Equations by Factorisation (Product = 0)Revision from Grade 9The 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 paperSolving Linear Equations: Every Type in the ExamRevision from Grade 9One balancing method solves every linear equation. Here it is applied to all the exam types — one-step, two-step, variables on both sides, brackets, negatives and fractions — plus word problems and a full worksheet.15min read · lesson, worksheet & exam paper
Algebraic Expressions
Term 14 lessons to masterAlgebraic 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: Trinomials, Grouping in Pairs & the Cubes (Grade 10)A decision guide based on counting the terms, then the three new Grade 10 methods: a trinomial with a number in front of x² (splitting the middle term), grouping four terms in pairs, and the sum and difference of two cubes.10min 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 paper
Exponents, Equations and Inequalities
Term 14 lessons to masterLaws 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)Solve linear inequalities and write the answer in interval notation. Covers number lines, compound inequalities and the rule that catches everybody: dividing by a negative flips the sign.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 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 paper
Trigonometry
Term 14 lessons to masterSpecial 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 paperTrig Ratios for Any Angle: CAST & Reference Angles (Grade 10)What sin, cos and tan mean once the angle grows past 90° — the x, y and r definitions, the CAST diagram for signs, reference angles, reading every ratio off a point, working backwards from one ratio, the reciprocals cosec, sec and cot, and a Grade 11 preview of solving a trig equation across 0° to 360°.18min read · lesson, worksheet & exam paperTrigonometry: SOH-CAH-TOA, Sides and AnglesThe right-angled trig questions of 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
Step 2 · Choose a topic in Term 2
Analytical Geometry
Term 21 lesson to masterEuclidean Geometry
Term 24 lessons to masterCongruent & 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 paperEuclidean Geometry Riders: Proving It, With Reasons (Grade 10)The question that carries the most marks in Paper 2 — finding angles with reasons and proving results. The statement-and-reason discipline, every reason a Grade 10 may quote, how to read a diagram before you write anything, and four full riders worked from first line to conclusion.20min 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 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
Functions and Graphs
Term 23 lessons to masterSketching the Parabola y = ax² + q (Grade 10)The Grade 10 parabola y = ax² + q: what a and q do, the turning point (0 ; q), the intercepts, domain and range, and finding a and q from a graph — each worked in full, with a diagram and a worksheet, plus a short Grade 11 preview of y = ax² + bx + c.15min read · lesson, worksheet & exam paperThe Hyperbola & Exponential Graph (Grade 10)Sketching y = a/x and y = abˣ, 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 paperWhat a Function Really Is: Words, Tables, Formulae & Graphs (Grade 10)The idea underneath every graph you will sketch this year — one input, exactly one output. The four ways to show a function and how to move between them, function notation f(x), domain and range, the vertical line test, and how to find a rule from a table.16min read · lesson, worksheet & exam paper
Step 2 · Choose a topic in Term 3
Finance and Growth
Term 32 lessons to masterHire 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 paperSimple & Compound Interest: The Grade 10 Question TypesBoth interest formulas and the question types a Grade 10 exam sets — finding the final amount, the interest earned, working back to the principal or rate, and inflation — each worked in full, with a worksheet. Depreciation is shown only as a preview of Grade 11.14min read · lesson, worksheet & exam paper
Probability
Term 31 lesson to masterStatistics
Term 32 lessons to masterGrouped 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 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 of data.10min read · lesson, worksheet & exam paper
Step 2 · Choose a topic in Term 4
📖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, DBE 2026 teaching plan)
Term 1
Algebraic expressions (the real number system, products, factorisation, algebraic fractions), exponents, equations and inequalities (linear, quadratic, literal and simultaneous equations, linear inequalities), and trigonometry (the ratios, special angles and right-angled triangles).
Term 2
Euclidean geometry (triangles, quadrilaterals and the midpoint theorem), analytical geometry (distance, midpoint, gradient), functions (linear, parabola, hyperbola and exponential graphs), and the June examination.
Term 3
Trigonometric functions (graphs of sin, cos and tan), trigonometry in two dimensions, statistics, probability (Venn diagrams, mutually exclusive and complementary events), and finance and growth (simple and compound interest, hire purchase, inflation, exchange rates).
Term 4
Measurement (surface area and volume), number patterns, revision of algebra, trigonometry and geometry, 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.