📚 Grade 9 lessons(49)
Every lesson is one focused sub-topic, worked in full, with a printable worksheet and an exam paper with its memo.
Term 1
Adding and Subtracting IntegersOrdering integers on a number line, then the two adding rules and the 'add the opposite' trick for subtracting — with a number-line diagram, exam-style worked examples, a worksheet with memo and a quick quiz.9min read · lesson, worksheet & exam paperExtending Numeric & Geometric PatternsSpotting what a pattern is doing — a constant difference, a constant ratio, or something else entirely — and extending it, including patterns given as diagrams or tables, with worked examples, a worksheet with memo and a quiz.8min read · lesson, worksheet & exam paperFactorising: The Complete Exam Guide (Every Type)A full walkthrough of every kind of factorising you can be asked in an exam — common factors, difference of squares, all four trinomial sign patterns, leading coefficients and grouping — with a worked example for each and a worksheet to practise.16min read · lesson, worksheet & exam paperFactors, Multiples & Prime FactorisationWhat factors and multiples really are (and how never to mix them up), what makes a number prime, and how to break any number into its prime factors with a factor tree — worked examples, a clear diagram and an exam-style worksheet with memo.8min read · lesson, worksheet & exam paperFunctions & Relationships (Grade 9)Input values, output values and rules shown as flow diagrams, tables, formulae and equations — how to move between these equivalent forms and how to find a missing input, output or rule.8min read · lesson, worksheet & exam paperHCF and LCM (Highest Common Factor & Lowest Common Multiple)Highest Common Factor and Lowest Common Multiple made simple by reading them straight off the prime factors — with a Venn-diagram picture, exam-style worked examples and word problems, plus a worksheet with memo.9min read · lesson, worksheet & exam paperIntegers: Squares, Cubes, Roots & Mixed OperationsSquares, cubes, square roots and cube roots of integers, the crucial difference between (−3)^2 and −3^2, and how to run BODMAS through a calculation containing negatives — worked examples, worksheet with memo and a quiz.8min read · lesson, worksheet & exam paperMultiplying and Dividing IntegersThe one sign rule that covers both × and ÷ — same signs give a positive, different signs give a negative — shown as a grid, with exam-style worked examples, a worksheet with memo and a quick quiz.7min read · lesson, worksheet & exam paperMultiplying Binomials: (x + 2)(x + 3) and BeyondExpanding the product of two binomials with the area model and the FOIL order, plus squaring a binomial and the difference of two squares — the Grade 9 algebra skill that factorising later reverses. With a diagram, worked examples and a quiz.9min read · lesson, worksheet & exam paperNegative Exponents & Scientific Notation (Grade 9)What a negative exponent really means, how to rewrite it as a fraction, and how to write very large and very small numbers in scientific notation — the Grade 9 extension of the exponent laws, with worked examples and a quiz.8min read · lesson, worksheet & exam paperNumber Patterns: Finding and Using the RuleEvery linear-pattern question type — finding the rule Tₙ = dn + c, predicting a far term, working backwards to find which term equals a value, decreasing patterns, and patterns from diagrams — each worked in full, with a worksheet.13min read · lesson, worksheet & exam paperPattern Rules: In Words and in AlgebraTurning a pattern into a general rule — first described in words, then written algebraically as Tₙ = dn + c — and using that rule to find far-off terms or to work backwards, with worked examples, a worksheet with memo and a quiz.9min read · lesson, worksheet & exam paperProperties of Integers & InversesThe commutative, associative and distributive properties applied to integers, plus additive and multiplicative inverses — what they are, how exams ask for them, with worked examples, a worksheet with memo and a quiz.7min read · lesson, worksheet & exam paperProperties of Whole NumbersThe commutative, associative and distributive properties, the identity roles of 0 and 1, and why dividing by 0 is undefined — the rules that let you rearrange any calculation, with a diagram, worked examples and an exam-style worksheet with memo.8min read · lesson, worksheet & exam paperThe Laws of Exponents: Complete Exam GuideEvery exponent law with its own worked example — multiplying, dividing, powers of powers and products, zero and negative exponents — plus combined exam-style questions and a full worksheet with answers.15min read · lesson, worksheet & exam paperThe Real Number System: Rational & Irrational NumbersNaming and sorting numbers — natural, whole, integers, rational and irrational — how each set sits inside the next, and how to tell a rational number from an irrational one.8min read · lesson, worksheet & exam paper
Term 2
Algebraic Fractions (Grade 9)Simplifying algebraic fractions by factorising and cancelling, and adding, subtracting, multiplying and dividing them — including why you may only cancel factors.10min read · lesson, worksheet & exam paperAlgebraic Language: Terms, Coefficients & Like TermsThe vocabulary of algebra — variables, constants, terms, coefficients and exponents — how to spot like terms, and how to add and subtract them correctly, with worked examples and a quiz.8min read · lesson, worksheet & exam paperExpanding & Simplifying Algebraic ExpressionsMultiplying a monomial into brackets, dividing expressions by a monomial, and substituting values to find the numerical value of an expression — the core Grade 8 algebra skills, with worked examples and a quiz.9min read · lesson, worksheet & exam paperExponents: Notation, Squares, Cubes & RootsWhat exponential notation actually means, how to read and write it, squares, cubes, square roots and cube roots, and scientific notation — with a labelled diagram, worked examples and a quiz.9min read · lesson, worksheet & exam paperFunctions & Relationships: Flow Diagrams, Tables and FormulaeInput values, output values and rules — how the same relationship can be shown as a flow diagram, a table or a formula, and how to find a missing input, output or rule, with a clear diagram and a quiz.8min read · lesson, worksheet & exam paperInterpreting & Drawing GraphsReading global graphs — increasing, decreasing and constant sections, linear versus non-linear, maximum and minimum points, and discrete versus continuous data — plus plotting points on the Cartesian plane, with diagrams and a quiz.9min read · lesson, worksheet & exam paperSolving Algebraic Equations (Grade 8)Solving equations by inspection and by using inverse operations — one-step, two-step, brackets and equations with exponents — plus setting up equations from word problems, with worked examples and a quiz.10min 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 paperSolving Linear Equations: Every Type in the ExamOne 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 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 paper
Term 3
Angle Relationships: Straight, Intersecting & Perpendicular LinesAngles on a straight line, angles round a point, vertically opposite angles and perpendicular lines — the four relationships every geometry rider is built from, with a diagram, worked examples and a quiz.8min read · lesson, worksheet & exam paperAngles in Triangles and Quadrilaterals: Full GuideFind any missing angle in triangles and quadrilaterals — including isosceles, right-angled, the exterior-angle rule, solving for x, and the special quadrilaterals — each worked in full, with a worksheet.13min read · lesson, worksheet & exam paperAngles on Parallel Lines: The Complete Exam GuideEvery angle relationship a parallel-lines question uses — corresponding, alternate, co-interior, plus straight-line and vertically-opposite angles — with worked examples for finding angles, solving for x, and multi-step reasoning, and a full worksheet.13min read · lesson, worksheet & exam paperArea & Perimeter of 2-D Shapes (Grade 9)Area and perimeter formulae for squares, rectangles, triangles, parallelograms, trapeziums and circles, plus composite shapes, unit conversions and what happens to area when the dimensions double.10min read · lesson, worksheet & exam paperCollect, Organise & Summarise Data (Grade 9)Running a data investigation properly — samples and bias, grouping data into class intervals, drawing and reading histograms, and choosing between the mean, median and mode when the data has outliers.9min read · lesson, worksheet & exam paperCollecting & Organising DataHow a statistics investigation actually works — asking a good question, samples versus populations, questionnaires, and organising results with tally tables, stem-and-leaf displays and grouped intervals, with a worked diagram and a quiz.9min read · lesson, worksheet & exam paperCongruent & Similar 2D ShapesThe difference between congruent shapes (identical) and similar shapes (same shape, different size), how to spot each, and how to use proportion to find missing sides — with a clear diagram, worked examples and a quiz.8min read · lesson, worksheet & exam paperCongruent & Similar Triangles: The Four ConditionsThe four conditions that prove two triangles congruent — SSS, SAS, AAS and RHS — how to write the correspondence correctly, and how similarity differs. With drawn figures for every condition, worked proofs and a quiz.10min read · lesson, worksheet & exam paperConstruction of Geometric FiguresUsing only a compass and ruler to bisect a line, bisect an angle, construct 60° and 90°, and build a triangle from given sides — the constructions that appear as their own exam question, with step-by-step diagrams.9min read · lesson, worksheet & exam paperDirect & Indirect ProportionTelling direct from indirect (inverse) proportion, setting up each correctly, and solving the classic exam problems — unit costs, workers and time, speed and journey time.8min read · lesson, worksheet & exam paperFinancial Maths: Interest, Hire Purchase & Exchange RatesSimple and compound interest, hire purchase, rentals, exchange rates and commission — the real-world money maths of Grade 9, taught with the formulas, fully worked examples and a quiz.10min read · lesson, worksheet & exam paperMean, Median, Mode and Range: Complete GuideThe four everyday statistics, and every twist an exam adds — odd and even data sets, the median between two middle values, finding a missing value from the mean, and working back from a total — each worked in full, with a worksheet.13min read · lesson, worksheet & exam paperPercentages: The Complete Money-Maths GuideEvery percentage question in the Grade 8–9 syllabus — finding a percentage, increase and decrease, one number as a percentage of another, percentage change, VAT, profit and loss, and reverse percentages — each worked in full, with a worksheet.15min read · lesson, worksheet & exam paperProbability: The Complete Grade 8–9 GuideEvery probability question in the Grade 8–9 syllabus — single events, the complement (not happening), relative frequency, and simple two-event experiments — each worked in full, with a worksheet.13min read · lesson, worksheet & exam paperPythagoras' Theorem: Finding the Missing SideIn any right-angled triangle, a^2 + b^2 = c^2. Here's how to use it to find a missing side — and the one thing you must check first.6min read · lesson, worksheet & exam paperRatio and Rate: Every Exam Question TypeAll the ratio and rate skills a Grade 8–9 exam tests — simplifying, sharing in a ratio, finding a missing part, equivalent ratios, increasing/decreasing in a ratio, and unit rates — each worked in full, with a worksheet.14min read · lesson, worksheet & exam paperTransformation Geometry: All Four TransformationsEvery transformation an exam sets — reflection in the axes and y = x, translation, rotation about the origin, and enlargement — with the coordinate rule for each, worked examples and a worksheet.13min read · lesson, worksheet & exam paper
Term 4
Area and Perimeter: Every Shape (Complete Guide)Perimeter and area for every shape in the Grade 8–9 syllabus — rectangles, squares, triangles, circles (and half-circles), plus composite shapes and working backwards from the area — each worked in full, with a worksheet.14min read · lesson, worksheet & exam paperGeometry of 3-D Objects: Faces, Vertices, Edges & NetsClassifying 3-D objects by their faces, vertices and edges, the five Platonic solids, Euler's formula, the properties of spheres and cylinders, and how nets fold into solids — with drawn figures, worked examples and a quiz.9min read · lesson, worksheet & exam paperSurface Area & Volume of 3-D Objects (Grade 9)Volume and surface area of cubes, rectangular prisms, triangular prisms and cylinders, SI unit conversions, and what happens to volume when you double the dimensions — with drawn solids, worked examples and a quiz.10min read · lesson, worksheet & exam paperSurface Area and Volume: Complete GuideVolume and surface area for every 3D object in the syllabus — cubes, rectangular prisms and triangular prisms — plus capacity, unit conversions and working backwards, each worked in full, with a worksheet.14min read · lesson, worksheet & exam paperThe Theorem of Pythagoras (Grade 8)The relationship between the three sides of a right-angled triangle — finding the hypotenuse, finding a shorter side, leaving answers in surd form, and testing whether a triangle is right-angled — with a labelled diagram, worked examples and a quiz.9min read · lesson, worksheet & exam paperTransformation Geometry (Grade 9)Reflecting, translating, rotating, enlarging and reducing whole figures on the Cartesian plane, the coordinate rules for each, working backwards from an image, and the effect of enlargement on perimeter and area.10min read · lesson, worksheet & exam paper
📖Grade 9 Mathematics: curriculum guide & study tipsRead more ▾Show less ▴
Grade 9 is a decisive year: at the end of it, learners choose between Mathematics and Mathematical Literacy for the FET Phase (Grades 10–12). The CAPS Grade 9 curriculum deepens the algebra started in Grade 8 — factorisation, algebraic fractions and simultaneous-style thinking — and introduces the graph work that becomes Functions in Grade 10. A strong Grade 9 result keeps the door open for Mathematics, which is required for many university programmes including engineering, medicine and commerce.
Topics by term (CAPS)
Term 1
Whole numbers, integers, common fractions and decimal fractions, exponents (including scientific notation), and numeric and geometric patterns.
Term 2
Functions and relationships, algebraic expressions (including expanding and factorising), algebraic equations, and the June (mid-year) examination.
Term 3
Graphs (plotting and interpreting linear graphs), geometry of straight lines and 2D shapes, geometry of 3D objects, and transformation geometry.
Term 4
Surface area and volume, data handling, probability, and the end-of-year examination — historically written as a common provincial or national assessment in many districts.
How you'll be assessed
Grade 9 assessments frequently come from provincial common papers, which is why this page carries papers from Gauteng, Limpopo, the Eastern Cape and other provinces. Working through papers from more than one province is excellent preparation, because each province words questions slightly differently while testing the same CAPS content.
Study tips from the classroom
- Factorisation (common factor, difference of squares, trinomials) is the single most important Grade 9 skill for surviving Grade 10 — over-practise it.
- Learn to sketch and read straight-line graphs quickly: gradient, intercepts and the meaning of points.
- Geometry marks come from stating reasons; memorise the accepted reason wording for angle relationships.
- If you are choosing Mathematics for Grade 10, aim for consistent 60%+ in Grade 9 papers — use the papers on this page to track yourself term by term.