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Open resources📚 Grade 11 Mathematics lessons by term & topic(23)
Choose your term, then the topic you have been told to study, and you will see every lesson you need to master for it.
Step 1 · Choose a term
Step 2 · Choose a topic in Term 1
Equations and Inequalities
Term 15 lessons to masterDiscriminant (Δ) & Nature of RootsThe discriminant is Δ = b² − 4ac, and its sign tells you the nature of the roots before you solve — two real, one equal, or non-real. Each question type worked in full, with a worksheet.14min read · lesson, worksheet & exam paperQuadratic Inequalities (Grade 11)Solving inequalities such as x² − x − 6 > 0 by factorising, finding the critical values, and using a sign table or parabola sketch — with the answer in interval notation.9min read · lesson, worksheet & exam paperSimultaneous Equations: One Linear, One Quadratic (Grade 11)Solving a linear equation together with a quadratic one by substitution, why there are up to two solution pairs, and what those pairs mean on a graph.10min read · lesson, worksheet & exam paperSolving Quadratic Equations: Factorising, Formula and Completing the SquareAll the ways to solve a quadratic — factorising, completing the square, the formula, rearranging first, a leading coefficient, and quadratics hidden in fractions — plus a worked example for each and a full worksheet.15min read · lesson, worksheet & exam paperWord Problems with Quadratics (Grade 11)Turning a sentence into an equation, solving it, and — the step that costs the most marks — rejecting the answer that does not make sense in the context.10min read · lesson, worksheet & exam paper
Exponents and Surds
Term 12 lessons to masterExponent Laws & Exponential Equations (Grade 11)The exponent laws including rational exponents, simplifying expressions with different bases, and solving exponential equations by making the bases the same or by factorising.11min read · lesson, worksheet & exam paperSurds: Simplifying & Rationalising (Grade 11)Simplifying surds using perfect-square factors, adding and subtracting like surds, multiplying them out, rationalising a denominator with the conjugate method, and solving equations that contain a surd — including the extraneous-root check that costs marks.12min read · lesson, worksheet & exam paper
Trigonometry
Term 12 lessons to masterTrig Equations & General Solutions (Grade 11)Finding the reference angle, writing the general solution with + k·360° or + k·180°, and then listing the specific solutions that fall inside a given interval.12min read · lesson, worksheet & exam paperTrig Identities & Reduction Formulae: Full GuideThe identities and reduction rules that crack Paper 2 trig — simplifying, proving identities, using the CAST diagram, reducing angles and finding exact values — each worked in full, with a worksheet.15min read · lesson, worksheet & exam paper
Step 2 · Choose a topic in Term 2
Analytical Geometry
Term 21 lesson to masterEuclidean Geometry
Term 22 lessons to masterCircle Geometry Riders: Proofs, Converses & Method (Grade 11)The biggest block of marks in Paper 2. How the circle theorems are proved rather than just quoted, every converse and when you need it, the reason wording a marker expects, how to read a circle diagram, and four full riders worked from the given information to the conclusion.22min read · lesson, worksheet & exam paperCircle Geometry: The Theorems, With ExamplesThe theorems that decide Paper 2 marks — centre vs circumference, semicircle, same segment, cyclic quadrilateral, tangent–radius and tangent–chord — each with the reason to quote, a worked example, a diagram and a worksheet.15min read · lesson, worksheet & exam paper
Functions and Graphs
Term 23 lessons to masterAverage Gradient on a Curve (Grade 11)Why a curve has no single gradient, how to find the average gradient between two points, what happens as the two points slide together — and how that idea becomes the gradient at a single point, which is where calculus begins.14min read · lesson, worksheet & exam paperHyperbola & Exponential Graphs (Grade 11)y = a/(x + p) + q and y = a·b^x + p + q — locating the asymptotes, finding intercepts, sketching, and stating domain and range.12min read · lesson, worksheet & exam paperThe Parabola: y = a(x + p)² + q (Grade 11)The turning-point form of the parabola, what a, p and q each do to the graph, finding intercepts and the axis of symmetry, and writing down domain and range.12min read · lesson, worksheet & exam paper
Step 2 · Choose a topic in Term 3
Finance, Growth and Decay
Term 31 lesson to masterProbability
Term 32 lessons to masterProbability: Venn Diagrams & Rules (Grade 11)The addition rule, mutually exclusive and complementary events, reading and filling in Venn diagrams, and testing whether two events are independent.11min read · lesson, worksheet & exam paperTree Diagrams & Two-Way Tables (Grade 11)Drawing a two-stage tree diagram, the difference between drawing with and without replacement, reading a two-way contingency table, and testing independence from one.11min read · lesson, worksheet & exam paper
Statistics
Term 31 lesson to masterTrigonometry
Term 32 lessons to masterSine, Cosine & Area Rules (Grade 11)The sine rule, the cosine rule and the area of a triangle: which one to use, and how to solve any non-right-angled triangle, with worked exam examples.12min read · lesson, worksheet & exam paperTrigonometric Graphs (Grade 11)y = a sin k(x + p), y = a cos k(x + p) and y = a tan k(x + p) — amplitude, period, horizontal shift, asymptotes, and reading the graphs to answer questions.13min read · lesson, worksheet & exam paper
Step 2 · Choose a topic in Term 4
Number Patterns, Sequences and Series
Term 41 lesson to master📖How to use these Grade 11 Mathematics resourcesRead more ▾Show less ▴
Mathematics in the CAPS curriculum is a cumulative subject: each year builds directly on the last, and each term's work feeds into the next. The resources below are organised the same way your school year is — by term — so you can revise exactly what will be assessed next. Term cards contain full tests and examinations with their memorandums; topic cards collect papers and worksheets that focus on one area of the curriculum.
The most effective way to use this page is simple. Before a test or exam, open the matching term card, download a paper, and write it under timed conditions without looking at the memo. Then mark yourself honestly, identify the question types you lost marks on, and redo those questions a few days later. Learners who repeat this cycle three or four times before an exam consistently outperform those who only read through notes.
Grade 11 is widely considered the hardest year of high school mathematics — and the most important. Almost every Grade 11 topic is directly examinable in the Grade 12 NSC papers: the trigonometric identities, reduction formulae, circle geometry theorems and quadratic theory learned this year all reappear in matric. Universities also look closely at Grade 11 final marks when making provisional offers, so the November examination carries real weight beyond school. See the full Grade 11 curriculum guide →