Every distinction begins with one topic at a time.- start now
The clever learner learns the maths. The distinction learner also learns the paper: where the marks live, how they are earned, and how to bank them before the clock runs out.· read the exam, not just the syllabus
This is the map of the whole Grade 11 Mathematics exam, not a re-teach of the content. Read it once, then use the mark-weighting tables to decide where every remaining revision hour should go. Grade 11 is a school and provincial examination, not the external National Senior Certificate, so your papers are set against the national curriculum by your province, and every question is compulsory: there is no choice.
| Paper | Core topics | Total marks | Duration |
|---|---|---|---|
| Paper 1 | Algebra, equations and inequalities; number patterns (linear and quadratic); functions and graphs; finance, growth and decay; probability | 150 | 3 hours |
| Paper 2 | Statistics; analytical geometry; trigonometry; Euclidean (circle) geometry and measurement | 150 | 3 hours |
The only split the curriculum fixes exactly is 150 marks per paper. The figures below are the official content weightings, each with the small year-to-year tolerance the curriculum allows. Read the "why it matters" column as your action list.
| Topic | Approx. marks | Priority | Why it matters |
|---|---|---|---|
| Algebra, equations and inequalities | 45 ± 3 | High | The single largest block in Paper 1. Solving quadratics, quadratic inequalities, simultaneous equations, and the nature of roots through the discriminant. Almost every downstream topic reuses this algebra. |
| Functions and graphs | 45 ± 3 | High | Equal top weight. The parabola, hyperbola and exponential graph, their intercepts, turning points, asymptotes, and reading equations off a sketch. |
| Number patterns | 25 ± 3 | Medium-High | Quadratic number patterns: the second difference names them and hands you Tn = an² + bn + c. A reliable, self-contained block. |
| Probability | 20 ± 3 | Medium | Venn diagrams, the addition rule, mutually exclusive, complementary and independent events, plus tree diagrams and contingency tables. |
| Finance, growth and decay | 15 ± 3 | Medium | Compound growth and decay, and the nominal-versus-effective rate conversion. Small but heavily method-driven and quick to secure. |
| Topic | Approx. marks | Priority | Why it matters |
|---|---|---|---|
| Trigonometry | 50 ± 3 | High | The heaviest topic in the whole exam. Reduction formulae, identities, general solutions, trig graphs, and the sine, cosine and area rules for 2D triangles. |
| Euclidean geometry and measurement | 50 ± 3 | High | Circle-geometry theorems and riders carry the bulk, with surface area and volume of solids added on. Statement-and-reason work makes every step count. |
| Analytical geometry | 30 ± 3 | Medium-High | Distance, midpoint, gradient, the equation of a line, and the inclination angle m = tanθ. No circle equation at this level. |
| Statistics | 20 ± 3 | Medium | Univariate data only: central tendency, five-number summary, box-and-whisker, standard deviation and ogives. |
Paper 1: 150 marks, 3 hours, covering algebra and equations, number patterns, functions, finance and probability.
Paper 2: 150 marks, 3 hours, covering statistics, analytical geometry, trigonometry, and Euclidean geometry with measurement.
Cognitive split across each paper: 20% knowledge, 35% routine procedures, 30% complex procedures, 15% problem solving.
Round final answers to two decimal places unless the question says otherwise.
Only a non-programmable, non-graphical scientific calculator is allowed.
| Level | Typical weighting | What earns these marks | Command words to expect |
|---|---|---|---|
| Knowledge | 20% | Stating a definition, formula or fact with no calculation | write down, state, define |
| Routine procedures | 35% | A standard method applied to a familiar, mostly one-step question | calculate, solve, determine |
| Complex procedures | 30% | Several steps or concepts linked in a less familiar setting | hence, show that, prove |
| Problem solving | 15% | An unseen context where you choose your own strategy | investigate, hence or otherwise |
Q: A functions question on Paper 1 is worth 20 marks. Using the standard cognitive-level weighting for the paper, estimate how many of those 20 marks typically sit at each level. (Practice scenario, our own numbers.)
Knowledge: 20% of 20 = 4 marks
Routine procedures: 35% of 20 = 7 marks
Complex procedures: 30% of 20 = 6 marks
Problem solving: 15% of 20 = 3 marks
∴ 4 + 7 + 6 + 3 = 20 marks, so more than half the question (11 of the 20 marks) is earnable through direct recall and a well-rehearsed method alone.
Paper 1 and Paper 2 are each 150 marks over 3 hours. Paper 1 is led by algebra and functions (45 marks each), then number patterns (25), probability (20) and finance (15). Paper 2 is led by trigonometry and Euclidean geometry with measurement (50 marks each), then analytical geometry (30) and statistics (20). Marks also split by cognitive level, roughly 20% knowledge, 35% routine, 30% complex and 15% problem solving, so most marks reward a drilled method rather than exotic insight. Round only the final answer to two decimals, use only a non-programmable calculator, and answer Paper 2 in its special answer book, on the printed diagrams.
Exponent laws (memorise, not on the sheet)
Surds
The quadratic formula, which the handed-out sheet usually prints but is never guaranteed to, so memorise it:
x = [ −b ± √(b² − 4ac) ] ÷ 2a
The discriminant that lives inside it: Δ = b² − 4ac. When a quadratic will not factorise with whole numbers, the formula always finishes the job.
Q: Solve for x: (a) x² − x − 12 = 0, and (b) 2x² − 5x − 4 = 0, correct to two decimal places.
(a) Factorise: (x − 4)(x + 3) = 0, so x = 4 or x = −3. Check: 4² − 4 − 12 = 0 ✓ and (−3)² − (−3) − 12 = 0 ✓
(b) This will not factorise with whole numbers, so use the formula with a = 2, b = −5, c = −4.
Δ = (−5)² − 4(2)(−4) = 25 + 32 = 57
x = [ 5 ± √57 ] ÷ 4 = [ 5 ± 7,5498… ] ÷ 4
∴ x ≈ 3,14 or x ≈ −0,64
Q: Solve for x: x² − 2x − 8 ≥ 0.
Factorise the matching equation: (x − 4)(x + 2) = 0, so the critical values are x = −2 and x = 4.
The parabola y = x² − 2x − 8 opens upward, so it sits ON or ABOVE the x-axis (≥ 0) OUTSIDE the roots.
Quick check at x = 0 (between the roots): 0 − 0 − 8 = −8, which is below zero, confirming the middle is excluded.
∴ x ≤ −2 or x ≥ 4
Q: Solve simultaneously: 2x + y = 7 and xy = 6.
Make y the subject of the linear equation: y = 7 − 2x
Substitute into the second equation: x(7 − 2x) = 6, giving 7x − 2x² = 6
Rearrange: 2x² − 7x + 6 = 0, then factorise: (2x − 3)(x − 2) = 0
So x = 3⁄2 or x = 2. Substitute back into y = 7 − 2x:
If x = 3⁄2, then y = 7 − 3 = 4. If x = 2, then y = 7 − 4 = 3.
∴ (x ; y) = (3⁄2 ; 4) or (2 ; 3)
Q: (a) Without solving, describe the nature of the roots of x² − 6x + 2 = 0. (b) For which values of k will x² + (k − 1)x + 4 = 0 have two equal roots?
(a) Δ = (−6)² − 4(1)(2) = 36 − 8 = 28. Since 28 is positive but not a perfect square, the roots are real, unequal and irrational.
(b) Equal roots require Δ = 0: (k − 1)² − 4(1)(4) = 0, so (k − 1)² = 16
k − 1 = ±4, giving k = 5 or k = −3
∴ k = 5 or k = −3 (a quick check: k = 5 gives x² + 4x + 4 = (x + 2)², a perfect square, so the roots are indeed equal)
Q: Solve for x: √(x + 7) = x + 1.
Square both sides: x + 7 = (x + 1)² = x² + 2x + 1
Rearrange: x² + x − 6 = 0, then factorise: (x + 3)(x − 2) = 0, so x = −3 or x = 2
Test each in the ORIGINAL equation. x = 2: √9 = 3 and 2 + 1 = 3 ✓. x = −3: √4 = 2 but −3 + 1 = −2, and 2 ≠ −2, so reject.
∴ x = 2 only (x = −3 is extraneous, introduced by squaring)
Q: Solve for x: 22x − 5·2x + 4 = 0.
Notice 22x = (2x)². Let k = 2x, turning the equation into k² − 5k + 4 = 0
Factorise: (k − 1)(k − 4) = 0, so k = 1 or k = 4
Return to 2x: 2x = 1 = 20 gives x = 0, and 2x = 4 = 22 gives x = 2
∴ x = 0 or x = 2
Q: Solve x² − 6x + 2 = 0 by completing the square, and write y = x² − 6x + 2 in turning-point form. (Invented for practice.)
x² − 6x = −2; add (half of 6)² = 9 to both sides: x² − 6x + 9 = 7
(x − 3)² = 7, so x − 3 = ±√7 and x = 3 ± √7
The same steps give y = (x − 3)² − 7
∴ x = 3 + √7 ≈ 5,65 or x = 3 − √7 ≈ 0,35; turning point (3 ; −7)
A quadratic hands you its roots the moment you name a, b and c correctly. Every later mark in Paper 1 is built on getting that first line right.· on the algebra everything rests on
Try factorisation on every quadratic first, and reach for x = [−b ± √(b²−4ac)] ÷ 2a only when it will not factorise, rounding to two decimals when asked. For an inequality, find the critical values then decide, from an upward parabola, whether you want OUTSIDE the roots (≥ 0) or BETWEEN them (≤ 0). Solve one-linear-one-quadratic systems by substituting the linear equation and answering in coordinate pairs. Let the discriminant b²−4ac describe the nature of the roots or solve for an unknown that forces a stated nature. Always check surd-equation answers in the original equation and reject any extraneous root.
This is a free preview of Topic 1. The full guide has every topic, the self-marking quizzes, mock exams, planner, journal and wellbeing tools.
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Exam stress is completely normal. Here are a few things that actually work. None of this replaces a doctor or a trusted adult.
Box breathing: 4 counts in, 4 hold, 4 out, 4 hold. Do it four times.
Look at the worked example below first, then make your own. Tick off each topic as you finish it.
Example (already filled in)
| Date | Subject | Topic | Done |
|---|---|---|---|
| Mon 8 Jul | Mathematics | Your weakest topic, notes + summary | ✓ |
| Tue 9 Jul | Mathematics | Next topic + 10 practice questions | ✓ |
| Wed 10 Jul | Mathematics | A full past paper under time | – |
| Thu 11 Jul | Mathematics | Mark the paper, revise weak spots | – |
Your plan
| Date | Subject | Topic | Done |
|---|---|---|---|
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A winner is a loser who tried one more time.- keep going, all the way to the exam