MATHEMATICS
N S C F I N A L E X A M I N AT I O N S · N O V E M B E R 2 0 2 6 · C A P S
PAPER 1
Grade 12 · NSC 2026
SUMMARY NOTES · ALGEBRA, FUNCTIONS & CALCULUS
Every one of the 150 marks mapped — and the 12 question types that
keep coming back, each with the answer format that collects every tick.
★ 12 repeat questions — 11 of them in all 4 ★ Answer formats that earn full marks, tick
recent papers checked by tick
★ A worked example for every topic, step by ★ Every formula NOT on the information
step sheet
★ Examiner traps and a night-before ★ What is NOT examined — so you stop
checklist revising it
Written by a matric student who got 7 distinctions in the 2026 prelims, built with AI help
from 6 real past papers and memos.
DBE NSC Nov 2025 and May/June 2025 (papers + memos) · Grade 12 June 2024 common paper (paper + memo) · Gauteng prelims Sept
2022 (memo), 2025 and 2026 (papers) · plus the DBE Mathematics Examination Guidelines.
Functions 35 Calculus 35 Algebra 25 Patterns 25 Finance 15 Prob. 15
Where the 150 marks are — Functions and Calculus alone are 70.
150
MARKS
3 hours
180 MINUTES
10–11
QUESTIONS · ALL
28
PAGES OF NOTES
Maths P1 Summary Notes · NSC 2026 · For personal study only. Do not redistribute. 1
,T H E P R E V I E W T H AT PAY S F O R I T S E L F
The questions that keep coming back
Four recent Paper 1s were checked question by question: DBE NSC Nov 2025, DBE NSC May/June 2025, a Grade 12 June
2024 common paper and the GDE Prelim Sept 2026. These twelve question types turned up again and again. Learn the
format and the marks follow.
TOPIC / QUESTION HOW
TYPE OFTEN WHERE (PAPER · Q) MARKS ANSWER FORMAT THAT EARNS THE MARKS
★ Derivative from in 4 of 4 Nov 25 Q8.1 · May/Jun 25 Q8.1 · 4–5 f(x+h) ✓ → f(x+h) − f(x) simplified ✓ → lim
first principles Jun 24 Q8.1 · GDE 26 Q7.1 over h, factor out h ✓ → answer ✓. lim on
every line.
★ Quadratic "correct in 4 of 4 Q1.1.2 in all four papers 3–4 standard form ✓ · substitution into the
to TWO decimals" correct formula ✓ · x₁ ✓ · x₂ ✓
★ Quadratic in 4 of 4 Nov 25 Q1.1.3 · May/Jun 25 Q1.1.4 3–5 standard form ✓ · factors → critical values
inequality · Jun 24 Q1.1.3 · GDE 26 Q1.1.3 ✓ · interval with the right "or" and ≤ ✓✓
★ Simultaneous: one in 4 of 4 Nov 25 Q1.2 · May/Jun 25 Q1.2 · 6 subject of linear eqn ✓ · substitution ✓ ·
linear, one quadratic Jun 24 Q1.3 · GDE 26 Q1.2 standard form ✓ · x-values ✓ · y-values ✓,
as pairs
★ Quadratic pattern: in 4 of 4 Nov 25 Q3.2 · May/Jun 25 Q3.1 · 3–5 2a = 2nd difference ✓ · 3a + b = T₂ − T₁ ✓ · a
find Tₙ Jun 24 Q2.2 · GDE 26 Q2 + b + c = T₁ ✓
Cubic: turning points in 4 of 4 Nov 25 Q9.1–9.2 · May/Jun 25 2–4 per part f′(x) ✓ · f′(x) = 0 ✓ · x-values ✓ · y-values as
& concavity Q9.2–9.3 · Jun 24 Q9.4–9.6 · (x ; y) ✓ · concavity from the sign of f″
GDE 26 Q8
Hyperbola: in 4 of 4 Nov 25 Q6.2 · May/Jun 25 Q4.3 · 2–5 y = ±(x − p) + q · substitute the centre (p ; q)
asymptotes & axis of Jun 24 Q4.1 · GDE 26 Q4 ✓ · value ✓
symmetry
Tangent to a curve in 4 of 4 Nov 25 Q5.6 & Q9.4 · May/Jun 3–6 m = f′(a) ✓ · point (a ; f(a)) ✓ · y − y₁ = m(x −
25 Q8.3 · Jun 24 Q8.3 · GDE 26 x₁) ✓
Q8
Surd equation with a in 4 of 4 Nov 25 Q1.1.5 · May/Jun 25 Q1.1.5 4–5 isolate the surd ✓ · square both sides ✓ ·
root to reject · Jun 24 Q1.2.2 · GDE 26 Q1.2 standard form ✓ · answer with selection ✓
Geometric series: in 4 of 4 Nov 25 Q2.1.3 · May/Jun 25 2–4 −1 < r < 1 ✓ · substitution into a/(1 − r) ✓ ·
converge / S∞ Q2.2.3 · Jun 24 Q3.1 · GDE 26 Q3 answer ✓
Independent / in 4 of 4 Nov 25 Q11.1.1 · May/Jun 25 Q10.1 1–3 state the rule ✓ · substitute ✓ · compare,
mutually exclusive · Jun 24 Q10.1 · GDE 26 Q10.1 then conclude ✓
events
Finance: loan / in 3 of 4 Nov 25 Q7.3 · May/Jun 25 Q7.2 · 5 i and n per period ✓ · substitution ✓ ·
withdrawals, "how GDE 26 Q6 correct use of logs ✓ · n ✓ · answer in
long?" with logs context ✓
Also in 3 of 4: counting & arrangements (Nov 25 Q11.3 · In 2 of 4 — worth big marks: practical optimisation (Nov 25 Q10
May/Jun 25 Q11 · GDE 26 Q11), and the parabola's equation from · GDE 26 Q9) and the maximum vertical distance between two
its turning point (Nov 25 Q5.4 · May/Jun 25 Q5.1 · GDE 26 Q5). graphs (May/Jun 25 Q9.5 · GDE 26 Q5).
How the counts were made: each paper's questions were read against its marking guidelines (the GDE 2026 paper against its question paper
only) and a type was counted once per paper. Marks are the range shown on the papers. The answer formats paraphrase where the marks sit;
they are not copied memo answers. The full method for each row is in the section named on the Contents page.
Maths P1 Summary Notes · NSC 2026 · For personal study only. Do not redistribute. 2
, CONTENTS
What is inside
Where the 150 marks are
01 Topic weightings, cognitive levels, the shape of the 150 READ FIRST 4
paper, a time budget
How Paper 1 is marked
02 Consistent accuracy, the first-attempt rule, collecting all HIGH MARKS EXAMINER TRAP 6
every method mark
The formula sheet
03 What you are given — and the nine things you must — EXAMINER TRAP 8
know that are NOT on it
Algebra, equations & inequalities
04 Quadratic formula, inequalities, surds, k-method, 25 ★ ASKED EVERY YEAR 9
simultaneous, nature of roots
05 Number patterns, sequences & series 25 ★ ASKED EVERY YEAR 12
Arithmetic, quadratic, geometric, sigma, convergence
Functions & graphs
06 Parabola, hyperbola, exponential, log, inverses, 35 ★ ASKED EVERY YEAR HIGH MARKS 14
transformations, reading graphs
Finance, growth & decay
07 Annuities, loans, deferred payments, nominal vs 15 ★ ASKED EVERY YEAR EXAMINER TRAP 17
effective, solving for n
Differential calculus
08 First principles, rules, cubic graphs, tangents, 35 ★ ASKED EVERY YEAR HIGH MARKS 19
optimisation, rates of change
Counting principle & probability
09 Venn and tree diagrams, independence, mutually 15 ★ ASKED EVERY YEAR 22
exclusive, arrangements
What is NOT in Paper 1
10 Officially excluded by the DBE — and what is — SAVES TIME 24
examinable but often assumed not to be
Question bank: "if the question says…"
11 30 question stems with the opening move that — ★ REPEAT QUESTIONS 25
answers each
The trap list & night-before checklist
12 How marks are really lost, 15 things to be able to do, — EXAMINER TRAP 27
exam-room routine, sources
K E Y T O T H E TAG S A N D B OX E S
★ ASKED EVERY YEAR in every paper checked HIGH MARKS the biggest mark blocks
EXAMINER TRAP where strong candidates lose marks SAVES TIME cross it off your list
★ REPEATED QUESTION box: where it was asked, ANSWER FORMAT box: the structure that earns ticks
paraphrased
KEY DEFINITION box: the rule to know exactly WORKED EXAMPLE an original question, fully solved
Maths P1 Summary Notes · NSC 2026 · For personal study only. Do not redistribute. 3
N S C F I N A L E X A M I N AT I O N S · N O V E M B E R 2 0 2 6 · C A P S
PAPER 1
Grade 12 · NSC 2026
SUMMARY NOTES · ALGEBRA, FUNCTIONS & CALCULUS
Every one of the 150 marks mapped — and the 12 question types that
keep coming back, each with the answer format that collects every tick.
★ 12 repeat questions — 11 of them in all 4 ★ Answer formats that earn full marks, tick
recent papers checked by tick
★ A worked example for every topic, step by ★ Every formula NOT on the information
step sheet
★ Examiner traps and a night-before ★ What is NOT examined — so you stop
checklist revising it
Written by a matric student who got 7 distinctions in the 2026 prelims, built with AI help
from 6 real past papers and memos.
DBE NSC Nov 2025 and May/June 2025 (papers + memos) · Grade 12 June 2024 common paper (paper + memo) · Gauteng prelims Sept
2022 (memo), 2025 and 2026 (papers) · plus the DBE Mathematics Examination Guidelines.
Functions 35 Calculus 35 Algebra 25 Patterns 25 Finance 15 Prob. 15
Where the 150 marks are — Functions and Calculus alone are 70.
150
MARKS
3 hours
180 MINUTES
10–11
QUESTIONS · ALL
28
PAGES OF NOTES
Maths P1 Summary Notes · NSC 2026 · For personal study only. Do not redistribute. 1
,T H E P R E V I E W T H AT PAY S F O R I T S E L F
The questions that keep coming back
Four recent Paper 1s were checked question by question: DBE NSC Nov 2025, DBE NSC May/June 2025, a Grade 12 June
2024 common paper and the GDE Prelim Sept 2026. These twelve question types turned up again and again. Learn the
format and the marks follow.
TOPIC / QUESTION HOW
TYPE OFTEN WHERE (PAPER · Q) MARKS ANSWER FORMAT THAT EARNS THE MARKS
★ Derivative from in 4 of 4 Nov 25 Q8.1 · May/Jun 25 Q8.1 · 4–5 f(x+h) ✓ → f(x+h) − f(x) simplified ✓ → lim
first principles Jun 24 Q8.1 · GDE 26 Q7.1 over h, factor out h ✓ → answer ✓. lim on
every line.
★ Quadratic "correct in 4 of 4 Q1.1.2 in all four papers 3–4 standard form ✓ · substitution into the
to TWO decimals" correct formula ✓ · x₁ ✓ · x₂ ✓
★ Quadratic in 4 of 4 Nov 25 Q1.1.3 · May/Jun 25 Q1.1.4 3–5 standard form ✓ · factors → critical values
inequality · Jun 24 Q1.1.3 · GDE 26 Q1.1.3 ✓ · interval with the right "or" and ≤ ✓✓
★ Simultaneous: one in 4 of 4 Nov 25 Q1.2 · May/Jun 25 Q1.2 · 6 subject of linear eqn ✓ · substitution ✓ ·
linear, one quadratic Jun 24 Q1.3 · GDE 26 Q1.2 standard form ✓ · x-values ✓ · y-values ✓,
as pairs
★ Quadratic pattern: in 4 of 4 Nov 25 Q3.2 · May/Jun 25 Q3.1 · 3–5 2a = 2nd difference ✓ · 3a + b = T₂ − T₁ ✓ · a
find Tₙ Jun 24 Q2.2 · GDE 26 Q2 + b + c = T₁ ✓
Cubic: turning points in 4 of 4 Nov 25 Q9.1–9.2 · May/Jun 25 2–4 per part f′(x) ✓ · f′(x) = 0 ✓ · x-values ✓ · y-values as
& concavity Q9.2–9.3 · Jun 24 Q9.4–9.6 · (x ; y) ✓ · concavity from the sign of f″
GDE 26 Q8
Hyperbola: in 4 of 4 Nov 25 Q6.2 · May/Jun 25 Q4.3 · 2–5 y = ±(x − p) + q · substitute the centre (p ; q)
asymptotes & axis of Jun 24 Q4.1 · GDE 26 Q4 ✓ · value ✓
symmetry
Tangent to a curve in 4 of 4 Nov 25 Q5.6 & Q9.4 · May/Jun 3–6 m = f′(a) ✓ · point (a ; f(a)) ✓ · y − y₁ = m(x −
25 Q8.3 · Jun 24 Q8.3 · GDE 26 x₁) ✓
Q8
Surd equation with a in 4 of 4 Nov 25 Q1.1.5 · May/Jun 25 Q1.1.5 4–5 isolate the surd ✓ · square both sides ✓ ·
root to reject · Jun 24 Q1.2.2 · GDE 26 Q1.2 standard form ✓ · answer with selection ✓
Geometric series: in 4 of 4 Nov 25 Q2.1.3 · May/Jun 25 2–4 −1 < r < 1 ✓ · substitution into a/(1 − r) ✓ ·
converge / S∞ Q2.2.3 · Jun 24 Q3.1 · GDE 26 Q3 answer ✓
Independent / in 4 of 4 Nov 25 Q11.1.1 · May/Jun 25 Q10.1 1–3 state the rule ✓ · substitute ✓ · compare,
mutually exclusive · Jun 24 Q10.1 · GDE 26 Q10.1 then conclude ✓
events
Finance: loan / in 3 of 4 Nov 25 Q7.3 · May/Jun 25 Q7.2 · 5 i and n per period ✓ · substitution ✓ ·
withdrawals, "how GDE 26 Q6 correct use of logs ✓ · n ✓ · answer in
long?" with logs context ✓
Also in 3 of 4: counting & arrangements (Nov 25 Q11.3 · In 2 of 4 — worth big marks: practical optimisation (Nov 25 Q10
May/Jun 25 Q11 · GDE 26 Q11), and the parabola's equation from · GDE 26 Q9) and the maximum vertical distance between two
its turning point (Nov 25 Q5.4 · May/Jun 25 Q5.1 · GDE 26 Q5). graphs (May/Jun 25 Q9.5 · GDE 26 Q5).
How the counts were made: each paper's questions were read against its marking guidelines (the GDE 2026 paper against its question paper
only) and a type was counted once per paper. Marks are the range shown on the papers. The answer formats paraphrase where the marks sit;
they are not copied memo answers. The full method for each row is in the section named on the Contents page.
Maths P1 Summary Notes · NSC 2026 · For personal study only. Do not redistribute. 2
, CONTENTS
What is inside
Where the 150 marks are
01 Topic weightings, cognitive levels, the shape of the 150 READ FIRST 4
paper, a time budget
How Paper 1 is marked
02 Consistent accuracy, the first-attempt rule, collecting all HIGH MARKS EXAMINER TRAP 6
every method mark
The formula sheet
03 What you are given — and the nine things you must — EXAMINER TRAP 8
know that are NOT on it
Algebra, equations & inequalities
04 Quadratic formula, inequalities, surds, k-method, 25 ★ ASKED EVERY YEAR 9
simultaneous, nature of roots
05 Number patterns, sequences & series 25 ★ ASKED EVERY YEAR 12
Arithmetic, quadratic, geometric, sigma, convergence
Functions & graphs
06 Parabola, hyperbola, exponential, log, inverses, 35 ★ ASKED EVERY YEAR HIGH MARKS 14
transformations, reading graphs
Finance, growth & decay
07 Annuities, loans, deferred payments, nominal vs 15 ★ ASKED EVERY YEAR EXAMINER TRAP 17
effective, solving for n
Differential calculus
08 First principles, rules, cubic graphs, tangents, 35 ★ ASKED EVERY YEAR HIGH MARKS 19
optimisation, rates of change
Counting principle & probability
09 Venn and tree diagrams, independence, mutually 15 ★ ASKED EVERY YEAR 22
exclusive, arrangements
What is NOT in Paper 1
10 Officially excluded by the DBE — and what is — SAVES TIME 24
examinable but often assumed not to be
Question bank: "if the question says…"
11 30 question stems with the opening move that — ★ REPEAT QUESTIONS 25
answers each
The trap list & night-before checklist
12 How marks are really lost, 15 things to be able to do, — EXAMINER TRAP 27
exam-room routine, sources
K E Y T O T H E TAG S A N D B OX E S
★ ASKED EVERY YEAR in every paper checked HIGH MARKS the biggest mark blocks
EXAMINER TRAP where strong candidates lose marks SAVES TIME cross it off your list
★ REPEATED QUESTION box: where it was asked, ANSWER FORMAT box: the structure that earns ticks
paraphrased
KEY DEFINITION box: the rule to know exactly WORKED EXAMPLE an original question, fully solved
Maths P1 Summary Notes · NSC 2026 · For personal study only. Do not redistribute. 3
