Grade 12 Maths · Paper 1

Functions Grade 12

Real past paper questions and answers from 2024 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 103 past paper questions
skills: 20 skills
videos: 20 videos

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Question 4.1 · May/June 2025 · Paper 1 · National (DBE) · 2 marks

The graph of

f (x) = \frac{4}{x - 3} + 4

is drawn below. M is the point where the asymptotes of

f

intersect. C and D are the x- and y-intercepts respectively of

f

. A is the point on

f

that is closest to M. Diagram for this question

4.1 Write down the coordinates of M.(2)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

What's in Functions Grade 12

Each skill is one thing a memo gives a tick for. Tap a skill for its own questions, notes and videos.

Function Types63 past paper questions

Inverse Graphs29 past paper questions

The Logarithmic Function and Laws of Logarithms16 past paper questions

More Functions Grade 12 questions and answers

Try each one on paper before you open the memo.

1. Question 4.1 · November 2024 · Paper 1 · National (DBE) · 2 marks
Given: $f (x) = a^{x} - 1$ for $a > 0$ . $B (2; \frac{- 5}{9})$ is a point on $f$ .
4.1 Calculate the value of $a$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute point B into equation $y = a^{x} - 1$
  $- \frac{5}{9} = a^{2} - 1$
  1 mark · Find equation of exponential graph
2. ✓
  Solve for a $a^{2} = 1 - \frac{5}{9}$
  $a^{2} = \frac{4}{9}$
  $a = \frac{2}{3}$ (since $a > 0$ )
  1 mark · Find equation of exponential graph
2. Question 8.3.3 · November 2024 · Paper 1 · National (DBE) · 3 marks
8.3 Given: $f (x) = - 6 x^{2}$
8.3.3 Determine the equation of $f^{- 1}$ for $f^{- 1} (x) \leq 0$ . Write your answer in the form $y = ...$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Swap x and y $x = - 6 y^{2}$
  1 mark · Find the equation of an inverse
2. ✓
  Solve for y $y^{2} = - \frac{x}{6}$
  $y = \pm - \frac{x}{6}$
  1 mark · Find the equation of an inverse
3. ✓
  Apply restrictionSince $y \leq 0$ :
  $y = - - \frac{x}{6}$
  1 mark · Restrict domain for an inverse
3. Question 4.1 · March 2025 · Provincial · 2 marks
The diagram below shows the graph of $k (x) = a^{x}$ . Point $B (3; 3 \frac{3}{8})$ lies on $k$ .
4.1 Show that $a = \frac{3}{2}$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute point B into equation $3 \frac{3}{8} = a^{3}$
  $\frac{27}{8} = a^{3}$
  1 mark · Find equation of exponential graph
2. ✓
  Solve for a $a = 3 \frac{27}{8}$
  $a = \frac{3}{2}$
  1 mark · Solve an equation with rational exponents
4. Question 4.1 · May/June 2024 · Paper 1 · National (DBE) · 2 marks
Given: $g (x) = \frac{1}{x - 1} + 2$
4.1 Write down the equations of the asymptotes of $g$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Vertical asymptote $x = 1$
  1 mark · State the asymptotes
2. ✓
  Horizontal asymptote $y = 2$
  1 mark · State the asymptotes
5. Question 3.2.3 · March 2025 · Provincial · 3 marks
Given: $f (x) = (x - 1)^{2} - 9$
3.2 Consider the function $g (x) = x^{2}$ .
3.2.3 Determine the inverse of $g$ in the form $y = ...$ (include all restrictions).(3)
Show the memo (3 ticks)Memo
1. ✓
  Interchange x and y $x = y^{2}$
  1 mark · Find the equation of an inverse
2. ✓
  Solve for y $y = \pm x$
  1 mark · Find the equation of an inverse
3. ✓
  State restriction $x \geq 0$
  1 mark · Restrict domain for an inverse

Functions Grade 12 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

Grade 9 Mathematics - Calculating the x and y intercepts of a straight lineMrs Townsend Mathematics - South Africa

1) Vertical line test gr 12Kevinmathscience

Draw Parabola Grade 11 | Part 1 | Grade 11 FunctionsKevinmathscience

Grade 12 Functions Student Question Find equation of p(x) if f(x) is shifted 2 units left | NTENTE \ New Technological Education

Functions : Horizontal Translations - Horizontal Shift - y = f(x - c) Examples and ExplanationRadford Mathematics

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