Grade 11 Maths · Functions · Paper 1

Exponential Function Grade 11

Real Exponential Function past paper questions and answers from 2023 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: 19 past paper questions
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Question 5.2 · November 2025 · Paper 1 · Provincial · 3 marks

The graphs of

f (x) = \frac{a}{x + p} + q

and

g (x) = \frac{x}{3} + c

are drawn below. C

(3; - 1)

is the point of intersection between the asymptotes of

f

. A and B are

x

- and

y

-intercepts of

f

and

g

respectively. E

(4; 2)

is a point on

f

in the first quadrant. $Diagram for this question$

5.2 Determine the equation of

f

.(3)

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

Exponential Function skills

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More Exponential Function Grade 11 questions and answers

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4. Question 7.1.3 · November 2025 · Paper 1 · Provincial · 3 marks
7.1 Given: $f (x) = (\frac{1}{3})^{x + 1} - 3$
7.1.3 Sketch the graph of $f$ . Indicate the horizontal asymptote as well as the intercepts with the axes.(3)
Show the memo (3 ticks)Memo
1. ✓
  ShapeA decreasing exponential curve (base $\frac{1}{3} < 1$ ), rising steeply to the left and flattening towards the asymptote on the right. $Memo diagram$
  1 mark · Sketch a graph from its equation
2. ✓
  $x$ - and $y$ -interceptsThe curve cuts the $x$ -axis at $(- 2; 0)$ and the $y$ -axis at $(0; - 2, 67)$ .
  1 mark · Find the x-intercepts
3. ✓
  AsymptoteHorizontal asymptote $y = - 3$ drawn as a dashed line; the curve approaches it but never touches it.
  1 mark · State the asymptotes
5. Question 7.2 · November 2024 · Paper 1 · Provincial · 2 marks
The graphs of $f (x) = - (b)^{x} + 8$ and $g (x) = \frac{3}{2} x + 7$ are drawn below.

A $(- 2; 4)$ and B are points of intersection of $f$ and $g$ . B is the $y$ -intercept of both graphs $f$ and $g$ . $Diagram for this question$
7.2 Show that $b = \frac{1}{2}$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitution of $(- 2; 4)$ $f (x) = - b^{x} + 8$
  subst. $(- 2; 4)$ :
  $4 = - b^{- 2} + 8$
  1 mark · Find equation of exponential graph
2. ✓
  $b = \pm \frac{1}{4}$ $b^{- 2} = 4$
  $\frac{1}{b ^{2}} = 4$
  $b^{2} = \frac{1}{4}$
  $b = \pm \frac{1}{4}$
  $∴ b = \frac{1}{2}$ ; $b > 0$
  1 mark · Find equation of exponential graph
6. Question 5.1 · November 2023 · Paper 1 · Provincial · 2 marks
The diagram below shows the graph of $f (x) = \frac{a}{x + p} + q$ . The asymptotes of $f$ intersect at $(- 3; - 1)$ and $f$ cuts the $x$ -axis at $x = - 5$ . $Diagram for this question$
5.1 Write down the values of $p$ and $q$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  $p = 3$ $p = 3$
  1 mark · State the asymptotes
2. ✓
  $q = - 1$ $q = - 1$
  1 mark · State the asymptotes
7. Question 6.2 · November 2023 · Paper 1 · Provincial · 2 marks
Given: $f (x) = 2 (3^{x}) + 1$
6.2 Write down the equation of asymptote of $f$ .(2)
Show the memo (1 tick)Memo
1. ✓
  Answer $y = 1$
  2 marks · State the asymptotes

Exponential Function Grade 11 videos

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

Hyperbola grade 10: The BasicsKevinmathscience

Hyperbola Equation Given Graph | Grade 11 FunctionsKevinmathscience

Exponential Equation Given Graph | Grade 11 FunctionsKevinmathscience

Parabola Grade 10: How to drawKevinmathscience

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