Grade 11 Maths · Paper 1

Functions Grade 11

Real past paper questions and answers from 2020 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: 36 past paper questions
skills: 25 skills
videos: 25 videos

Try a real exam question

No sign-up. Takes 3 minutes.

Question 5.2 · June 2024 · Paper 1 · Provincial · 5 marks

Sketched below are the graphs of

f (x) = a x^{2} + b x + c

and

g (x) = m x + k

. The x-intercepts of f are at points A and C. The graphs of f and g intersect at points A and B respectively. Point P is the turning point of f. Q is a point on g such that line PQ is parallel to the y-axis. Points given:

A (- 4; 0)

C (2; 0)

B (0; 8)

5.2 Calculate the values of

a

b

and

c

f (x) = a x^{2} + b x + c

.(5)

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

What's in Functions Grade 11

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

The Parabola (Quadratic Function)5 past paper questions

The Hyperbola3 past paper questions

The Exponential Function5 past paper questions

Translations and Reflections of Graphs

Graph Interpretation

Trigonometric Functions24 past paper questions

Interpretation of Trigonometric Functions

More Functions Grade 11 questions and answers

Try each one on paper before you open the memo.

1. Question 3.1.3 · March 2025 · Paper 1 · Provincial · 3 marks
In the diagram, $P (- 6; 8)$ is a point in the Cartesian plane. $A$ is the point on the positive x-axis. $∠ A OP = θ$ .
3.1 Determine, with the aid of a diagram, the following:
3.1.3 $sin θ + cos θ$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Substitution for $sin θ$ $sin θ = \frac{8}{10}$
  1 mark · Find trig ratios from a sketch
2. ✓
  Substitution for $cos θ$ $cos θ = - \frac{6}{10}$
  1 mark · Find trig ratios from a sketch
3. ✓
  Answer $\frac{8}{10} - \frac{6}{10} = \frac{1}{5}$
  1 mark · Find trig ratios from a sketch
2. Question 1.4 · March 2020 · Provincial · 4 marks
1.4 Determine the value(s) of p if $g (x) = - 2 x^{2} - p x + 3$ has a maximum value of $3 \frac{1}{8}$ .(4)
Show the memo (4 ticks)Memo
1. ✓
  Axis of symmetry $x = \frac{- b}{2 a} = \frac{- ( - p )}{2 ( - 2 )} = \frac{- p}{4}$
  1 mark · Find turning point of a parabola
2. ✓
  Substitution $y = - 2 (\frac{- p}{4})^{2} - p (\frac{- p}{4}) + 3 = 3 \frac{1}{8}$
  1 mark · Find turning point of a parabola
3. ✓
  Simplification $- \frac{p ^{2}}{8} + \frac{2 p ^{2}}{8} = \frac{1}{8}$
  1 mark · Collect like terms
4. ✓
  Values of p $p^{2} = 1$
  $p = \pm 1$
  1 mark · Solve a quadratic by factorising
3. Question 2.3.1 · June 2024 · Paper 2 · Provincial · 4 marks
2.3 Given: $k sin β = - 5$ and $k cos β - 1 = 0$ where $k > 0$ .
2.3.1 Explain why $β \in [27 0^{\circ}; 36 0^{\circ}]$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Isolate sin beta $sin β = - \frac{5}{k}$
  1 mark · Solve a linear equation
2. ✓
  Isolate cos beta $cos β = \frac{1}{k}$
  1 mark · Solve a linear equation
3. ✓
  DiagramSketch: terminal arm through the point $(1; - 5)$ with $r = k$ , in quadrant IV (see diagram).
  1 mark · Decide the quadrant and sign
4. ✓
  ExplanationSince $k > 0$ : $sin β$ is negative and $cos β$ is positive, which happens only in quadrant IV, so $β \in [27 0^{\circ}; 36 0^{\circ}]$ . OR In quadrant IV, $y$ is negative and $x$ is positive.
  1 mark · Decide the quadrant and sign
4. Question 3.1 · June 2024 · Paper 2 · Provincial · 2 marks
In the diagram below, the graphs of $f (x) = a cos x$ and $g (x) = sin (x + p)$ are drawn for $x \in [- 18 0^{\circ}; 18 0^{\circ}]$ .
3.1 Determine the values of $a$ and $p$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Identify a from amplitudeAt $x = 0^{\circ}$ , $f (0) = - 2$ (amplitude 2, reflected), so $a = - 2$
  1 mark · Find equation of a trig graph
2. ✓
  Identify p from shift $g$ is $y = sin x$ shifted $3 0^{\circ}$ right (it cuts the $x$ -axis at $3 0^{\circ}$ and $- 15 0^{\circ}$ ): $g (x) = sin (x - 3 0^{\circ})$ , so $p = - 3 0^{\circ}$
  1 mark · Find equation of a trig graph
5. Question 3.1.2 · March 2024 · Paper 1 · Provincial · 3 marks
Do not use a calculator when answering Question 3.
In the diagram, $P (- 6; 8)$ is a point in the Cartesian plane. A is a point on the positive x-axis. $∠ A OP = θ$ .
3.1 Determine, with the aid of the diagram, the following:
3.1.2 $sin θ + cos θ$ (3)
Show the memo (2 ticks)Memo
1. ✓
  Determine ratios $sin θ = \frac{y}{r} = \frac{8}{10}$
  $cos θ = \frac{x}{r} = \frac{- 6}{10}$
  2 marks · Find trig ratios from a sketch
2. ✓
  Calculate sum $\frac{8}{10} - \frac{6}{10} = \frac{2}{10} = \frac{1}{5}$
  1 mark · Find trig ratios from a sketch

Functions Grade 11 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

Draw Parabola Grade 11 | Part 1 | Grade 11 FunctionsKevinmathscience

Hyperbola Equation Given Graph | Grade 11 FunctionsKevinmathscience

Exponential Domain Range| Grade 11 FunctionsKevinmathscience

Parabola Equation Grade 11 | Grade 11 FunctionsKevinmathscience

Free on Android

Know exactly which skill is costing you marks.

Mark past papers tick by tick in the NavyBlue app. It remembers every mark you lose, shows you the skills to fix first, and picks your next questions.

The NavyBlue app showing a learner's weak skills