Grade 11 Maths · Functions · Paper 1

Parabola Grade 11

Real Parabola 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: 36 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.

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More Parabola Grade 11 questions and answers

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4. Question 3.2.2 · March 2025 · Provincial · 4 marks
3.2 Sketched below is the parabola $f$ and the straight line $g (x) = 3 x + 6$ . R and S are the x-intercepts of $f$ , and $P (- \frac{1}{2}; 9)$ is its turning point. $g$ has its x-intercept at R.
3.2.2 Determine the equation of the parabola.(4)
Show the memo (4 ticks)Memo
1. ✓
  Use Turning Point form $y = a (x + \frac{1}{2})^{2} + 9$
  1 mark · Find the equation of a parabola
2. ✓
  Substitute point R(-2; 0) $0 = a (- 2 + \frac{1}{2})^{2} + 9$
  $0 = a (- \frac{3}{2})^{2} + 9$
  $0 = \frac{9}{4} a + 9$
  1 mark · Find the equation of a parabola
3. ✓
  Solve for a $\frac{9}{4} a = - 9 \to a = - 4$
  1 mark · Solve a linear equation
4. ✓
  Write final equation $y = - 4 (x + \frac{1}{2})^{2} + 9$ or $y = - 4 x^{2} - 4 x + 8$
  1 mark · Find the equation of a parabola
5. Question 2.3 · June 2024 · Paper 2 · Provincial · 2 marks
In the diagram below, $A (- 2; 4)$ , $B (- 2; - 1)$ and $C (p; - 4)$ are the vertices of $Δ A BC$ . $Q$ is the x-intercept of the line $A C$ .
$θ$ is the angle of inclination of $A C$ and $B \hat{A} C = 3 7^{\circ}$ .
2.3 Calculate the coordinate of $Q$ , the x-intercept of $A C$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Let y = 0 $- 1, 33 x + 1, 34 = 0$
  1 mark · Find the x-intercepts
2. ✓
  x-intercept $x = 1$ , so $Q (1; 0)$
  1 mark · Find the x-intercepts
6. Question 4.3.1 · November 2024 · Paper 2 · Provincial · 3 marks
In the diagram, $Δ$ ABC is drawn with vertices A $(- 7; 0)$ , B $(3; 8)$ and C. P is the midpoint of line AB. Q is a point on line AC. AQC is a line on the $x$ -axis. E $(- \frac{1}{2}; 2)$ is a point on line PQ. PQ $∥$ BC $Diagram for this question$
4.3 Calculate the:
4.3.1 Length of AC(3)
Show the memo (3 ticks)Memo
1. ✓
  $y = 0$ $- \frac{4}{3} x + 12 = 0$
  1 mark · Find the x-intercepts
2. ✓
  $x = 9$ $x = 9$
  1 mark · Find the x-intercepts
3. ✓
  AC = 16AC $= 9 - (- 7) = 16$
  1 mark · Find a horizontal or vertical length
7. Question 5.2 · November 2024 · Paper 1 · Provincial · 2 marks
The lines $y = - x + 4$ and $y = x - 2$ are the axes of symmetry of the function $f (x) = \frac{- 3}{x + p} + q$ .
5.2 Calculate the $x$ -intercept of $f$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Letting $y = 0$ $x$ -int: $(y = 0)$
  $\frac{- 3}{x - 3} + 1 = 0$
  1 mark · Find the x-intercepts
2. ✓
  $x = 6$ $\frac{- 3}{x - 3} = - 1$
  $- x + 3 = - 3$
  $x = 6$
  1 mark · Find the x-intercepts
8. Question 6.2 · November 2024 · Paper 1 · Provincial · 3 marks
Sketched below is the graph of $f (x) = x^{2} - 4 x - 5$ for $x \in (- \infty; 6]$ .

A and B are the $x$ -intercepts and C the $y$ -intercept of $f$ . $Diagram for this question$
6.2 Determine the coordinates of A and B.(3)
Show the memo (3 ticks)Memo
1. ✓
  Factors $x^{2} - 4 x - 5 = 0$
  $(x - 5) (x + 1) = 0$
  1 mark · Factorise a trinomial
2. ✓
  Coordinates of A $x = - 1$
  A $(- 1; 0)$
  1 mark · Find the x-intercepts
3. ✓
  Coordinates of B $x = 5$
  B $(5; 0)$
  1 mark · Find the x-intercepts
9. Question 5.2 · November 2023 · Paper 1 · Provincial · 3 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 $x = - 5$ . $Diagram for this question$
5.2 Determine the value of $a$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Substituting for $p$ and $q$ $f (x) = \frac{a}{x + p} + q$
  $= \frac{a}{x + 3} - 1$
  1 mark · Find the equation of a graph
2. ✓
  Substituting for $x$ and $y$ $0 = \frac{a}{- 5 + 3} - 1$
  1 mark · Find the equation of a graph
3. ✓
  Answer $1 = \frac{a}{- 2}$
  $a = - 2$
  1 mark · Find the equation of a graph
10. Question 6.3 · November 2023 · Paper 1 · Provincial · 3 marks
Given: $f (x) = 2 (3^{x}) + 1$
6.3 Draw a sketch of $f$ , showing clearly the asymptote and intercept(s) with the axes.(3)
Show the memo (3 ticks)Memo
1. ✓
  $y$ -interceptThe graph cuts the $y$ -axis at $3$ .
  1 mark · Find the y-intercept
2. ✓
  AsymptoteDotted horizontal asymptote $y = 1$ .
  1 mark · State the asymptotes
3. ✓
  ShapeIncreasing exponential curve, approaching $y = 1$ to the left and rising steeply to the right. $Memo diagram$
  1 mark · Sketch a graph from its equation

Parabola 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

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Parabola Equation Grade 11 | Grade 11 FunctionsKevinmathscience

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