Grade 11 Maths · Paper 2

Analytical Geometry Grade 11

Real past paper questions and answers from 2022 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: 48 past paper questions
skills: 11 skills
videos: 11 videos

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Question 5.1 · June 2024 · Paper 1 · Provincial · 3 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)

5.1 Determine the equation of g.(3)

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What's in Analytical Geometry Grade 11

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Analytical Geometry48 past paper questions

More Analytical Geometry Grade 11 questions and answers

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1. Question 3.1.1 · March 2025 · Paper 1 · Provincial · 2 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:
3.1.1 The length of OP.(2)
Show the memo (2 ticks)Memo
1. ✓
  Apply Pythagoras $r^{2} = x^{2} + y^{2}$
  $r^{2} = (- 6)^{2} + (8)^{2}$
  $r^{2} = 36 + 64 = 100$
  1 mark · Use the theorem of Pythagoras
2. ✓
  Calculate r $r = 10$
  1 mark · Use the theorem of Pythagoras
2. Question 3.1.1 · March 2024 · Paper 1 · Provincial · 2 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:
3.1.1 The length of OP.(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute into distance formula/Pythagoras $O P^{2} = (- 6)^{2} + (8)^{2}$
  $O P^{2} = 36 + 64 = 100$
  1 mark · Use the theorem of Pythagoras
2. ✓
  Answer $OP = 10$
  1 mark · Use the theorem of Pythagoras
3. Question 1.1 · June 2024 · Paper 2 · Provincial · 4 marks
$PQRS$ is a quadrilateral with vertices $P (- 5; 0)$ , $Q (0; t)$ , $R (3; - 2)$ and $S (- 2; - 5)$ .
$P$ is on the x-axis and $Q$ is on the y-axis.
1.1 Determine the lengths of $PS$ and $RS$ .(4)
Show the memo (4 ticks)Memo
1. ✓
  Substitution into the distance formula for PS $PS = (- 2 + 5)^{2} + (- 5 - 0)^{2}$
  1 mark · Calculate distance between two points
2. ✓
  Length of PS $PS = 34$
  1 mark · Calculate distance between two points
3. ✓
  Substitution into the distance formula for RS $RS = (3 + 2)^{2} + (- 2 + 5)^{2}$
  1 mark · Calculate distance between two points
4. ✓
  Length of RS $RS = 34$
  1 mark · Calculate distance between two points
4. Question 3.1.1 · March 2023 · Paper 1 · Provincial · 2 marks
In the diagram, $P (x; - 9)$ is a point in the Cartesian plane such that $OP = 15$ units. $S (- 2; c)$ lies on $OP$ . $R$ is a point on the positive x-axis and $R \hat{O} P = θ$ .
3.1 Determine, with the aid of the diagram, the following:
3.1.1 The value of x.(2)
Show the memo (2 ticks)Memo
1. ✓
  Use Pythagoras theorem $x^{2} + y^{2} = r^{2}$
  $x^{2} + (- 9)^{2} = 1 5^{2}$
  $x^{2} = 225 - 81 = 144$
  1 mark · Use the theorem of Pythagoras
2. ✓
  Determine sign based on quadrantP is in 3rd quadrant (diagram shows x < 0).
  $x = - 12$
  1 mark · Decide the quadrant and sign
5. Question 3.3.4 · March 2022 · Provincial · 3 marks
Give reasons for your statements and calculations in Question 3.
3.3 In the diagram, O is centre of the circle. Points A, B, C and D lie on the circumference of the circle. BOD is a diameter. $\hat{A}_{1} = 5 1^{\circ}$ and $\hat{B}_{1} = 2 9^{\circ}$ . A line is drawn from O to F such that the length of BC = 24 m and radius of the circle centred O is 13 m.
3.3.4 Determine the length of OF.(3)
Show the memo (3 ticks)Memo
1. ✓
  Statement and reason $CF = \frac{1}{2} (24) = 12$ m (line from centre $⊥$ to chord bisects chord)
  1 mark · Use line from centre to chord
2. ✓
  Substitute into Pythagoras $O C^{2} = C F^{2} + O F^{2}$ (Pythagoras) $1 3^{2} = 1 2^{2} + O F^{2}$
  1 mark · Use the theorem of Pythagoras
3. ✓
  Answer $O F^{2} = 169 - 144 = 25$ $OF = 5$ m
  1 mark · Use the theorem of Pythagoras

Analytical Geometry Grade 11 videos

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

Introduction to TRANSFORMATION in Mathematics - Grade 8SHFT - Your Learning

Gr 8 Mathematics QuadrilateralsMrs Townsend Mathematics - South Africa

Straight line graphs grade 9: Gradient Part 1Kevinmathscience

Vertical Distance Grade 11 FunctionsKevinmathscience

Parabola + Straight Line| Grade 11 FunctionsKevinmathscience

How to Find Equation of Straight Line grade 10 maths: IntroductionKevinmathscience

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