Grade 11 Maths · Paper 2

Euclidean Geometry Grade 11

Real past paper questions and answers from 2020 to 2024, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 54 past paper questions
skills: 17 skills
videos: 17 videos

Try a real exam question

No sign-up. Takes 3 minutes.

Question 6.1 · June 2024 · Paper 2 · Provincial · 4 marks

PQ

is a tangent to the circle at

C

EBC D

is a cyclic quadrilateral.

A EB

and

A D C

are straight lines with

A B ∣∣ QP

. Prove with reasons that: Diagram for this question

6.1

\hat{A} = \hat{B}_{2}

(4)

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

What's in Euclidean Geometry Grade 11

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

Lines and Triangles17 past paper questions

Circle Terminology

Circle Theorems37 past paper questions

Mixed Examples

More Euclidean Geometry Grade 11 questions and answers

Try each one on paper before you open the memo.

1. Question 4.2.2 · June 2024 · Paper 2 · Provincial · 2 marks
4.2 In the given figure, $D \hat{C} O = 2 5^{\circ}$ , $O$ is the center of the circle. $A$ , $B$ , $E$ , $C$ and $D$ are points on the circumference. Calculate with reasons, the size of:
4.2.2 $\hat{O}_{1}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  S $\hat{O}_{1} = 2 5^{\circ} + 2 5^{\circ} = 5 0^{\circ}$
  1 mark · Use exterior angle of a triangle
2. ✓
  Rext $∠$ of $△$
  1 mark · Use exterior angle of a triangle
2. Question 3.2.1 · March 2020 · Provincial · 3 marks
3.2 In the figure, AB and CD are chords of the circle with centre O. $OE ⊥ A B$ . $CF = F D$ , $OE = 4 c m$ , $OF = 3 c m$ and $C D = 8 c m$ .
3.2.1 Calculate the length of OD.(3)
Show the memo (3 ticks)Memo
1. ✓
  Pythagoras $OF ⊥ C D$ (line from centre to mid-point of chord), $F D = \frac{1}{2} (8) = 4$ cm
  $O D^{2} = O F^{2} + F D^{2}$
  1 mark · Use the theorem of Pythagoras
2. ✓
  Method (substitution) $O D^{2} = 3^{2} + 4^{2} = 25$
  1 mark · Use the theorem of Pythagoras
3. ✓
  Answer $O D = 5$ cm
  1 mark · Use the theorem of Pythagoras
3. Question 3.2 · March 2022 · Provincial · 5 marks
Give reasons for your statements and calculations in Question 3.
3.2 In the diagram below, O is the centre of the circle. A, B and C are points on the circumference of the circle. AB, AC and OC are drawn.
Prove the theorem which states that $B \hat{O} C = 2 \times B \hat{A} C$ .(5)
Show the memo (5 ticks)Memo
1. ✓
  ConstructionJoin AO (and produce it). Label $\hat{A}_{1}$ , $\hat{A}_{2}$ at A and $\hat{O}_{1}$ , $\hat{O}_{2}$ at O.
  1 mark · State the construction
2. ✓
  Exterior angle statement with reasonIn $Δ A OB$ : $\hat{O}_{1} = \hat{A}_{1} + \hat{B}$ (ext $∠$ of $Δ$ )
  1 mark · Prove a theorem or formula
3. ✓
  Equal angles opposite radiiBut $\hat{A}_{1} = \hat{B}$ (radii, OA = OB) $∴ \hat{O}_{1} = 2 \hat{A}_{1}$
  1 mark · Prove a theorem or formula
4. ✓
  Add the two resultsSimilarly in $Δ A OC$ : $\hat{O}_{2} = 2 \hat{A}_{2}$ $∴ \hat{O}_{1} + \hat{O}_{2} = 2 \hat{A}_{1} + 2 \hat{A}_{2}$
  1 mark · Prove a theorem or formula
5. ✓
  Conclusion $B \hat{O} C = 2 (\hat{A}_{1} + \hat{A}_{2})$ $∴ B \hat{O} C = 2 \times B \hat{A} C$
  1 mark · Prove a theorem or formula
4. Question 4.1.2(d) · March 2020 · Provincial · 2 marks
In the diagram below, points A, B, C and D lie on the circumference of a circle. FG and FD are tangents to the circle at C and D respectively. CD is produced to meet AE at E. Furthermore, $∠ GC A = 7 8^{\circ}$ , $∠ CB D = 4 1^{\circ}$ and $∠ B D A = 3 4^{\circ}$ .
4.1.2 Determine with reasons the sizes of the following angles:
4.1.2(d) $\hat{F}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Statement and reason $\hat{F} + 4 1^{\circ} + 4 1^{\circ} = 18 0^{\circ}$ (int $∠$ s of $Δ FC D$ )
  1 mark · Use angle sum of a triangle
2. ✓
  Answer $\hat{F} = 9 8^{\circ}$
  1 mark · Use angle sum of a triangle
5. Question 4.2 · March 2021 · Paper 1 · Provincial · 5 marks
4.2 Prove the theorem which states that $F \hat{O} G = 2 F \hat{H} G$ .(5)
Show the memo (5 ticks)Memo
1. ✓
  ConstructionDraw line HO produced to J (or similar)
  1 mark · State the construction
2. ✓
  S/R: $\hat{F} = x$ Let $\hat{H}_{1} = x$ . $\hat{F} = x$ [radii; $∠$ s opp. $=$ sides]
  1 mark · Prove a theorem or formula
3. ✓
  S/R: $\hat{O}_{1} = 2 x$ $\hat{O}_{1} = 2 x$ [ext. $∠$ of $Δ H FO$ ]
  1 mark · Prove a theorem or formula
4. ✓
  S: $\hat{O}_{2} = 2 y$ Let $\hat{H}_{2} = y$ . $\hat{G} = y$ [radii; $∠$ s opp. $=$ sides]
  $\hat{O}_{2} = 2 y$ [ext. $∠$ of $Δ H GO$ ]
  1 mark · Prove a theorem or formula
5. ✓
  S: $F \hat{O} G = 2 (x + y)$ $\hat{O}_{1} + \hat{O}_{2} = 2 x + 2 y$
  $F \hat{O} G = 2 (x + y) = 2 F \hat{H} G$
  1 mark · Prove a theorem or formula

Euclidean Geometry Grade 11 videos

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

Gr 9 Geometry: Parallel linesKevinmathscience

Finding the Missing Angle of a Triangle: A Step-by-Step GuideMath with Mr. J

Finding Missing Angles in Isosceles Triangles | Problem Solving Using Geometric RelationshipsKyle Pearce

Exterior Angle Theorem For Triangles, Practice Problems - GeometryThe Organic Chemistry Tutor

Circle Geometry Grade 11 : Line from CenterKevinmathscience

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