Grade 11 Maths · Euclidean Geometry · Paper 2

Mixed Examples Grade 11

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past paper questions: 5 past paper questions
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Question 3.6 · November 2024 · Paper 2 · Provincial · 5 marks

In the figure quadrilateral KLMN with vertices K(7 ; -2), L(0 ; -3), M(8 ; -9) and N(9 ; -6) are given. Extend NK to intersect the

x

-axis and form the angle

β

.
Extend LK to intersect the

x

-axis and form the angle

θ

. $Diagram for this question$

3.6 Prove that KLMN is a cyclic quadrilateral.(5)

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4. Question 5.2.3 · June 2024 · Paper 2 · Provincial · 2 marks
5.2 In the diagram below, $O$ is the centre of the circle and $A C$ is the diameter.
$A C$ is produced to meet $E D$ produced at $G$ . $OE ∥ C D$ and $\hat{B} = 7 2^{\circ}$ .
5.2.3 Is $OE D C$ a cyclic quadrilateral? Give a reason for your answer.(2)
Show the memo (2 ticks)Memo
1. ✓
  ConclusionNo, $OE D C$ is not a cyclic quadrilateral.
  1 mark · Prove a quadrilateral is cyclic
2. ✓
  Statement and reason $\hat{E}_{2} + \hat{C}_{1} = 5 4^{\circ} + 7 2^{\circ} = 12 6^{\circ} \neq = 18 0^{\circ}$ (opposite angles not supplementary)
  1 mark · Prove a quadrilateral is cyclic
5. Question 10.1.2(a) · November 2024 · Paper 2 · Provincial · 4 marks
10.1 In the diagram, O is the centre of circle ABP. PB is extended to C. AC is drawn. PN is a tangent to the circle at P. OC intersects AP perpendicularly at point O. $\hat{P}_{2} = 37°$

Answer the questions that follow. $Diagram for question 10.1$
10.1.2 Prove that:
10.1.2(a) OACB is a cyclic quadrilateral(4)
Show the memo (4 ticks)Memo
1. ✓
  SA $\hat{B}$ P $= 90°$
  1 mark · Use angle in a semicircle
2. ✓
  R[ $∠$ in a semi-circle]
  $∴ \hat{B}_{1} = 90°$ [ $∠$ s on a str. line]
  1 mark · Use angle in a semicircle
3. ✓
  S $\hat{O}_{3} = 90°$ [given]
  1 mark · Prove a quadrilateral is cyclic
4. ✓
  ROACB is a cyclic quadrilateral [converse $∠$ s same seg]
  1 mark · Prove a quadrilateral is cyclic

Mixed Examples Grade 11 videos

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

Grade 11 Circle Geometry: To Prove a Quad is Cyclic Page 254 Ex 7Maths Matters

Grade 11 Circle Geometry: To Prove a Line is a Tangent Pg 260 Ex 8gMaths Matters

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