Grade 11 Maths · Trigonometry · Paper 2

Sine, Cosine and Area Rules Grade 11

Real Sine, Cosine and Area Rules past paper questions and answers from 2024 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: 12 past paper questions
skills: 4 skills
videos: 4 videos

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Question 5.6 · November 2025 · Paper 1 · Provincial · 5 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. $Diagram for this question$

5.6 Calculate the area of

△

ABE if the length AB

= 210

units.(5)

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

Sine, Cosine and Area Rules skills

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More Sine, Cosine and Area Rules Grade 11 questions and answers

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4. Question 4.3.2 · November 2024 · Paper 2 · Provincial · 6 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:
4.3.2 Area of trapezium PBCQ(6)
Show the memo (6 ticks)Memo
1. ✓
  AB = $164$ AB $= (3 + 7)^{2} + (8 - 0)^{2}$
  $= 164$
  1 mark · Calculate distance between two points
2. ✓
  Correct substitution in area of $Δ$ ABCArea $Δ$ ABC $= \frac{1}{2} \times 164 \times 16 sin 38, 65°$
  1 mark · Use the area rule
3. ✓
  63,99 $= 63, 99$
  1 mark · Use the area rule
4. ✓
  Correct substitution in area of $Δ$ APQArea $Δ$ APQ $= \frac{1}{2} \times \frac{164}{2} \times 8 sin 38, 65°$
  1 mark · Use the area rule
5. ✓
  16,00 $= 16, 00$
  1 mark · Use the area rule
6. ✓
  AnswerArea PBCQ $= 63, 99 - 16, 00 = 47, 99$
  1 mark · Calculate area or perimeter
5. Question 7.2 · November 2024 · Paper 2 · Provincial · 3 marks
In the diagram, VP $=$ PQ $= 5$ units, R $\hat{Q}$ P $=$ S $\hat{P}$ V $= α$ , S $\hat{P}$ R $= β$ and PS $∥$ QR. SV is perpendicular to VP. $Diagram for this question$
7.2 Determine RP in terms of $α$ and $β$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  P $\hat{R}$ Q $= β$ P $\hat{R}$ Q $= β$ (alt $∠$ s; RQ $∥$ SP)
  1 mark · Use angles on parallel lines
2. ✓
  Application of sine rule $\frac{s i n α}{RP} = \frac{s i n β}{5}$
  1 mark · Use the sine rule
3. ✓
  AnswerRP $= \frac{5 s i n α}{s i n β}$
  1 mark · Use the sine rule
6. Question 7.1 · November 2024 · Paper 2 · Provincial · 2 marks
In the diagram below, circle ACD is given where AC is a diameter. DC is produced to B and AB = 8 units.
$\hat{B} = 30°$ and BC = 5 units. $Diagram for this question$
7.1 Prove that AC = 4,44 units (rounded off to TWO decimal places.)(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitution into cosine rule $A C^{2} = A B^{2} + B C^{2} - 2 (A B) (BC) cos \hat{B}$
  $A C^{2} = 8^{2} + 5^{2} - 2 (8) (5) cos 30°$
  1 mark · Use the cosine rule
2. ✓
  $A C = 19, 71796$ $A C = 19, 71796...$
  $A C = 4, 44$
  1 mark · Use the cosine rule
7. Question 9.1 · November 2024 · Paper 2 · Provincial · 5 marks
9.1 In the diagram, AB is a chord of a circle with center O. Prove the theorem that states: If M is the midpoint of AB, then OM $⊥$ AB.(5) $Diagram for question 9.1$
Show the memo (5 ticks)Memo
1. ✓
  ConstructionConstruction: Connect AO and OB $Memo diagram$
  1 mark · State the construction
2. ✓
  S: three pairs of equal sidesIn $Δ A OM$ and $Δ BOM$ :
  1. $A O = BO$
  2. $OM = OM$
  3. $A M = MB$
  1 mark · Prove a theorem or formula
3. ✓
  R: reasons for the sides(Radii), (Common side), (Given)
  1 mark · Prove a theorem or formula
4. ✓
  S/R: congruence $∴ Δ A OM \equiv Δ BOM$ (S S S)
  $∴ \hat{M}_{1} = \hat{M}_{2}$
  1 mark · Prove a theorem or formula
5. ✓
  S/R: conclusionBut $\hat{M}_{1} + \hat{M}_{2} = 180°$ (AMB is a straight line)
  $∴ \hat{M}_{1} = \hat{M}_{2} = 90°$
  $∴ OM ⊥ A B$
  1 mark · Prove a theorem or formula

Sine, Cosine and Area Rules Grade 11 videos

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

Sine Rule grade 11: IntroductionKevinmathscience

Cos Rule grade 11: IntroductionKevinmathscience

Area Rule grade 11: IntroductionKevinmathscience

Euclidean geometry proofs in less than 10 minutes - Grade 11 and12 NSC & IEBMathew's Academy Of Sciences

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