Grade 11 Maths · Paper 2

Trigonometry Grade 11

Real 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: 39 past paper questions
skills: 15 skills
videos: 15 videos

Try a real exam question

No sign-up. Takes 3 minutes.

Question 4.3 · March 2025 · Provincial · 4 marks

4.3 Evaluate:

\frac{s i n 21 0 ^{\circ} \cdot s i n 22 5 ^{\circ} \cdot c o s ( θ - 18 0 ^{\circ} )}{s i n 13 5 ^{\circ} \cdot c o s θ}

(4)

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

What's in Trigonometry Grade 11

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

Identities13 past paper questions

Reduction Formulas20 past paper questions

Trigonometric Equations6 past paper questions

Restrictions in Trigonometric Equations

Find where trig expression is undefinedFind the angles where a trig expression has no value, for example tan x is undefined at 90°, and 1/sin x is undefined when sin x = 0.3 past paper questions · 3 videos

Sine, Cosine and Area Rules

More Trigonometry Grade 11 questions and answers

Try each one on paper before you open the memo.

1. Question 3.4.1 · March 2025 · Provincial · 5 marks
3.4 Given: $(1 - cos^{2} x) (tan x + \frac{c o s x}{s i n x})$
3.4.1 Prove that $(1 - cos^{2} x) (tan x + \frac{c o s x}{s i n x}) = tan x$ (5)
Show the memo (5 ticks)Memo
1. ✓
  Identify square identity $1 - cos^{2} x = sin^{2} x$
  1 mark · Use the square identity
2. ✓
  Replace $tan x$ by $\frac{s i n x}{c o s x}$ $sin^{2} x (\frac{s i n x}{c o s x} + \frac{c o s x}{s i n x})$
  1 mark · Write tan as sin over cos
3. ✓
  LCD $(cos x sin x)$ $= sin^{2} x (\frac{s i n ^{2} x + c o s ^{2} x}{c o s x s i n x})$
  1 mark · Add or subtract algebraic fractions
4. ✓
  $sin^{2} x + cos^{2} x = 1$ $= sin^{2} x (\frac{1}{c o s x s i n x})$
  1 mark · Use the square identity
5. ✓
  Simplification to $\frac{s i n x}{c o s x}$ $= \frac{s i n x}{c o s x} = tan x = R H S$
  1 mark · Simplify an algebraic fraction
2. Question 2.1.3 · June 2024 · Paper 2 · Provincial · 3 marks
2.1 Given: $sin 2 0^{\circ} = p$ . Determine the following in terms of $p$ :
2.1.3 $1 - sin^{2} 7 0^{\circ}$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Use identity $1 - sin^{2} 7 0^{\circ} = cos^{2} 7 0^{\circ}$
  1 mark · Use the square identity
2. ✓
  Co-function $cos^{2} 7 0^{\circ} = sin^{2} (9 0^{\circ} - 7 0^{\circ}) = sin^{2} 2 0^{\circ}$
  1 mark · Use co-ratio identities
3. ✓
  Substitute p $p^{2}$
  1 mark · Use co-ratio identities
3. Question 3.2.1 · March 2023 · Paper 1 · Provincial · 4 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 $R \hat{O} P = θ$ .
3.2 Without using a calculator, determine the value of each of the following expressions:
3.2.1 $\frac{s i n ( 18 0 ^{\circ} - x )}{c o s ( 9 0 ^{\circ} + x ) + s i n ( 36 0 ^{\circ} - x )}$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Reduce numerator $sin (18 0^{\circ} - x) = sin x$
  1 mark · Use a reduction formula
2. ✓
  Reduce denominator $cos (9 0^{\circ} + x) = - sin x$
  $sin (36 0^{\circ} - x) = - sin x$
  2 marks · Use a reduction formula
3. ✓
  Simplify $\frac{s i n x}{- 2 s i n x} = - \frac{1}{2}$
  1 mark · Simplify an algebraic fraction
4. Question 3.5 · June 2024 · Paper 2 · Provincial · 2 marks
In the diagram below, the graphs of $f (x) = a cos x$ and $g (x) = sin (x + p)$ are drawn for $x \in [- 18 0^{\circ}; 18 0^{\circ}]$ .
3.5 If $k (x) = cos (2 x + t)$ , determine the value of $t$ if $k (x) = g (2 x)$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Write g(2x) as a cosine $g (2 x) = sin (2 x - 3 0^{\circ}) = cos (9 0^{\circ} - (2 x - 3 0^{\circ})) = cos (12 0^{\circ} - 2 x)$
  1 mark · Use co-ratio identities
2. ✓
  Value of t $cos (12 0^{\circ} - 2 x) = cos (2 x - 12 0^{\circ})$ , therefore $t = - 12 0^{\circ}$
  1 mark · Use a reduction formula
5. Question 3.2 · March 2023 · Paper 1 · Provincial · 6 marks
3.2 Simplify: $\frac{s i n ( 36 0 ^{\circ} - x ) \cdot t a n ( - x )}{c o s ( 18 0 ^{\circ} + x ) \cdot ( s i n ^{2} A + c o s ^{2} A )}$ (6)
Show the memo (6 ticks)Memo
1. ✓
  $- sin x$ $sin (36 0^{\circ} - x) = - sin x$
  1 mark · Use a reduction formula
2. ✓
  $- tan x$ $tan (- x) = - tan x$
  1 mark · Use a reduction formula
3. ✓
  $- cos x$ $cos (18 0^{\circ} + x) = - cos x$
  1 mark · Use a reduction formula
4. ✓
  $1$ $sin^{2} A + cos^{2} A = 1$
  1 mark · Use the square identity
5. ✓
  $- \frac{s i n x}{c o s x}$ $= \frac{- s i n x ( - \frac{s i n x}{c o s x} )}{- c o s x \cdot 1}$
  1 mark · Write tan as sin over cos
6. ✓
  Answer $= - sin x$
  1 mark · Simplify an algebraic fraction