Grade 10 Maths · Paper 2

Trigonometry Grade 10

Real past paper questions and answers from 2018 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: 50 past paper questions
skills: 9 skills
videos: 9 videos

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Question 6.1 · November 2024 · Paper 2 · Provincial · 2 marks

An observer on the top of a cliff, 200 m above the sea level, observes the angles of depression of the two ships to be

4 5^{\circ}

for ship A, and

3 0^{\circ}

for ship B. Diagram for this question

6.1 Determine the size of

B \hat{D} C

.(2)

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

What's in Trigonometry Grade 10

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

Trigonometric Ratios40 past paper questions

Special Angles8 past paper questions

Use special angle valuesGive exact trig values for 0°, 30°, 45°, 60° and 90° without a calculator, for example sin 30° = ½ and tan 45° = 1.15 past paper questions · 2 videos

Angles of Elevation and Depression3 past paper questions

More Trigonometry Grade 10 questions and answers

Try each one on paper before you open the memo.

1. Question 3.1.2 · March 2025 · Provincial · 3 marks
In $Δ PQR$ , $QR = 4 cm$ , $PR = 5 cm$ and $QP = 3 cm$ . $PQ$ is perpendicular to $QR$ and $\hat{P} = θ$ , $P \hat{R} Q = α$ .
3.1 Calculate the following ratios:
3.1.2 $sec α$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Recall definition of secant $sec α = \frac{1}{c o s α}$
  1 mark · Use cosec, sec and cot
2. ✓
  Substitute cosine ratio $cos α = \frac{QR}{PR} = \frac{4}{5}$
  $sec α = \frac{1}{\frac{4}{5}}$
  1 mark · Write trig ratios in a triangle
3. ✓
  Calculate final value $= \frac{5}{4}$
  1 mark · Use cosec, sec and cot
2. Question 3.2.1 · March 2025 · Provincial · 2 marks
In the diagram, $△ PQR$ is a right-angled triangle, $\hat{Q} = 9 0^{\circ}$ , $\hat{P} = θ$ , $PQ = 5$ and $PR = 13$ units.
3.2 If $\hat{A} = 3 4^{\circ}$ and $\hat{B} = 5 3^{\circ}$ , use your calculator to evaluate the following (correct to TWO decimal places).
3.2.1 $cos (B - A)$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute $cos (5 3^{\circ} - 3 4^{\circ}) = cos (1 9^{\circ})$
  1 mark · Calculate trig values on a calculator
2. ✓
  Calculate $0, 95$
  1 mark · Calculate trig values on a calculator
3. Question 2.1.1 · June 2024 · Paper 2 · Provincial · 2 marks
2.1 If $A = 7 8^{\circ}$ and $B = 3 4^{\circ}$ , calculate the values of the following expressions, correct to two decimal places.
2.1.1 $sin A - sin B$ (2)
Show the memo (1 tick)Memo
1. ✓
  Substitute and calculate $sin 7 8^{\circ} - sin 3 4^{\circ}$
  $= 0, 42$
  2 marks · Calculate trig values on a calculator
4. Question 4.1 · June 2024 · Paper 2 · Provincial · 4 marks
In the diagram below, $\hat{A} = θ$ and $A \hat{B} D = 9 0^{\circ}$ . $BC = x$ m, $\hat{C} = β$ and $B \hat{D} C = 9 0^{\circ}$ .
4.1 Show that $A B = \frac{x s i n β}{t a n θ}$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Express BD in terms of x and betaIn $Δ BC D$ :
  $sin β = \frac{B D}{x}$
  $B D = x sin β$
  2 marks · Calculate a side using trig
2. ✓
  Express AB in terms of BD and thetaIn $Δ A B D$ :
  $tan θ = \frac{B D}{A B}$
  $A B = \frac{B D}{t a n θ}$
  1 mark · Calculate a side using trig
3. ✓
  Substitute BD to prove formula $A B = \frac{x s i n β}{t a n θ}$
  1 mark · Calculate a side using trig
5. Question 3.3 · March 2024 · Provincial · 5 marks
A right angled triangle with sides $p$ , $q$ and $s$ and the angle $θ$ is given. (Based on diagram: $p$ = Hypotenuse, $q$ = Adjacent, $s$ = Opposite to $θ$ )
3.3 Without the use of the calculator, showing all your working, determine the value of: $\frac{s i n 4 5 ^{\circ} \cdot t a n ^{2} 6 0 ^{\circ}}{c o s 4 5 ^{\circ}} + sin 3 0^{\circ}$ (5)
Show the memo (3 ticks)Memo
1. ✓
  Substitute special angles $\frac{( \frac{2}{2} ) \cdot ( 3 ) ^{2}}{\frac{2}{2}} + \frac{1}{2}$
  3 marks · Use special angle values
2. ✓
  Simplify $(\frac{2}{2} \div \frac{2}{2}) \cdot 3 + \frac{1}{2}$
  $= 1 \cdot 3 + \frac{1}{2}$
  1 mark · Use special angle values
3. ✓
  Final Answer $3 \frac{1}{2}$ or $\frac{7}{2}$
  1 mark · Use special angle values

Trigonometry Grade 10 videos

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

Pythagoras Theorem grade 9Kevinmathscience

Grade 10 Trigonometry: Trig Ratios Sin, Cos and TanMiss Martins Maths and Science

Grade 10 Trigonometry: Reciprocals of trig ratiosMiss Martins Maths and Science

Trigonometry - Calculator Work (Grade 10 Mathematics)MatheNatic

Trig Triangles Grade 10: Find angleKevinmathscience

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