Grade 10 Maths · Trigonometry · Paper 2

Trigonometric Ratios Grade 10

Real Trigonometric Ratios 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: 44 past paper questions
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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

\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)

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

Trigonometric Ratios skills

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More Trigonometric Ratios Grade 10 questions and answers

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4. 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
5. Question 3.1.1(a) · March 2025 · Provincial · 2 marks
3.1 In the diagram, $△ PQR$ is a right-angled triangle, $\hat{Q} = 9 0^{\circ}$ , $\hat{P} = θ$ , $PQ = 5$ and $PR = 13$ units.

Refer to the diagram:
3.1.1 Determine the numerical value of:
3.1.1(a) QR(2)
Show the memo (2 ticks)Memo
1. ✓
  Pythagoras $Q R^{2} = P R^{2} - P Q^{2}$
  $Q R^{2} = 1 3^{2} - 5^{2} = 169 - 25 = 144$
  1 mark · Use the theorem of Pythagoras
2. ✓
  Answer $QR = 12$
  1 mark · Use the theorem of Pythagoras
6. 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
7. Question 6.2.1 · September 2024 · Provincial · 3 marks
6.2 A handy man attempts to reach the roof of a hall with a ladder 5 metres in length. Unfortunately, the ladder is too short, and a new ladder will be required. Suppose that the length of the ladder needed to reach the top has to be double the distance from the foot of the ladder to the wall. Also, the angle between his current ladder and the ground will need to be equal to the angle between the two ladders.

The above situation is depicted in the diagram below.
6.2.1 Calculate the value of $θ$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Set up trigonometric ratio $cos 2 θ = \frac{x}{2 x} = \frac{1}{2}$
  1 mark · Calculate an angle from a ratio
2. ✓
  Solve for 2theta $2 θ = 6 0^{\circ}$
  1 mark · Calculate an angle from a ratio
3. ✓
  Answer $θ = 3 0^{\circ}$
  1 mark · Calculate an angle from a ratio
8. Question 4.1.3 · November 2024 · Paper 2 · Provincial · 3 marks
4.1 In the diagram is a right-angled triangle has sides a, b and c and the $\hat{B} = 9 0^{\circ}$ .

Write down the following in terms of a, b and c.
4.1.3 If it is given that $a = 5$ and $A = 5 0^{\circ}$ calculate the numerical value of c.(3)
Show the memo (3 ticks)Memo
1. ✓
  Answer $c = \frac{5}{c o t 4 0 ^{\circ}} = \frac{5}{t a n 5 0 ^{\circ}} \approx 4, 20$
  1 mark · Calculate a side using trig
2. ✓
  S/R: size of Ĉ $\hat{C} = 18 0^{\circ} - 9 0^{\circ} - 5 0^{\circ} = 4 0^{\circ}$ (sum of $∠$ s of $Δ$ )
  1 mark · Use angle sum of a triangle
3. ✓
  Substitution into cot C $cot C = \frac{a}{c}$ | $cot 4 0^{\circ} = \frac{5}{c}$
  1 mark · Calculate a side using trig
9. Question 3.1.1(c) · March 2024 · Provincial · 2 marks
3.1 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 $θ$ )

Refer to the diagram:
3.1.1 Write down the values of:
3.1.1(c) $sec^{2} θ$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Substitution $sec^{2} θ = (\frac{p}{q})^{2}$
  1 mark · Use cosec, sec and cot
2. ✓
  Answer $= \frac{p ^{2}}{q ^{2}}$
  1 mark · Use cosec, sec and cot
10. Question 10.2.5 · November 2024 · Paper 2 · Provincial · 3 marks
10.2 In the diagram, PAT is the common tangent of the smaller and larger circles at A. AMB is the diameter of the larger circle with M on the circumference of the smaller circle. ASC and BC are chords of the larger circle and MS chord of the smaller circle. M is the centre of the larger circle.

It is also given that, the length of AM $= p$ units, AS $= (p - 1)$ units and BC $= 6$ units.

Answer the questions that follow. $Diagram for question 10.2$
10.2.5 Calculate the value of $p$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Apply Pyth theorem $p^{2} = (p - 1)^{2} + 3^{2}$ [Pyth. theorem]
  1 mark · Use the theorem of Pythagoras
2. ✓
  Simplification $p^{2} = p^{2} - 2 p + 1 + 9$
  $2 p = 10$
  1 mark · Square a binomial
3. ✓
  Answer $p = 5$
  1 mark · Use the theorem of Pythagoras

Trigonometric Ratios 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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