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0580/41 May/Jun 2022, Question 3: Trigonometric Graphs and Equations

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 16 marks

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The question, in short

Form equations from fruit counts and costs, solve a linear equation and its exponential variant, then solve linear simultaneous equations and apply them to trigonometric ones.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (ai) · 3 marks

Use the given fruit expressions summing to 30 to find the apple count x.

  1. 1x + (x + 7) + (2x − 1) = 30
  2. 24x + 6 = 30
  3. 34x = 24, x = 6 apples

Answer6

Part (aii) · 3 marks

With apples at 15 cents and oranges at 18 cents, total cost $5.55, find one banana's cost in cents.

  1. 1Oranges = 6 + 7 = 13, bananas = 2 × 6 − 1 = 11
  2. 2Apples cost 6 × 15 = 90 c, oranges cost 13 × 18 = 234 c
  3. 3Bananas cost 555 − 90 − 234 = 231 c
  4. 4One banana = 231 ÷ 11 = 21 cents

Answer21

Part (bi) · 2 marks

Solve the linear equation 3w/16 − 1 = 1/2 for w.

  1. 13w/16 = 1/2 + 1 = 3/2
  2. 23w = 24
  3. 3w = 8

Answer8

Part (bii) · 2 marks

Solve 3(2⁻ʸ)/16 − 1 = 1/2 for the exponent y.

  1. 1This is part (i) with w = 2⁻ʸ, so 2⁻ʸ = 8
  2. 22⁻ʸ = 2³, so −y = 3
  3. 3y = −3

Answer−3

Part (ci) · 2 marks

Solve the pair 2p + q = 2 and p − q = −1/2 for p and q.

  1. 1Add the equations: 3p = 2 − 1/2 = 3/2, so p = 1/2
  2. 22 × 1/2 + q = 2, so q = 1
  3. 3p = 1/2, q = 1

Answerp = 1/2, q = 1

Part (cii) · 4 marks

Use the p, q results with sin u and cos v to find u and v in 0° to 360°.

  1. 1p = sin u = 1/2 and q = cos v = 1
  2. 2sin u = 1/2: u = 30° or 180 − 30 = 150°
  3. 3cos v = 1: v = 0° or 360°
  4. 4u = 30 and 150, v = 0 and 360

Answeru = 30 and 150, v = 0 and 360

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Also searched as: 0580/41/M/J/22 · 0580_s22_qp_41 · 0580 s22 41 · question 3.
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