4024/21 May/Jun 2021, Question 4: The Cosine Rule
Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 13 marks
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The question, in short
Construct quadrilateral ABCD from given lengths and an angle and measure from it, then use Pythagoras and trigonometry in a cuboid of 15, 10 and 8 cm.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (ai) · 3 marks
Accurate construction of ABCD on the given line AC.
- 1At A draw angle DAC = 50° and mark D on it with AD = 4.5 cm
- 2Arc radius 8 cm centre A and arc radius 6 cm centre C meet at B (other side of AC)
- 3Join AB, BC, CD
AnswerCorrect quadrilateral with construction arcs
Part (aii) · 1 mark
Measure angle ADC from the drawing.
- 1Measure angle ADC with a protractor
- 2Angle ADC ≈ 104°
Answer104 (accept 102 to 106)
Part (aiii) · 1 mark
Measure the missing side to find the perimeter.
- 1Measure DC ≈ 7.9 cm
- 2Perimeter = 8 + 6 + 4.5 + 7.9 = 18.5 + 7.9 = 26.4 cm
Answer26.4 (accept 26.2 to 26.6)
Part (bi) · 3 marks
Show the space diagonal TR is 19.7 cm.
- 1TV² = 15² + 10² = 325
- 2TR² = 325 + 8² = 389
- 3TR = √389 = 19.72… = 19.7 cm (1 d.p.)
Answer19.72…
Part (bii) · 5 marks
X is the middle of PQ: find angle TRX.
- 1TX² = 8² + 5² = 89
- 2RX² = 15² + 5² = 250
- 3cos TRX = (389 + 250 − 89)/(2 × √389 × √250) = 550/623.7…
- 4cos TRX = 0.8818…
- 5Angle TRX = 28.13…° ≈ 28.1°
Answer28.0 to 28.2
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Also searched as: 4024/21/M/J/21 · 4024_s21_qp_21 · 4024 s21 21 · question 4.
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