Mathematics · May / June 2024 · Paper 41 · Question 6
0580
As printed in the paper
The question as text
A B H C 25° 55° 14 km 11 km North 32 km NOT TO SCALE The diagram shows the positions of two lighthouses A and B, a boat C and a harbour H . C is due east of B.
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6(a)[1]
245 [1]
6(b)(i)[1]
180 – (55 + 25) [=100] [1]
M1
6(b)(ii)[3]
32 × sin 25 oe sin100 13.73… [4]
M2 M1 for sin 25 sin100 = oe BH 32 A1
6(c)[5]
258 or 257.9 to 258.0… [5]
B4 for 67.9 to 68.0… OR + − 11 2 13.7 2 14 2
M2 for [cos =] × × 2 13.7 11
A1 for 0.3738 to 0.376
or M1 for 142 = 112 + 13.72 – 2× 11 × 13.7 × cos B M1dep on at least
M1 for 190 + their angle B
6(d)(i)[4]
2 44 pm or 14 44 cao [4]
B3 for 1 hour 44 or 1 hour 43.6 to 1 hour 43.8 or 104 or 103.6 to 103.8
or B2 for 1.727 to 1.73 32 10 1.852 ×
or M2 for 60 ×
or M1 for 32 ÷ (10 × 1.852)
6(d)(ii)[3]
7.857 to 7.88 [3]
x 13.7 =
M2 for cos55 oe
or M1 for dist to H occurs when perpendicular from B meets CH soi
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