Mathematics · Oct / Nov 2022 · Paper 41 · Question 8
0580
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The question as text
A Q B P C NOT TO SCALE 15 m 8 m 20 m 3 m 4 m The diagram shows triangle ABC on horizontal ground. m AC 15 = , m BC 8 = and m AB 20 = . BP and CQ are vertical poles of different heights. m BP 3 = and m CQ 4 = . AQ and PQ are straight wires.
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8(a)[4]
2 + 2 − 2 15 8 20 [cos ] = 2.15.8 117.54 to 117.55 [6]
( )
M2 M1 for 2 = 2 + 2 − 20 15 8 2.15.8cos
A2 A1 for 37 111 − − or or –[0].4625 80 240
8(b)[2]
53.2 or 53.19 to 53.23 [2]
M1 for 0.5 × 8 × 15 × sin(117.5) oe
8(c)[2]
15.5 or 15.52 to 15.53 [2]
M1 for 152 + 42 oe
8(d)[3]
7.1 or 7.13 or 7.125 to 7.126 [3]
M2 for tan [P]= 4 − 3 oe or for 7.1 or 8 7.13 or 7.125 to 7.126 seen
or M1 for vertical line = 4 – 3 soi After 0 scored
SC1 for correct angle identified
8(e)[5]
11.5 nfww or 11.48 to 11.49... [5]
B1 for height of 3.5 soi
M2 for 15 2 + 4 2 − 2.15.4cos(117.5) 15 2 + 4 2 − (...) 2 =
or M1 for cos117.5 2.15.4 3.5
M1 for tan = oe their 17.216... After M0 scored
SC1 for correct angle identified
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