Mathematics · May / June 2023 · Paper 41 · Question 2
0580
As printed in the paper
The question as text
NOT TO SCALE E D A B C F The diagram shows a solid triangular prism ABCDEF of length 15 cm. . AB 6 4 = cm, . B E 5 7 = cm and the volume of the prism is 145 cm3.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
2(a)[3]
145 [sin =] 1 × × × 6.4 5.7 15 2 32.0[0] [4]
× × × ×
M2 M1 for 145 = 1 6.4 5.7 sin x 15 oe 2 or for 1 =h 2 × ×× = 6.4 h 15 145 and sin x 5.7 A1 If M0,
SC1 for 145 = × × × × 0.5 6.4 5.7 sin 32 15 oe
2(b)[3]
3.4[0] or 3.402 to 3.403 nfww [4]
( ) 3
M2 for + − × × × 6.4 2 5.7 2 2 6.4 5.7 cos 32 OR ( ) 2 + 2 − × × ×
M1 for 6.4 5.7 2 6.4 5.7 cos 32
A1 for 11.6 or 11.57 to 11.58
2(c)[3]
3.02 or 3.020 to 3.021 [3]
M2 for =x ( ) sin 32 5.7 80 2 + 50 2 − 2 80 × × 50 × cos75
or M1 for recognition that the line from E is perpendicular to AB e.g. right angle seen or 1 2 × ×h 6.4
2(d)[4]
10.8 or 10.9 or 10.84 to 10.85... [4]
M3 for [sin =] their(c) 2 + 2 15 5.7 their (c) or [ ] = tan ( ) × + 5.7 cos 32) 2 15 2 or ( ) 15 2 + 5.7 2 × 2 + 2
or M2 for 5.7 cos32 15 oe
or M1 for recognition of correct angle
2(e)[3]
136 or 136.0... [3]
M2 for 1000 × × 938 145 1000000 oe
or M1 for figs 136 or 13601
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