Mathematics · May / June 2023 · Paper 42 · Question 3
0580
As printed in the paper
The question as text
NOT TO SCALE C A B ( ) x 3 + ( ) x 2 5 + cm cm The diagram shows a right-angled triangle ABC.
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3(a)(i)[3]
( ) + + x 3 (2 x 5) = 60 2 2x2 + 6x + 5x + 15 seen 2x2 + 11x – 105 = 0 [5]
M1 Accept (x + 3)(2x + 5) = 2 × 60 or 120 Accept e.g. (x + 3) (x + 2.5) = 60 without division by 2 shown for M1 (but not A1) B1 Accept 2x2 + 11x + 15 seen A1 Correct completion after M1B1 with the fraction seen removed with no errors or omissions seen
3(a)(ii)[3]
(2x + 21) (x – 5) [= 0] –10.5 and 5 [4]
M2 M1 for partial factors 2x (x – 5) + 21(x – 5) [ = 0] or x (2x + 21) – 5 (2x + 21) [ = 0] OR (2x + a)(x + b) [ = 0] where ab = – 105 or 2b + a = 11 B1
3(a)(iii)[3]
61.9 or 61.92 to 61.93 [3]
× + 3
M2 for tan = 2 their 5 5 oe + their 5 3 or B1FT for 2 × their 5 + 5 and their 5 + 3
3(b)(i)[1]
28.1 or 28.07 to 28.08 [1]
FT their 90 – their (a)(iii) unless their (a)(iii) < 45, in which case FT their (a)(iii)
3(b)(ii)[3]
10 [3]
93.75 + ×
M2 for ( their 5 3) oe 60 93.75 60
or M1 for or 93.75 oe seen 60 + 2 their 5 3 = 60 or oe x 93.75
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