Mathematics · May / June 2026 · Paper 42 · Question 20
0580
As printed in the paper
The question as text
NOT TO SCALE North C Ð A Ģ 79ß 112ß 103ß 38.2 m 50.3 m 86.8 m The diagram shows a field AÐCĢ with a straight footpath from A to C.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
20(a)[1]
257 cao [1]
20(b)[3]
87.9 or 87.90 to 87.91 [3]
Mark at most accurate. + − × × M2 may be done in stages. Allow M2 after
M2 for 38.2 2 86.8 2 2 38.2 86.8cos79 oe correct substitution in cosine rule and square root OR soi later. 2 + 2 −× ×
M1 for 38.2 86.8 2 38.2 86.8cos79 oe
A1 for 7728.[…]
20(c)[6]
29.2 or 29.20 to 29.21 nfww [6]
Mark at most accurate. nfww, do not accept 29.2 from 43.4tan 34
B3 for ∠ACB = 32.5 or 32.49… OR 50.3sin112 =
M2 for [sin ACB ] oe [sin ACB = ] 0.537 or 0.5372 to 0.5373 86.8
or M1 for sin ACB sin112 = oe 50.3 86.8 AND M2 dep on at least
M1 for distance = − ∠ sin(68 their ACB oe ) Alternative method using BC and sin(theirACB) 50.3 BC = 54.4 or 54.36 to 54.38 or 1 1 × × × = × × 86.8 50.3 sin( theirBAC ) 86.8 h 2 2 oe May be on diagram – must indicate right angle.
or M1 for recognition of shortest distance perpendicular to AC soi Accept 1 2 × ×h seen. 86.8 Allow
M1 for e.g. distance = sin( theirBAC ) 50.3 provided BAC is stated or shown on diagram.
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