O-LevelMathematicsTrigonometry4024/21 · Oct/Nov 2015 · Q28 Marks
ABCDE is a pentagon with one line of symmetry. BC = DE = 10cm, DC = 30 cm and BCD = CDE = 90°. The shortest distance between A and DC is 22 cm. Calculate AB.
- (a)(i)ABCDE is a pentagon with one line of symmetry. BC = DE = 10cm, DC = 30 cm and BCD = CDE = 90°. The shortest distance between A and DC is 22 cm. Calculate AB.[2]
- (a)(ii)Calculate ∠ABC.[3]
- (b)In triangle PQR, PQ = 7 cm, PR = 9cm and PQR = 65°. Calculate PRQ.[3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.
- [2] 19.2[...] or 3√41
- M1 for [AB² = ] 12² + 15² or better
- [3] 128.6 to 128.7 or 129
- M1 for tan θ = their12 / 15 oe
- A1 for 38.6 to 38.7
- B1ft for [ ABC = ] their θ + 90
- Alternative method
- M2 for complete method using cosine rule for cos ABC using their 19.2
- [3] 44.8[2...]
- M2 for 7 sin 65 / 9
- Or M1 for 9 / sin 65 = 7 / sin x
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →