BVSS 2024 Prelim EM Paper 2 (Marking Scheme)

Answer all the questions. 1. (a) Factorise completely 2 44x x xy y− − + . Answer ………………………… [2] (b) Given that 11 1244 8 2 x− += , find the exact value of x. Answer x = …………………… [3] (c) Given that 13 12 − += h hk , express h in terms of k. Answer h = …………………… [2] (d) Solve 4 73 2 12 3 2 ++ xxx . Answer ………………………… [3] S4E/5N EM Prelim 2024 Paper 2 Marking Scheme 2 44x x xy y− − + = ( 4) ( 4)x x y x− − − ------ M1 (1st level) = ( )( 4)x y x−− ------ A1 11 1244 8 2 x− += 112( ) 3( ) 1242 2 2 x− += ------ M1 (base 2 for at least one term) 3 ( 1)1 422 x−+− = 311 4 x− = − − ------ M1 (compare power, no ECF) 3 4x= ------ A1 13 12 − += h hk (3 1) 2 1k h h− = + 3 2 1kh k h− = + ------ M1 (linear and expand correctly) 3 2 1kh h k− = + (3 2) 1h k k− = + 1 32 kh k += − ------ A1 accept 1 32 kh k −−= −+ 2 2 1 32 xx + and 2 1 3 7 24 xx++ 4 6 3xx+ ------- M1 (linear) 8 4 6 14xx+  + ------- M1 (linear) 23x− 2 10x 3 2x− 5x 3 52 x −   ------- A1

2 2. The diagram shows three points, A, B and C on the ground. AB = 174 m and BC = 195 m. The bearing of A from B is 238°.The bearing of C from A is 108°. A point D lies on the path AC such that it is equidistant to A and to B (a) Show that angle BAC = 50. [3] (b) Find the angle BCA. Answer ………….………….. [2] North A B C 174 195 360 238x = − (angles at a point) ---------- M1 (with reason) = 122 y = 180 – 122 (int angles) ---------- M1 (with reason) = 58 108 58BAC = − ---------- A1 (shown) = 50 (MUST label angles clearly to be awarded full marks) 238 x sin sin 50 174 195 BCA= ---------- M1 1sin (0.683547)BCA −= = 43.12147 = 43.1 ---------- A1 D y

3 (c) Find the area of triangle ABC. Answer ………….………… m2 [3] (d) Find distance from C to D. Answer ………….………… m [4] ---------------------------------------------------------------------------------------------------------------- 180 43.12147 50ABC = − − ---------- M1 = 86.87853 Area of triangle = 1 174 195 sin86.878532   ---------- M1 (using ‘their’ ABC) = 16939.82 = 16900 m2 ---------- A1 (or any accurate higher approximation) Since AD = BD, ABD is isosceles triangle. BDC = 50 + 50 (ext  of ) ---------- M1 = 100 DBC = 180 – 100 – 43.12147 ---------- M1 = 36.87853 Using sine rule 195 sin 36.87853 sin100 CD =  ---------- M1 (using their DBC) 118.8287782CD= = 119 m (3 sf) ---------- A1 (accep