Answers - 3E NV AM EOY 2023

2 MARKING SCHEME Qn Marks Remarks 1 Curved surface area = 10 5 18 2 (3 2 5) 10 5 18 6 4 5 6 4 5 6 4 5 60 5 40(5) 18(6) 72 5 44 132 5 308 44 3 5 7 height   −= + −−= +− − − += − −= − =− + ( ) ( ) 22 2 5 9 2 (3 2 5) 5 5 9 3 2 5 3 2 5 3 2 5 15 5 50 27 18 5 3 2 5 33 5 77 9 20 3 5 7 height   − = + −−= +− − − += − −= − =− + M1 (form equation / find height) M1 (rationalise) M1 (expansion) A1 Wrong formula for curved surface area – award zero. Candidates do not possess the habit of reducing the fraction to the lowest term before simplifying. Resulting in “slips”. 2(a)(i) B1 (negative angles) This question is badly done by most candidates. They are completely clueless about what the question is asking. The inability to apply CAST diagram to solve this question is very apparent. Candidates can write the exact form but unable to (ii) 1tan(90 ) tan 12 5 A A−= =− B1 (complementary angles) (iii) M1, A1

3 Qn Marks Remarks (b) ( ) 12sin cos tan 36 4 3 2 2 36 2     + = +    += M1 (exact form of special angles) A1 perform expansion. 3(i) 2 22 2 2 8 14 2 ( 2) (2) 7 2( 2) 22 y x x x x =− + + =− − − − =− − + M1 (completing the square) A1 Generally well done. Weaker students are unable to complete the square. 3(ii) Turning point = (2, 22) y-intercept = (0, 14) Correct shape with y-intercept given in coordinates form – M1 Correct max point with label given in coordinates form – M1 Candidates do not label the axes and the coordinates of both the max point and y - intercept. They only gave the former in coordinates form. 4 ( ) 3 2 2 22 2 7 5 12 8 7 14 1 ( 1)( 2)( 1) 2 1 1 2 x x x x x xxxx A Bx C x x + − + − + =+ −+−+ += + +− + M1 (long division – obtain ) M1 M1, M1, M1 (values of A, B and C) Award zero when the form of the partial fractions is incorrect right from the start. If form is partially correct, only award the M1 for performing the long division. Candidates who fail to solve successfully didn’t 22 8 14y x x=− + +

4 Qn Marks Remarks A1 (conclusion with correct signs) realised that the fraction improper. 5(a) ---------(1) ------- (2) Solving simultaneously, M1 (obtain equation (1)) M1 (substitution) M1 (obtain equation (2)) A1 (value of b) Many candidates compute the value of b before proving that a = 2. Formulating eqn (2) poses a challenge to some candidates. 5(b) 32 2 4 2 14 12 0 ( 2)(4 10 6) 0 2( 2)( 1)(2 3) 0 x x x x x x x x x + − − = − + + = − + + = M1, M1 (obtain from comparing coefficients or long division) M1 (factorise) A1 Well done. 6(a) Method1 Method 2 M1 (substitution) M1 (factorisation) M1 (values of y) Algebraic manipulation is a huge concern for equation 2. Common mista