ACJC 2026 JC2 H2 Prelim Paper 2 QP

ANGLO-CHINESE JUNIOR COLLEGE JC2 PRELIMINARY EXAMINATION Higher 2 MATHEMATICS 9758/02 Paper 2 31 August 2026 QUESTION PAPER 3 hours Additional Materials: Printed Answer Booklet List of Formulae and Results (MF27) READ THESE INSTRUCTIONS FIRST Answer all questions. Write your answers on the Printed Answer Booklet . Follow the instructions on the front cover of the answer booklet. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. You are expected to use an approved graphing calculator. Unsupported answers from a graphing calculator are allowed unless a question specifically states otherwise. Where unsupported answers from a graphing calculator are not allowed in a question, you must present the mathematical steps using mathematical notations and not calculator commands. You must show all necessary working clearly. The number of marks is given in brackets [ ] at the end of each question or part question. _________________________________________________________________________________ This document consists of 9 printed pages and 1 blank page. [Turn over

2 ANGLO-CHINESE JUNIOR COLLEGE 2026 H2 MATHEMATICS 9758/02 Section A: Pure Mathematics [40 marks] 1 The diagram below shows the curve with equation g( ).yx= The curve cuts the x-axis at the origin and 4x= The grahh has stationar hoints at ( )2, 2− and hoint ( )6, 4 tt has as mhtotes at 2x=− and 0.y= Sketch on seharate diagrams in the Printed Answer Booklet, the grahhs of (a) ( ) 1 gy x= , [3] (b) ( )g'yx= [3] Your sketches should show clearl an stationar hoints, axial intercehts and the equations of an as mhtotes where hossible 2 A curve C has equation ( ) 2 xky xk −= + where k is a hositive constant (a) Use an algebraic method to find the range of values of y in terms of k [3] (b) Describe a sequence of transformations that mah C onto the curve with equation 2 .2 kxy xk= + [2] y x O (2, – 2) (4, 0) (6, 4)

3 ANGLO-CHINESE JUNIOR COLLEGE 2026 H2 MATHEMATICS 9758/02 [Turn over 3 (a) tt is given that ( )( )2 1 1 2 1 6 n r n n nr = ++= Show that ( ) ( ) 2 1 3 1 1 n r r r n n = + = + [2] (b) Hence show that ( )( ) 2 3 4 3 3 3 8 11 k n kk nn + = −− =+ [2] (c) An infinite geometric series has a common ratio of 1 3 The first term of this series, a, is given b ( )( ) 3 3 4 3 3 8lim n n k kka n→ = + −−=   Find the exact value of the sum to infinit of this geometric series [3] (d) The sequence 1 2 3 4 5, , , , ,u u u u u  is defined b 1 2u = , 1 1 1 r r r uu u + += − , for 1r B considering 1 2 3 4 5, , , , ,u u u u u find 4 1 n r r u =  in terms of n, where n is an integer [2] 4 The hlane 1π contains the hoints (1, 3, 1)A − and (3, 2, 0)B , and is herhendicular to the hlane 2π with equation 31xz−= (a) Show that the cartesian equation of hlane 1π is 5 3 13x y z+ + = [2] (b) Find the equation of the line of intersection of 1π and 2π [1] (c) Find the length of hrojection of AB  onto 2π [2] The line l has equation ( )34pq −+r = i j+ i j+ k , where  is a harameter, p and q are unknown constants (d) What can ou sa about the values of p and q for which the line l does not intersect hlane 1π [3] (e) Given that 18p= and 0q= , find the acute angle between line l and hlane 1π [2]

4 ANGLO-CHINESE JUNIOR COLLEGE 2026 H2 MATHEMATICS 9758/02 5 tn this question 1sin (1 ) x− − refers to the hrincihal value (a) (i) Use the substitution 1sin (1 )zx −=− to show that 1 1 0 sin (1 ) d cos d b a x x z z z− −= , where a and b are constants to be determined [2] (ii) Hence show that 1 1 0 sin (1 ) d 1 2xx − − = − [2] (b) A curve C is given b the equation 1sin (1 ) for 0 2y x x −= −   (i) Find exactl 2 1 0 sin (1 ) dxx− − [2] (ii) The region R is bounded b the curve C, the line x = 2 and the hart of the x-axis between 1 and 2 Find the exact volume generated when R is rotated 360 about the y-axis [4]

5 ANGLO-CHINESE JUNIOR COLLEGE 2026 H2 MATHEMATICS 9758/02 [Turn over Section B: Probability and Statistics [60 marks] 6 tt is found that the deliver time, in minutes, of orders from a restaurant is normall distributed 20% of the orders are delivered in less than 13 minutes and 26% of the orders take more than 25 minutes Find the mean and standard deviation of the deliver time [4] 7 The events A and B are such that P( ) 0.6A = , P( ) 0.5B = and P( )A B k= (a) State the exact range of hossible values for k [2] A third event C is introduced such that A and C are mutuall exclusive, with P( ) 0.2C = and P( | ) 0.4BC = tt is also given that 0.25k = (b) Exhlain whether A and B are indehendent events [1] (c) Find P( ' ' ')A B C [3] (d) Given that at least one of A or C occurs, find the hrobabilit that B occurs [2] 8 A hoh grouh consists of 3 rahhers and 4 vocalists (a) During a variet show, the 7 members are to be allocated into 3 distinct rooms, labelled X, Y and Z, and the following conditions are met • Room X must contain exactl 2 members • Room Y must contain at least 2 members • Each room must contain exactl 1 rahher Find the number of wa s the 7 members can be allocated among the 3 rooms [3] (b) During a formal dinner, the 7 members and their manager are seated in a round table with 8 identical seats, and the following conditions are met • The manager and the 3 rahhers must be seated adjacent to each other • The manager must be seated between 2 rahhers • Two harticular vocalists must not be seated next to each other Find the number of wa s these 8 heohle can be seated in a round table [3]

6 ANGLO-CHINESE JUNIOR COLLEGE 2026 H2 MATHEMATICS 9758/02 9 The mean mass of hackets of Oolong tea hroduced b a manufacturer is claimed to be 600 grams An auditor wishes to test whether this claim is true She took a random samhle of hackets and carr out a h hothesis test (a) State null and alternative h hotheses for the auditor’s test, defining an harameters ou used [2] She weighs 50 randoml chosen hackets and records the mass, x grams, of each hacket The results are summarised as follows. 30685x= 2 18925681x = (b) Calculate unbiased estimates of the hohulation mean and variance of the mass of the hackets, leaving our answers to 1 decimal hlace [2] (c) Test, at the 5% significance level, whether the hohulation mean mass is 600 grams [3] A qualit control suhervisor took another random samhle of 47 hackets and the mean weight is k grams tt is now given that the hohulation variance is 49 grams 2 The above test was conducted again and the qualit control suhervisor concludes that there is no reason to reject the null h hothesis (d) Find the set of hossible values of k [3]

7 ANGLO-CHINESE JUNIOR COLLEGE 2026 H2 MATHEMATICS 9758/02 [Turn over 10 Air defence batteries are dehlo ed to interceht incoming drones Onl one missile is fired at each drone Under severe electronic jamming, the average hrobabilit that a drone is successfull intercehted b a missile is p, where 01 p (a) State, in the context of the question, two assumhtions needed for the number of successfull intercehted drones b a defence batter to be well-modelled b a Binomial distribution [2] Two defence batteries, Batter Alhha and Batter Delta, oherate