Northbrooks 4E5N E Math Prelim P2 2026 QP

DO NOT TURN THE PAGE UNTIL YOU ARE TOLD TO DO SO. This document consists of 24 printed pages. [Turn over O NORTHBROOKS SECONDARY SCHOOL Preliminary Examination 2026 Secondary 4 and 5 CANDIDATE NAME CLASS REGISTER NUMBER MATHEMATICS 4052/02 Paper 2 Select a time zone. 18 August 2026 2 hours 15 minutes Additional Materials: Nil Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and register number on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid/tape. Answer all the questions. The number of marks is given in brackets [ ] at the end of each question or part question. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. The total of the marks for this paper is 90. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For 𝜋, use either your calculator value or 3.142. FOR EXAMINER’S USE Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 90

2 Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = rl Surface area of a sphere = 4r2 Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of triangle ABC = Cba sin2 1 Arc length = r , where  is in radians Sector area = 2 2 1r , where  is in radians Trigonometry C c B b A a sinsinsin == a2 = b2 + c2 – 2bc cos A Statistics Mean =   f fx Standard deviation = 22       −     f fx f fx

3 [Turn over Answer all the questions. 1 (a) Solve 21 .2 3 4xx =+− Answer x = ……………....…………………… [2] (b) Factorise completely 223 48 .xy− Answer …………………....…………………… [2] (c) Write 85 15 15 15 15 33 333  ++ as a single power of 3. Answer …………………....…………………… [2]

4 (d) Solve these simultaneous equations. 3 2 2 7 3 43 xy xy −= += You must show your working. Answer x = ……………....…………………… y = ……………....…………………… [3] (e) Write 2 ( )( 3 ) 3 y x y x y x y y x −−+ − − as a single fraction in its simplest form. Answer …………………....…………………… [3]

5 [Turn over 2 (a) In the diagram, angle 60QPR = and : 3: 2PR PQ = . Show that 22: 9 : 7PR RQ = . Answer [3] P R Q

6 (b) ABCD is a parallelogram. AB = 13 cm, AD = 5 cm, AE = 12 cm and DE = 9 cm. (i) Find angle DAB. Answer Angle DAB = ………………………. [3] (ii) Find the area of the parallelogram ABCD. Answer ………………………………… cm² [2] 13 9 5 12

7 [Turn over (c) The diagram shows a solid cylinder of diameter 16 cm and height 14 cm. A cone, ABC that touches both ends of the cylinder is removed from the cylinder. The remaining solid is melted and made into exactly 7 identical solid spheres with radius r cm. Find the value of r. Answer r = .……………....………………… [3] C A B D 16 14

8 3 A bakery recorded the masses of a batch of 300 cookies. The cumulative frequency diagram represents the distribution of the masses of the cookies. 300 275 250 225 200 175 150 Cumulative frequency 125 100 75 50 25 0 30 35 40 45 50 55 60 65 70 Mass (g) (a) Use the curve to estimate (i) the median mass, Answer ………………………………… g [1] (ii) the interquartile range, Answer ………………………………… g [2]

[Turn over 9 (iii) the 10th percentile of the cookies. Answer ………………………………… g [1] (b) A cookie is labelled as ‘Medium’ if its mass is greater than or equal to 50 g but less than 56 g. Two cookies are chosen at random. Calculate the probability that both are ‘Medium’ cookies. Answer ...………………………………… [2] (c) The masses of a second batch of 300 cookies were also recorded. The box-and-whisker diagram shows the distribution of the mass. Mass (g) Make two comments comparing the masses of the cookies in the two batches. Use figures to support your answer. Answer ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………….…….. [2] 20 30 40 50 60 70 80

10 4 (a) Sophia pays a monthly rent of $3174.20. This is 18% more than her monthly rent last year. Calculate her monthly rent last year. Answer $ …………………………… [2] (b) A new building is drawn on two maps of different scales. The area of the building drawn on the first map with a scale of 1: 50 000 is 216 cm . Given that the area of the same building drawn on the second map is 225 cm , find the scale of the second map in the form of 1 : n. Answer 1 : …………………………… [4]