TKGS 2024 S4 Math Prelim P1 Question Paper (with Answer Key)

TANJONG KATONG GIRLS’ SCHOOL PRELIMINARY EXAMINATION SECONDARY FOUR EXPRESS CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS 4052/01 Paper 1 16 August 2024 2 hours 15 minutes Candidates answer on the Question Paper READ THESE INSTRUCTIONS FIRST Write your index number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE ON ANY BARCODES. 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. This document consists of 23 printed pages and 1 blank page. For Examiner’s use

Tanjong Katong Girls’ School 2 4052/S4Prelim/01/2024 Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = rl Surface area of a sphere = 4 2r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of triangle ABC = Cabsin2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin == Abccba cos2222 −+= Statistics Mean = f fx   Standard deviation = 22        −  f fx f fx

Tanjong Katong Girls’ School [Turn over 3 4052/S4Prelim/01/2024 Answer all the questions. 1 (a) Calculate 2 4165 75.125 11.2 ( 3) 3.142 + −  − . Write your answer correct to 2 significant figures. Answer …………….……………………. [1] (b) The number of people in a shopping mall is 1100, correct to the nearest hundred. Write down the minimum number of people there are in the mall. Answer …………….……………………. [1] 2 Simplify (a) 5 2(6 1)x−− , Answer …………….……………………. [1] (b) 1 9 3 6 27b a −   . Answer …………….……………………. [2]

Tanjong Katong Girls’ School 4 4052/S4Prelim/01/2024 3 Albert and Chris have some savings in the ratio 5 : 3. They spent $30 each from their savings and the new ratio of their savings is 2 : 1. Find the amount of savings Chris has at the start. Answer $ …………….…………………. [2] 4 (a) Express 1400 as a product of its prime factors. Answer …………….……………………. [1] (b) q is a number between 70 and 90. The highest common factor of q and 1400 is 28. Find the smallest possible value of q. Answer q= …………….………………. [2]

Tanjong Katong Girls’ School [Turn over 5 4052/S4Prelim/01/2024 5 Given that 3333 1 1 22222a− = + + + , find the value of a. Answer a= …………….………………. [2] 6 (a) Expand and simplify 22(5 3 )mn+ . Answer …………….…………………… [2] (b) Factorise completely 2324( ) 21mn mn− . Answer …………….……………………. [1]

Tanjong Katong Girls’ School 6 4052/S4Prelim/01/2024 7 The area of triangle XYZ is 12.6 cm2. 4.5 cmXY = and 7.1 cmYZ = . Find two possible values for angle XYZ. Give your answers in radians. Answer …...………rad or .….…..… rad [3] 8 P is inversely proportional to 3Q . Find the percentage change in P when Q is reduced by 20%. Answer …………….…………………% [2]

Tanjong Katong Girls’ School [Turn over 7 4052/S4Prelim/01/2024 9 It is given that 2 5 qrp q += − . (a) Find p when 1 5q= and 6r=− . Answer p= …………….……………… [1] (b) Express q in terms of p and r. Answer …………….……………………. [2]

Tanjong Katong Girls’ School 8 4052/S4Prelim/01/2024 10 The diagram shows a quadrilateral ABCD made up of two triangles. 20 cmAB= , 12 cmAD= , 32 cmCD= . Angle 90CBD= and angle 30BCD= . (a) Find BD. Answer …………….……………… cm [2] (b) Hence or otherwise, show that it is possible to form a circle with diameter AB such that point D lies on the circumference of the circle. Answer [2] A B C D 20 cm 12 cm 32 cm 30

Tanjong Katong Girls’ School [Turn over 9 4052/S4Prelim/01/2024 11 Write as a single fraction in its simplest form 2 38 (1 2 ) 2 1hh +−− . Answer …………….……………………. [3]

Tanjong Katong Girls’ School 10 4052/S4Prelim/01/2024 12 k is a positive integer. An odd number is formed when 5 is subtracted from twice of k. (a) Write down an expression for the odd number in terms of k. Answer …………….……………………. [1] (b) The sum between the odd number and the next consecutive odd number is greater than 16. Form an inequality in terms of k and solve it to find the smallest possible value of the larger odd number. Answer …………….……………………. [3]