XMSS E Math Prelim P1 2024 QP

This document consists of 20 printed pages. [Turn over XINMIN SECONDARY SCHOOL SEKOLAH MENENGAH XINMIN Preliminary Examination 2024 CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS Paper 1 Setter: Ms Low Yan Jin Vetter: Ms Vanessa Chia Moderator: Mr Johnson Chua 4052/01 21 August 2024 2 hour 15 minutes Candidates answer on the Question Paper READ THESE INSTRUCTIONS FIRST Write your name, index number and class in the spaces at the top of this page. 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. 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 in the space below the question. 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  , use either your calculator value or 3.142. Errors Qn No. Errors Qn No. Accuracy Simplification Brackets Units Geometry Marks Awarded Presentation Marks Penalised For Examiner’s Use 90 Parent’s/Guardian’s Signature:

2 Mathematical Formulae Compound Interest Total amount = 1 100 n rP+ Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = 21 3 rh Volume of a sphere = 34 3 r Area of triangle ABC = 1 sin2 ab C Arc length = r , where  is in radians Sector area = 21 2 r  , where  is in radians Trigonometry sin sin sin a b c ABC== 2 2 2 2 cosa b c bc A= + − Statistics Mean = fx f   Standard deviation = 22fx fx ff −  

3 [Turn over Answer all the questions. 1 Evaluate (a) 8.75 4.86 0.982+ , correct to 2 decimal places, Answer ……………………………. [1] (b) ( ) ( ) 625.87 10 3.94 10 −   , leaving your answer in standard form, correct to 3 significant figures. Answer ……………………………. [1] 2 (a) Express 540 as a product of its prime factors. Answer ……………………………. [1] (b) The number 540x y is a perfect square, where x and y are prime numbers and x > y. Find the value of x and of y. Answer x = ……………………………. y = ……………………………. [1]

4 3 (a) Simplify 2 5 6 224 8a b a b − . Leave your answer in positive index form. Answer ……………………………. [1] (b) Given that 193 729 kk= , find the value of k. Answer k = ……………………………. [2] 4 During a school’s anniversary, Joey sold x cookies at 50 cents each and (x + 30) chocolates at 90 cents each. Form an inequality in x and solve it to find the minimum value of x in order for her to receive at least $152 from the sales. Answer x = ……………………………. [3]

5 [Turn over 5 Solve the simultaneous equations. 3 29 2 5 30 xy xy += =− Answer x = ……………………………. y = ……………………………. [3] 6 Rearrange the formula 2 210 xky x ++= to make x the subject. Answer ……………………………. [3]

6 7 In the figure, ACD is a straight line and CD = CE. Angle CDE = x and angle CAB = 2x . Determine if AB is parallel to CE, stating your reasons clearly. Answer …………………………………………………………………………………..…..... ………………………………………………………………………………………... [2] 8 Simplify. (a) 5(3 2 ) 2( 4 )x y x y− − + Answer ……………………………. [2] (b) 2212 8 (3 2)pp+ − − Answer ……………………………. [2] A C D E B x° 2x°

7 [Turn over 9 A map of Mount Fuji has a scale of 1 : 25 000. (a) The length of a trail on the map is 52.2 cm. Calculate the actual length, in kilometres, of the trail. Answer ……………………………. km [2] (b) A lake at the base of Mount Fuji has an actual area of 6.57 km2. Calculate the area, in square centimetres, of the lake on the map. Answer ……………………………. cm2 [2] 10 The diagram shows a regular octagon (8-sided) and part of an n-sided regular polygon. Find the value of n. Answer n = ……………………………. [4] 69°

8 11 The force, F Newtons, between two particles is inversely proportional to the square of the distance, d cm, between them. If the force is 5.5 Newtons when the distance between the two particles is 2 cm, find (a) an equation connecting F and d, Answer ……………………………. [2] (b) the distance between two particles when the force is 3 Newtons. Answer ……………………………. cm [1] 12 (a) Factorise 326 11 7x x x+− . Answer ……………………………. [2] (b) Write as a single fraction in its simplest form 2 23 4 25 2 5 x xx +−− . Answer ……………………………. [3]

9 [Turn over 13 (a) Express 2 67xx−− in the form 2()x p q−− . Answer ……………………………. [1] (b) Hence, or otherwise, sketch the graph of 2 67y x x= − − in the axes below. Indicate clearly the values where the graph crosses the axes and the coordinates of the turning point on the curve. Answer [3] x y O

10 14 An F-1 block is made up of 4 squares of sides 2 cm each. The F-1 blocks can be combined to form more blocks and F-2 and F-3 blocks are shown below. (a) Complete the table. Block F-1 F-2 F-3 F-4 Perimeter (cm) 20 28 [1] (b) Write down an expression, in terms of n, for the perimeter of an F-n block. Answer ……………………………. cm [1] (c) Hence, explain if it is possible to have a block with a perimeter of 100 cm. Answer …………………………………………………………………………………... …………………………………………………………………………………... [2] F-1 F-2 F-3