BSS 2023 Maths Sec 4E Prelim QP - P1

[Turn Over Name Class Index Number BROADRICK SECONDARY SCHOOL SECONDARY 4 EXPRESS PRELIMINARY EXAMINATION 2023 MATHEMATICS Paper 1 Candidates answer on the Question Paper 4052/01 Aug 2023 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your name, class and index number 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. Answer all questions. 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 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, unless the question requires the answer in terms of . The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 90. For Examiner’s Use Error In Question Number Marks Deducted Rounding-off Reasoning Presentation For Examiner’s Use This document consists of 19 printed pages. 90

Broadrick Secondary School, Preliminary Examination 2023, Sec Four Express, Mathematics Paper 1 2 Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curved Surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of triangle ABC = ab2 1 sin C Arc length = rθ, where θ is in radians Sector area = 2 2 1 r , where θ is in radians Trigonometry C c B b A a sinsinsin == Abccba cos2222 −+= Statistics f fxMean  = Standard deviation = 22        −  f fx f fx

3 Broadrick Secondary School, Preliminary Examination 2023, Sec Four Express, Mathematics Paper 1 [Turn Over Answer all the questions. 1 (a) Calculate 21009 ( 0.2)−− . Write down the first five digits on your calculator display. Answer ….........……………..…….. [1] (b) Write your answer to part (a) correct to 2 significant figures. Answer ….........……………..…….. [1] 2 (a) Simplify fully ( ) 4 33 p . Answer ….........……………..…….. [1] (b) Given that 5 2 nx xx− = , find n. Answer n = .…...……...…………... [1] 3 Graph A Graph B Graph C Graph D Graph E Identify and write down a possible graph for each of the equations below. (a) 23yx −= , Answer Graph ..……………..…….. [1] (b) 23yx=+ . Answer Graph ..……………..…….. [1] x y x y x y x y x y

Broadrick Secondary School, Preliminary Examination 2023, Sec Four Express, Mathematics Paper 1 4 4 The bar chart below shows the yearly average exchange rate of one Singapore dollar (SGD) to Malaysia Ringgit (MYR) from 2018 to 2022. State one aspect of the chart that may be misleading and explain how this may lead to a misinterpretation of the chart. Answer ............................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... [2] 5 The equations of two straight lines are 8 0 and 5 32 xyax y+ − = + = . Given that the lines are parallel, find the value of a. Answer a = .…...……...…………... [2] 2.85 2.9 2.95 3 3.05 3.1 3.15 3.2 3.25 2018 2019 2020 2021 2022 MYR Year Yearly Average Exchange Rate of 1SGD to MYR

5 Broadrick Secondary School, Preliminary Examination 2023, Sec Four Express, Mathematics Paper 1 [Turn Over 6 The diagram shows a vase of height 8 cm. Water is poured into the vase at a constant rate. It takes 10 seconds to fill the vase. On the axes in the answer space, sketch the graph showing how the depth varies during the 10 seconds. [2] 7 It is given that 108 = 2323 , 120 = 32 3 5 and 1800 = 3 2 22 3 5 . (a) Find the largest integer that will divide 108, 120 and 1800 exactly. Answer ….........……………..…….. [1] (b) m is a number between 500 and 1000. The lowest common multiple of 120 and m is 1800. Find the value of m. Answer m = …...…………………... [1] Depth (cm) Time (s) 8 10

Broadrick Secondary School, Preliminary Examination 2023, Sec Four Express, Mathematics Paper 1 6 8 (a) Solve the inequalities 531 2 xx −−  +  . Answer ….........……………..…….. [2] (b) Hence represent the solution on the number line given below. Answer [1] 9 Given that 2(1 ) 31 qp q += − , express q in terms of p. Answer q = .........………………….. [3]

7 Broadrick Secondary School, Preliminary Examination 2023, Sec Four Express, Mathematics Paper 1 [Turn Over 10 (a) Sketch the graph of 2( 1) 2yx=− + + , showing clearly the coordinates of the turning point and y-intercept. Answer [2] (b) Write down the equation of the line of symmetry of 2( 1) 2yx=− + + . Answer ….........……………..…….. [1] 11 Solve the equation 2 28 239xx +=+− . Answer x = .…….… or …………... [4] O y x

Broadrick Secondary School, Preliminary Examination 2023, Sec Four Express, Mathematics Paper 1 8 12 The diagram shows a cube of sides 10 cm each. A right-angled triangular pyramid of sides x cm is cut from a corner of the cube. Given that the volume of the remaining cube is 987.652 cm3, find the value of x. Answer x = .…...……...…………... [3] 13 Factorise completely. (a) 425 20yx− Answer ….........……………..…….. [1] (b) 3 6 2ax ay bx by− − + Answer ….........……………..…….. [2] 10 cm x 10 cm 10 cm x x

9 Broadrick Secondary School, Preliminary Examination 2023, Sec Four Express, Mathematics Paper 1 [Turn Over 14 Box A is 50% larger than Box B while Box C is 10% smaller than Box B. Find the ratio of the size of Box A to that of Box C. Answer …...........… : ……...….... [2] 15 The diagram shows a regular pentagon ABCDE. Y and Z are points on CD. AZ is perpendicular to CD. EY intersects AZ at X. Given that angle AXE is 50º, find angle CEY. Answer ….........……………..…… º [5] Z B A C D E Y X

Broadrick Secondary School, Preliminary Examination 2023, Sec Four Express, Mathematics Paper 1 10 16 Three of the vertices of a parallelogram ABCD are A (4,6) , B (8, 4) and C (6,0) respectively. (a) Find the coordinates of D. Answer D = (…………. , ……..….) [2] (b) Justify if ABCD is a rhombus. Show your workings clearly. Answer [2]