KSS 2023 4045 4NA P2 QP

Candidate Name Class: Secondary ) 4NA (Session 1) ONDARY SCHOOL Examination lormal (Academic) 4th August 2023 KRANJISECONDARY KRANJISECONDARY KRANJISECONDARY KRANJ' KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY XRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJISECONDARY KRANJISECONDARY KRANJISECONDARY KRANJISECONDARY Write your class, index number and name in the spaces at the top of this prg". 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. Section A Answer all questions Section B Answer one question. The number of marks is given in brackets [ ] at the end of each question or part question lf 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 70. The use of an approved scientific calculator is expected, where appropriate. lf 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 your answers in degrees to one decimal place. For r, use either your calculator value or 3.142. For Examiner's Use Total 70 Set by: Mr Aziz This question paper consists of 18 printedrpages, including the cover page. i [Turn over ,WT"EMATICS 'wi2' $W'm W 2h&{w

*--=--*j ir-:-) 2 Compound Interest Mensuration Trigonometry Statistics Mathematical Formulae 1+ ' 100 Mean: 'Zf*' Zr Total amount: Curved surface areaof a cone: nrl Surface area ofa sphere :4nf Volume of a cone - !*'h -1 Volume of a sphere: 7y' n T J 1 Sector area: lr'0 ,where I is inradians 2 Arc length : r0, where d is in radians a b c sinA sin-B sinC a' = b' + c' - 2bccos A Area of tria ngle ABC: labsinC2 Zf.Zr Zr.Standard deviation: \ Zr

1J Section A(62marks) Answer all the questions in this section. 1 (a) Calculate 1El4:. Answer (b) By rounding each number to 1 significant figure, estimate the value of 7.88x 551.7 0.0842 You must show your working. Answer t1l ....12) 2 (a) Write 0.000 987 in standard form. Answer (b) The population of Singapore in 2022 was 5.642x 106 . The area of Singapore is 7.18 xIO' ksr? . t1l Calculate the average number of people psr square kilomeke in Singapore in2022. Leave your answer in standard form. Answer \ . people twrr2 721 \

4 3 A B (b) the value of n. C D E The diagram above is made up of a square, a regular pentagon and parts of an incomplete regular polygon ABCDE of n sides. Find (a) IBCD, t Answer Answer 'l2l L

rt-ffi 5 4 The stem-andJeaf diagram shows the weight, in kilograms, of 20 Secondary I students in Kranji S'econdary School. 4 5 6 7 1 1 J 2 0 0 0 1 5799 5 91 1 4 9 6 6 Key:4l0means40 Find (a) the number of students with weight at least 51 kg, Answer (b) the standard deviation of all the weights Answer t1l \ kel2l 5 The general term of a sequence is T, = -1*lJ (a) Find the 3'd term in the sequence. Answer (b) Given that T, *7,*r = 9, find the value of n. t1l Answer n t3l

6 6 Ms Wong wants to invest for her retirement. 2 banks offered her the following investment plans. Ms Wong has $400 000 to invest. She wants to retire in 15 years Which bank should she invest her money in? Justifo your answer \ KBS Bank KCBC Bank Simple interest rate of 2.2Yo per annum Compound interest rate of Z.5Yoper annum for first 5 years only. For subsequent years, the compound interest rate is l.5Yoper annum. Answer: Ms Wong should invest in .. . . .. Bank as. .. . . I 14)

7 7 A Besla electric car costs $94 900. Elijah bought the car at a l0o/o discount. (a) He intends to sell it for a cash profit of $30 000 Calculate his selling price. Answer $ (b) Freya buys the car in (a) from Elijah on hire purchase. She pays a deposit of 20o/o of the selling price and 60 monthly instalments of$1700 each. Find 12) \ (D the amount of deposit paid, Answer $ (iD the total amount she has to pay for the car Answer $ t1l L

8 8 (a) Drarv the triangle ABC in which IABC:63" and BC :7.1 cm. The line AB is given below. l2l (b) Construct the perpendicular bisector of AB t1l (c) Construct the angle bisector of IABC . t1l (d) D is equidistant from points A and B and also equidistant from the lines AB and BC. Draw a circle with centre A andradius AD. tll \ BA L

9 (iii) *' - 4y' , Answer (iv) 2x2 -11x + 5 , Answer (v) 72ar 78bx +9cty - 6by Answer (b) Rearrange the equation to make k the subject. k+25k=- h Answer .... tll l2l 12) 12) I (a) Factorise

il--"....".-) 10 10 A family drove 350 km in a car from Singapore to Kuala Lumpur at an average speed ofx kmlh. (a) Write down an expression, in terms ofx, for the numtpr of hours taken to drive from Singapore to Kuala Lumpur. Answer hr [1] (b) The family continued their journey from Kuala Lumpur to Ipoh at anaverage speed of (x + 10) km/h. The distance from Kuala Lumpur to Ipoh is 210 km. Write down an expression, in terms of x, for the number of hours taken to drive from Kuala Lumpur to Ipoh. Answer hr l1l (c) The entire journey from Singapore to Ipoh took 6 hours. Form an equation in x and show that it neduces to 3x2 -250x-1750 = 0. Answer \ t3l (d) Solve the equation 3xz -250x-1750 = 0 and hence find the average speed of the car from Singapore to Kuala Lumpur. Answer t ... hr [3]