Bendemeer 2024 4E Prelim EMath P2 - MS

This document consists of 22 printed pages. [Turn over CANDIDATE NAME CLASS INDEX NUMBER ------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------- 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. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, 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 number of 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. FOR EXAMINER’S USE MATHEMATICS Paper 2 4052/02 21 August 2024 2 hours 15 minutes Candidates answer on the Question Paper. No additional materials are required. BENDEMEER SECONDARY SCHOOL 2024 PRELIMINARY EXAMINATION SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC) 90 MARKING SCHEME

2 4052/02/Sec 4E5N(A)/Prelim/BDMS 2024 MATHEMATICAL FORMULAE Compound Interest Total amount = P n r      + 1001 Mensuration Curved surface area of cone = rl Surface area of a sphere = 4  r2 Volume of a cone = hr 2 3 1 Volume of sphere = 3 3 4 r Area of triangle ABC = Cabsin2 1 Arc length = radiansin is where, r Sector area = radiansin is where,2 1 2 r Trigonometry C c B b A a sinsinsin == Abccba cos2222 −+= Statistics Mean =   f fx Standard Deviation =        −     22 f fx f fx

3 4052/02/Sec 4E5N(A)/Prelim/BDMS 2024 [Turn Over 1 (a) Simplify ( 3𝑎−3 2𝑏2 4 1 2𝑏3 ) −2 and leave your answer in positive index notation. = ( 4 1 2𝑏3 3𝑎−3 2𝑏2 ) 2 ………………. M1 = 4𝑏6 9𝑎−3𝑏4 …………………. M1 = 4𝑎3𝑏2 9 ……………………. A1 Answer (a) __________________________ [3] (b) Simplify (𝑎−5𝑏)2 𝑎2−25𝑏2 ÷ 𝑎−5𝑏 5𝑏 . = (𝑎−5𝑏)2 (𝑎−5𝑏)(𝑎+5𝑏) × 5𝑏 𝑎−5𝑏 ………… M1 for (𝑎 − 5𝑏)(𝑎 + 5𝑏) = 5𝑏 𝑎+5𝑏 ……………………………… A1 Answer (b) __________________________ [2]

4 4052/02/Sec 4E5N(A)/Prelim/BDMS 2024 2 The diagram below shows a school Tchoukball court of dimension 27m by 16m. On each end is a semicircle of radius 3m. The shaded part is to be painted yellow. (a) Find the area of the court that is painted yellow. Area that is painted yellow = (27 × 16) − (𝜋 × 32) − (16 × 4) ………. M1 = 339.726 = 340 m2 (3sf)…………………………………….. A1 Answer (a) _______________m2 [2]

5 4052/02/Sec 4E5N(A)/Prelim/BDMS 2024 [Turn Over (b) 3 workers can paint the court in 5 days. After painting the first day, the workers had to stop on the second and third day because it was raining. Teachers, Mr Chin and Mr Lee, decided to help with the painting on the fourth and fifth day. Assuming the 3 workers and 2 teachers paint at the same rate, can they finish painting the shaded area on the fifth day? Show your working clearly. Man-days needed to paint the court = 5 x 3 = 15 …………………. M1 Man-days needed after the first day = 15 – (3 x 1) = 12 Number of people needed for the fourth and fifth days = 12 ÷ 2 = 6 …………………. M1 Number of workers and teachers painting on the fourth and fifth days = 5 Therefore, they cannot finish painting on the fifth day. [3] A1

6 4052/02/Sec 4E5N(A)/Prelim/BDMS 2024 3 (a) In the diagram, ∠𝐴𝐵𝐷 = ∠𝐶𝐵𝐷 and ∠𝐵𝐴𝐷 = ∠𝐵𝐶𝐷. Prove that ∆𝐴𝐵𝐷 and ∆𝐶𝐵𝐷 are congruent. In ∆𝐴𝐵𝐷 and ∆𝐶𝐵𝐷 , 𝐵𝐷 is common ∠ABD = ∠CBD (given) ∠BAD = ∠BCD (given) Therefore, ∆𝐴𝐵𝐷 and ∆𝐶𝐵𝐷 are congruent (AAS) ………. B1 [3] B2 for 3 correct statements B1 for 2 correct statements

7 4052/02/Sec 4E5N(A)/Prelim/BDMS 2024 [Turn Over (b) In the diagram below, O is the centre of the circle and BDG is a straight line. PQ is a tangent to the circles at A and H respectively. ∠𝐴𝐵𝐷 = 270 and ∠𝐷𝐸𝐹 = 1530. Stating the angle properties of circles clearly, find (i) ∠𝐴𝐶𝐷 = 270 (Angle in the same segment) ………… B1 Answer (i) _______________0 (ii) ∠𝐷𝐴𝐻 ∠𝑂𝐴𝐻 = 900 (radius perpendicular to tangent) ∠𝐴𝑂𝐷 = 540 (Angle at centre = 2x angle at circumference) ∠𝑂𝐴𝐷 = 180 − 54 2 = 630 ∠𝐷𝐴𝐻 = 90 − 63 = 270 …………………… A1 Answer (ii) _______________0 [1] [2] (iii) Is BA parallel to FG? Justify your answer clearly with working. ∠𝐷𝐺𝐹 = 180 − 153 (Angles in opposite segments) = 270 ………………………….. M1 Since ∠𝐴𝐵𝐷 = ∠𝐷𝐺𝐹 = 270, ………………………………….. M1 By the converse of alternate angles, BA is parallel to FG ……….. A1 Note: Minus 1 mark from Q3(b) when angle properties of circles are not given / written wrongly. [3] M1 for either property

8 4052/02/Sec 4E5N(A)/Prelim/BDMS 2024 4 Starkids Centre is organising a talent competition for children. Children can choose to compete in 3 categories – singing, dancing and acting. Matrix E shows the number of boys and girls in each category for the age group 5 to 8 years old. Matrix F shows the number of boys and girls in each category for the age group 9 to 12 years old. (a) Evaluate the matrix T = E + F. 𝐓 = ( 5 8 7 4 6 7 ) + ( 12 9 8 10 15 11 ) = ( 17 17 15 14 21 18 ) ……………………. B1 Answer (a) T =_________________ [1] (b) Each child is charged a registration fee for the competition. The registration is $30 for singing, $25 for dancing and $22 for acting. Represent the fees in a 1 x 3 matrix C. 𝐂 = (30 25 22) …………………….. B1 Answer (b) C =_________________ [1] 𝐄 = ( 5 8 7 4 6 7 ) Boys Girls Singing Dancing Acting 𝐅 = ( 12 9 8 10 15 11 ) Boys Girls Singing Dancing Acting

9 4052/02/Sec 4E5N(A)/Prelim/BDMS 2024 [Turn Over (c) Evaluate the matrix M = CT and state what the elements in matrix M represent. 𝐌 = (30 25 22) ( 17 17 15 14 21 18 ) = (1347 1256) ………………….. B1, B1 M represents the registration fees collected from boys and girls respectively …….. B1 Answer (c) M =_________________ ________________________________________________________________________ ________________________________________________________________________ [2] [1] (d) Using matrix multiplication, calculate the total amount of registration fees collected for this competition. (1347 1256) × (1 1) …………… M1 = (2603) ………………………… A1 Answer (d) $_________________