Singapore Chinese Girls School Paper 2

SINGAPORE CHINESE GIRLS’ SCHOOL PRELIMINARY EXAMINATION 2022 SECONDARY FOUR O-LEVEL PROGRAMME CLASS 4 REGISTER NUMBER CENTRE NUMBER S INDEX NUMBER MATHEMATICS 4048/02 PAPER 2 Monday 29 August 2022 2 hours 30 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class, register number, centre number 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/tape. 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 π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 100. This document consists of 21 printed pages and 1 blank page. CANDIDATE NAME [Turn over For Examiner’s Use www.KiasuExamPaper.com 683

2 Mathematical Formulae Compound Interest Total amount = 1 100 nrP§·¨¸©¹ Mensuration Curved surface area of a cone = rlS Surface area of a sphere = 24 rS Volume of a cone = 21 3 rhS Volume of a sphere = 34 3 rS Area of triangle ABC = 1 sin2 ab C Arc length = rT , where T is in radians Sector area = 21 2 r T , where T is in radians Trigonometry sin sin sin abc ABC 22 2 2c o sabc b c A Statistics Mean = fx f 6 6 Standard Deviation = 22fx fx ff §·66 ¨¸66 ©¹ www.KiasuExamPaper.com 684

3 [Turn over 1 (a) (i) Solve the inequalities 31 2 1525 xx d . Answer ……………………………... [3] (ii) Hence, state the largest integer that satisfies 31 2 1525 xx d . Answer ……………………………... [1] (b) Simplify 2 2 (4 10) 10 21 10 x xx

. Answer ……………………………... [3] www.KiasuExamPaper.com 685

4 (c) Solve the equation 2 65 123 1 2 x xx . Answer x = …………………………. [4] 2 The stem-and-leaf diagram shows the scores of a group of students in an English test. 0 a 1 8 9 2 1 6 8 8 3 0 2 3 6 6 6 7 4 4 4 5 7 5 0 b Key: 1 8 represents 18 marks (a) Students who scored more than n marks were awarded a distinction. Given that 35% of the students were awarded a distinction, find the value of n. Answer n = …………………………. [2] www.KiasuExamPaper.com 686

5 [Turn over (b) The range of scores for the English test is 44 marks. The mean score for the English test is 33.3 marks. By forming two equations, find the value of a and of b. Answer a = ……….... , b = ……….... [3] (c) The same group of students also took a Science test. Their results for the Science test are summarised in the table. Mean 38 marks Standard Deviation 6 marks Make two comments comparing the performance of the students in both tests. Answer ……………………………………………………………………………... ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… [2] www.KiasuExamPaper.com 687

6 3 Jon and Lim are regular customers of the same fruit supplier. As regular customers, they are given a 10% discount off all their purchases. The matrix, T, shows the number of cartons of fruits they purchased from the supplier. 15 18 20 15 12 16 §· ¨¸ ¨¸¨¸©¹ T (a) Each carton of apples costs $45. Each carton of oranges costs $35. Each carton of pears costs $40. Represent these amounts in a 1×3 row matrix N. Answer N = §· ¨¸ ¨¸¨¸©¹ [1] (b) Evaluate the matrix C = 0.9NT. Answer C = [2] (c) State what each element of matrix C represents. Answer ……………………………………………………………………………... ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… [1] (d) The elements of the matrix R, where R = QT, represent the total number of each type of fruit that Jon and Lim purchased respectively. (i) Given that there are 32 apples in each carton of apples, 72 ora nges in each carton of oranges and 45 pears in each carton of pears, write d own a 3×3 matrix Q to represent these information. Answer Q = §· ¨¸ ¨¸¨¸©¹ [1] Apples Oranges Jon Lim Pears www.KiasuExamPaper.com 688

7 [Turn over (ii) Evaluate the matrix R. Answer R = [1] (e) Jon sold all his apples in bags of 5 and at $6 per bag. He sold all his pears at $1 each. He found that 15% of his oranges were rotten and could not be sold. He sold all the remaining oranges. Given that Jon made a profit of 20% from the sale of the fruits, c alculate the price at which he sold each orange. Give your answer correct to the nearest cent. Answer $ ………………………….. [4] www.KiasuExamPaper.com 689

8 4 The diagram shows a circle ABCD. BAE and CDE are straight lines. BT and CT are tangents to the circle. Angle EAD = 70°, angle ACB = 36° and angle BTC = 72°. (a) Find, giving reasons for each answer, (i) angle BCD, Answer Angle BCD = ……………… [2] (ii) angle ABD, Answer Angle ABD = ……………… [2] (iii) angle ACT. Answer Angle ACT = ………………. [2] A B C D E T 70° 36° 72° www.KiasuExamPaper.com 690

9 [Turn over (b) Hence, what can you deduce about the line AC? Give a reason for your answer. Answer ……………………………………………………………………………... ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… [2] (c) Q is a point on AC such that angle AQB = 72°. Explain clearly whether Q is the centre of the circle. Answer ……………………………………………………………………………... ………………………………………………………………………………………