2023 ZHSS EMATH P1 PRELIM QP

[Turn over] ZHONGHUA SECONDARY SCHOOL PRELIMINARY EXAMINATION 2023 SECONDARY 4 EXPRESS / 4 NORMAL (ACADEMIC) SBB Candidate’s Name Class Register Number MATHEMATICS 4052/01 PAPER 1 25 August 2023 2 hours 15 minutes Candidates answer on the Question Paper. 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 on both sides of the paper. You may use an HB pencil for any diagrams or graphs. Do not use 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 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 of the marks for this paper is 90. Setter：Mr GOH CP Vetter: Mr Francis Tan This question paper consists of 22 printed pages (including this cover page) 90

2 [Turn over] Mathematical Formulae Compound interest Total amount = Mensuration Curved surface area of a cone = Surface area of a sphere = Volume of a cone = Volume of a sphere = Area of triangle ABC = Arc length = , where is in radians Sector area = , where is in radians Trigonometry Statistics Mean = Standard deviation = n rP      + 1001 rl 24 r hr 2 3 1 3 3 4 r Cabsin2 1 r  2 2 1 r  C c B b A a sinsinsin == Acbcba cos))((2222 −+=   f fx 22       −     f fx f fx

3 [Turn over] Answer all the questions 1 Calculate 3 47 6.5 7.712.3 8.8 −− , give your answer correct to 5 significant figures. Answer ……………………..…………… [1] 2 Simplify (a) 53 4 .63 aa Answer ……………………..…………… [1] (b) 4 – 2(1 – 5x). Answer ……………………..…………… [1] 3 28 27.5 27.9 32.1 51.1 20.6 31.6 18.7 (a) Find the median of the set of numbers. Answer ……………………… [1] (b) Find the range for the set of numbers. Answer ……………………… [1]

4 [Turn over] 4 The first four diagrams in a sequence are shown below. Diagram 1 Diagram 2 Diagram 3 Diagram 4 5 dots 9 dots 13 dots 17 dots (a) Find the number of dots in Diagram 9. Answer ……………………… [1] (b) Find an expression, in terms of n, for the number of dots in Diagram n. Answer ……………………… [1] (c) Explain whether it is possible to have a diagram with 533 dots. ……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… [1]

5 [Turn over] 5(a) A spinner is divided into red, green and yellow regions. The probability that the spinner is in the red region is 1 3 . The probability that the spinner is in the green region is 5 12 . Find the probability that the spinner is in the yellow region. Answer ……………………………… [1] (b) A box contains 12 red balls, 14 blue balls and some yellow balls initially. 10 more yellow balls are added to the box. The probability of picking a yellow ball from the box at random is now 1 3 . Find the number of yellow balls in the box initially. Answer ……………………………… [2]

6 [Turn over] 6 A pen costs $2.10 and a pencil costs $1.35. Fyn buys a total of 11 pens and pencils. She spends $18.60 for x pens and y pencils. Find the number of pens and pencils Fyn bought. Answer Number of pens = …………………………………… … Number of pencils = ……………………………… [3]

7 [Turn over] 7 The figure is made up of a 7 sided regular polygon with centre O, a triangle and a quadrilateral. (a) Find angle OGF. Answer ……………………………… [2] The exact value of angle EFH is 612 7 degrees. GF is parallel to OH. (b) Show that quadrilateral FGOH is a parallelogram. …………………………………………………………………………………………………… …………………………………………………………………………………………………… …………………………………………………………………………………………………… …………………………………………………………………………………………………… ………….…………………………………………………………………..…………………… [2] (c) Find reflex angle AOH. Answer ……………………………… [2] O A B A C D E F G H

8 [Turn over] 8 A school sent 60 students from Class A and 105 students from Class B to a museum. The school divided these students into groups using the following rules. • Each group must have the same number of students. • All students in any group must be from the same Class. • There should be as few groups as possible. Find the number of students in each group and the total number of groups. Answer Number of students in each group = ........................................................ Total number of groups = ....................................................... [3]

9 [Turn over] 9 The diagram shows a square ABCD. The line AF meets the side BC at point E. E is the midpoint of BC and AF. The area of triangle BEF is 9 cm2. Find the length of the side of the square. Answer ……………………………… cm [4] F B D A C E

10 [Turn over] 10 In this scale drawing, A and B are two points in a garden. North North A B Amy starts walking towards a lamp post 500 metres away at a bearing of 165o from A. (a) Mark and label on the drawing the position, L, of the lamp post. [2] (b) Sandy walks from point B to meet Amy. When they meet, she had walked the shortest possible distance. Find the bearing of Sandy’s path. Answer ……………………………… [2] Scale : 1 cm represents 50 m