2023 BPGHS Prelim P1

Name of Candidate: _____________________ ( ) Class: ______ Calculator Model: This paper consists of 22 printed pages. BUKIT PANJANG GOVERNMENT HIGH SCHOOL PRELIMINARY EXAMINATION 2023 SECONDARY 4/5 GCE 'O' LEVEL SYLLABUS MATHEMATICS Paper 1 4052 / 01 Date: 21 August, 2023 Duration: 2 h 15 mins Time: 0750 – 1005 h 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 on both sides of the paper. 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 𝜋, use either your calculator value or 3.142, unless the question requires the answer in terms of 𝜋. At the end of the examination, fasten all your work securely together 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 90. Setter: Mr Sim Meng Hoe [Turn over] Additional Materials: NIL

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 = Cabsin2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin == Abccba cos2222 −+= Statistics Mean = f fx   Standard deviation = 22fx fx ff  − 

3 1 Calculate 33 2.13 81.23 3.23.524   , giving your answer correct to 4 significant figures. Answer ………..…………………… [1] ____________________________________________________________________ 2 At a warehouse sale, all prices are reduced by 15%. The price of a set of ear pods during the sale is $221. (i) Find its original price. Answer $ ……..…………………… [1] (ii) If the salesman still earns a profit of 10.5% during the sale, find the percentage profit he earns from selling the pair of ear pods if it is not on sale. Answer ……..………………….… % [3] ____________________________________________________________________

4 3 Ethan measures the amount of rain, in millimetres (mm), each day for 31 days. The bar chart shows his results. (a) Write down the median amount of rain. Answer ………..……………… mm [1] (b) Find the mean amount of rain per day. Answer ………..……………… mm [2] (c) Ethan picks one of these days at random. Find the probability that, on that day, the amount of rain was 3 mm or more. Answer ………..…………………… [1] ____________________________________________________________________

5 4(a) These are the first four terms in a sequence. 9 5 1 -3 Find an expression, in term of n, for the nth term of the sequence. Answer ………..…………………… [1] (b) The nth term of another sequence is given by 34 43 n nT n += + . Determine if it is possible to have a term in the sequence to be greater than 1. Explain your answer. ……………………………………………………………………………………………. ……………………………………………………………………………………………. ……………………………………………………………………………………………. ……………………………………………………………………………………………. ……………………………………………………………………………………………. ……………………………………………………………………………………………. ……………………………………………………………………………………………. ……………………………………………………………………………………………. ………………………………………………………………………………………... [2] ____________________________________________________________________

6 5 A drawer contains 40 balls. 15 balls are black, 5 balls are grey and 20 balls are white. Samuel chooses one ball from the drawer at random. (a) Find the probability that the ball is not black. Answer ………..…………………… [1] Samuel adds a few more grey balls. The probability of choosing a grey ball is now 2 7 . (b) Find the number of grey balls he added. Answer ………..…………… balls [2] ____________________________________________________________________

7 6 Solve the simultaneous equations. 7 2 8xy+= 2 3 13xy−= Answer x = ……… , y = ………… [3] ____________________________________________________________________

8 7 The diagram shows part of a polygon A and part of polygon B. A is a regular polygon with n sides. B is a regular hexagon. Find the value of n. Answer n = …..…………………… [4] ____________________________________________________________________

9 8 Mary needs to pack 210 oranges, 252 apples and 294 pears into identical fruit baskets. (i) What is the largest possible number of fruit baskets that can be packed? Answer ………..…… fruit baskets [1] (ii) State the number of each fruit in a fruit basket. Answer ………..…………… oranges .……………………. apples ………………..…… pears [1] ____________________________________________________________________

10 9 The diagram shows a sector OPR with centre O. ORQ is a straight line. Angle POQ = 0.6 radians. OP = 5 cm and RQ = 7 cm. (i) Calculate the perimeter of the shaded region PQR. Answer ………..……………… cm [3] (ii) Calculate the area of the shaded region PQR. Answer ………..……………… cm2 [2] ____________________________________________________________________ 5 cm 0.6 radians 7 cm O P Q R