2018 BPGHS Sec4 EMaths Prelim Exam - Paper 1&2 with ans

Candidate’s Name ____________________________Class __________Index No____ BUKIT PANJANG GOVERNMENT HIGH SCHOOL PRELIMINARY EXAMINATION 2018 SEC FOUR EXPRES S / FIVE NORMAL MATHEMATICS 4048 / 01 Paper 1 Date: 15 Aug 2018 Duration: 2 hours Time: 0745 - 0945 Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and index number in the spaces at the top of this page. 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. 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  , use either your calculator value or 3.142, unless the question requires the answer in terms of  . 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 80. FOR EXAMINER’S USE / 80 This document consists of 18 printed pages. Setter : KH Chiam [ Turn over

2 Mathematical Formulae Compound interest Total amount = n rP       1001 Mensuration Curved surface area of a cone = rl Su rface area of a sphere = 24 r Volume of a cone = h r2 3 1  Vol ume of a sphere = 3 3 4 r Area of triangle AB C = C absin2 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 sin sin sin  A bc c b acos 22 2 2   Statistics Mean = f fx   Standard deviation = 22fxf x f f    

3 Answer all the questions. 1. (a) Factorise ݔଶݕଶ . (b) Hence, for ݔଶݕଶ ൌ0 , f ind the ratio ݕ:ݔ . Answer (1a) ________________________[2] (1b) ________________________[1] 2. Red paint was mixed with blue paint in different combination s in an attempt to obtain purple paint. The table shows the combinations of red paint and blue paint. State a nd explain your answer, whether the amount of red paint used is proportional to the amount of blue paint used for the combinations. Answer (2) ________________________[1] 3. A group of students line up. If they lined up in 2s or 6s or 9s, there will be one student without a pa rtner. Calculate the least number of students in the contingen t . Answer (3) ________________________[2] Red paint (litres) 1 2 3 4 Blue paint (litres) 3 5 7 9

4 4. Arthur, Clement and John are to share a bag of sweets amongs t themselves in the ratio 2: 3: 4 John obtained 6 sweets more than Arthur, Find (a) the total number of sweets received by Arthur, (b) the number of sweets received by Clement. Answer (4a) ___________________[2] (4b) __________________[1] 5. The rectangular floor of a room measuring 456 m by 696 m is to be laid with square tiles. (a) Calculate the highest comm on factor of 456 and 696. (b) Hence, or otherwise, find the least number of identical square tiles that is required to cover t h e f l o o r . Answer (5a) ___________________[1] (5b) __________________[2]

5 6. The table below shows the number of boys and girls in a clas s with their dietary preferences. (a) A pupil is selected at random from the class. Calculate the probability that the pupil (i) is a boy who prefers chili, (i i ) i s a g i r l . (b) Two pupils are selected at random from the class. Calculate the probability that (i ) b o t h a r e b o y s , (ii) neither is a girl who prefers tomato sauce. Answer (6ai) _______________________[1] (6aii) ______________________[1] (6bi) _______________________[2] (6bii) ______________________ [2] NUMBER OF BOYS WHO PREFER GIRLS WHO PREFER CHILI TOMATO SAUCE CHILI TOMATO SAUCE 12 8 10 10

6 7. The diagram shows the graph of ݔଶܿThe line of symmetry is ൌ2 . 5 . The graph cuts t he y- axis at ሺ0,4ሻ. Calculate the value of ( a ) b, (b ) c , (c) the minimum y – value of the graph. Answer (7a) _________________________[2] (7b) _________________________[1] (7c) _________________________[1] 8. Simplify ݄ భ మ݇ య మ ݄ భ మ ݇ య మ ሻ Answer (8) _______________________ _[2] y x x =2.5 C

7 9. Consider the sequence 2, 5, 8, 11, ………… . (a) State the (i ) 6th term of the sequence, (i i ) nth t e r m o f t h e s e q u e n c e . ( b ) I f t h e pth term of the sequence is 56, find the value of p. Answer (9ai) _______________________[1] (9aii) _______________________[1] (9b) ________________________[1] 10. Given that x and y are integers such that ൑ 5 and ൑8 , find the (a) greatest value of ݔଶݕଶ, (b) smallest value of ௬ା௫ ௫ . Answer (10a) ________________________[2] (10b) ________________________[2]

8 11. p i s directly proportional to ݍଶ. If q is decreased by 75 %, find the percentage decrease in p. Answer (11) _________________________[2] 12. Adrian, Belle and Cindy were having a conversation, when Denzyl comes along. Commenting on a statistical finding that 1 in 4 Singaporeans in their 50s suffer from disease X, Adrian said,” Since all of us are in our 50s and the 3 of us do not have disease X, Denzyl must be suffering from disease X.” State with reason as to whether Adrian was right in his conclus i o n . Answer (12) ___________________________________________________________________________ ______________________________________________________________________________________ ____________________________________________________________________________________[2]

9 13. Sketch the graphs of ( a )ൌെ ଵ ௫ ൅2 [1] (b)ݔଷ ൅3 [ 1 ] y x y x

10 14. ABC is a straight line. Point B (on the y – axis) bisects line AC. Point C lies on the x-axis. FED is a straight line having the same length as AC and is parallel to AC. E is the mid-point of FD. (a) Show that point C has coordinates (4,0). (b) State the coordinates of point B. (c) Show that ሬሬሬሬሬԦ ൌ ቀ 8 െ8ቁ. (d) Hence, or otherwise, calculate the column vector ሬሬሬሬሬԦ. (e) Calculate area of parallelogram ACDF. Answer (14a) _______________________[2] (14b) _______________________[1] (14c) _______________________[1] (14d) _______________________ [1] (14e) _______________________ [1] C A(-4,8) B y xD E F 0 (Not drawn to scale)