Anglo- Chinese School (Barker Road)

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Additional Materials: Answer Paper Anglo- Chinese School (Barker Road) END OF YEAR EXAMINATION 01 SECONDARY TWO EXPRESS MATHEMATICS 4016 PAPER TWO 1 HOUR 30 MINUTES READ THESE INSTRUCTIONS FIRST Do

1 Additional Materials: Answer Paper Anglo- Chinese School (Barker Road) END OF YEAR EXAMINATION 01 SECONDARY TWO EXPRESS MATHEMATICS 4016 PAPER TWO 1 HOUR 30 MINUTES READ THESE INSTRUCTIONS FIRST Do not open this booklet until you are told to do so. Write your class and candidate number on the cover sheet. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, 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. Calculators should be used 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. Forπ, use either the calculator value or 3.14, unless the question requires the answer in terms ofπ. 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 of the marks for this paper is 50. This paper consists of 7 printed pages inclusive of this page. [Turn over

2 MATHEMATICS FORMULAE Compound Interest Mensuration! Total Amount = P 1+ r $ # & " 100 % Curved surface area of a cone = πrl n Surface area of a sphere = 4πr Volume of a cone = 1 3 πr h Volume of a sphere = 4 3 πr3 Area of triangle ABC = 1 absinc Arc length = rθ, where θ is in radians Sector area = 1 r θ, where θ is in radians Trigonometry a sin A = b sin B = c sinc a = b + c bccos A Statistics Mean = fx f Standard deviation = fx f # fx & % ( $ f ' End of Year Examination 01 Secondary Express Mathematics Syllabus 4016 Paper

3 Answer all questions [50 m] 1. (a) Simplify (b) Express x 7m 14 m m + m 6. [] + 11x 15 in the form (x + a) + b. [1] (c) Hence or otherwise, solve the equation x + 11x 15 = 0, giving your answers [3] correct to two decimal places.. (a) Given that ε = { x: 0 x 10 } and x is an integer, and A = { x : x is an odd number } B = { x : x is a prime number }, (b) (i) list the elements of A and B. [] (ii) find na ( B'). [] Copy the following Venn diagram and shade the region representing (i) A' B [1] (ii) ( A B)' [1] ε A B End of Year Examination 01 3 Secondary Express Mathematics Syllabus 4016 Paper

4 3. The diagram shows a regular octagon. Calculate the angles (a) x, [1] (b) y, [] (c) z. [3] A B z H C G D F y E x End of Year Examination 01 4 Secondary Express Mathematics Syllabus 4016 Paper

5 4. Diagram I shows a model consists of a solid sphere within a right square pyramid. The sphere is in contact with all 5 faces of the square pyramid. A side view of the setup is shown below in Diagram II. The dimensions are all in metres. Side view 4 O m 6 m Diagram II Diagram I Given that the radius of the sphere is 1.5 m, (a) Calculate the volume of the sphere. [] (b) Calculate the surface area of the pyramid. [] (c) If the remaining volume in the pyramid is to be completely filled with sand which costs $1.70 per m 3, find the total cost of sand required. [3] End of Year Examination 01 5 Secondary Express Mathematics Syllabus 4016 Paper

6 5. Port A is due north of another Port B. A cruise ship sets sail from Port B on a straight course with a bearing 050 to Port D until it passes a point C where it is the shortest distance from Port A. The distance BC is 3.6 km. The cruise ship finally reaches Port D. A + D 050 B Calculate (a) the bearing of C from A, [] (b) the bearing of A from C, [] (c) the distance AB. [] (d) If the distance from Port B to Port D is 10 km, find the area of ΔABD. [] End of Year Examination 01 6 Secondary Express Mathematics Syllabus 4016 Paper

7 6. Candice worked in London as a software engineer in 008. In 008, her monthly income was (a) (b) (c) (d) Given that the exchange rate of British pounds to Singapore dollars is 1 = S$.5, find her total income in 008 in Singapore dollars. Her monthly income is divided between her rental, living expenses, savings and allowance for her parents in the proportion 3 : 4 : 1 :. Calculate the amount she gives her parents every month in Singapore dollars. In 009, she was given a pay raise of 14%. What is her total income in British pounds in the first half of 009? In 009, her landlord increased her rental by 8% and her living expenses increased by 1%. Assuming that she wants to give her parents the same amount every month, how much is her savings each month now in British pounds? [1] [] [] [3] 7. A stamping machine produces either small or large bottle caps. (a) It can produce x small bottle caps in 5 minutes. [1] (b) (c) Write down an expression, in terms of x, for the time taken to produce a small cap in seconds. In 5 minutes, the machine can produce 0 more small bottle caps than large ones. Write down an expression, in terms of x, for the time taken to produce a large bottle cap in seconds. The machine takes 1.5 seconds longer to produce a large bottle cap than a small bottle cap. (i) Write down an equation in terms of x and show that it reduces to x 0x 4800 = 0. (ii) Solve the equation x 0x 4800 = 0. [3] (d) Hence, find the number of large bottle caps that can be produced in 1 minute. [1] [1] [3] END OF PAPER End of Year Examination 01 7 Secondary Express Mathematics Syllabus 4016 Paper

8 Sec Express Math EOY 01 Paper answer 1a. b. c. = 7m( m ) ( m+ 3)( m ) 7m m x + 4 ( )( ) ( ) 11± x = 1 = 1.3 ( d.p ) or ( d.p ) ai. A = { 1, 3, 5, 7, 9 } B = {, 3, 5, 7 } ii. B = { 0, 1, 4, 6, 8, 9, 10 } ' A B = 0,1,3, 4,5,6,7,8,9,10 { } ( A B ' ) = 10 bi. A B bii. A B End of Year Examination 01 8 Secondary Express Mathematics Syllabus 4016 Paper

9 3a. 45 b. y = 45 =.5 c. HAB = = 135 ABG = = 45 Z = ½ =.5 4a. Volume = 4 ( 1.5) 3 3 π = 9 π = 14.1 m 3 b. Surface area = 4 ½ = 84 m c. 1 9 Remaining Volume = π = ( 5s.f ) Total cost = = $57.57 ( d.p ) 5a. Bearing = = 140 b. Bearing = = 30 c. 3.6 cos50 = AB AB = 5.60km (3s.f.) d. Area = ½( )( 10 )sin50 1.5km 3 s. f. = ( ) 6a. S$ b. Amount : 4300 = = = S$1935 c. Total income = = 941 d. 009 rental: = End of Year Examination 01 9 Secondary Express Mathematics Syllabus 4016 Paper

10 7a. b. ci. cii. 009 living expenses: = Saving: = x 300 x = 1 x 0 x 4 100x 100 x 0 = 5x x 0 ( ) ( ) 5x + 100x+ 4000= 0 x 0x 4800 = 0 (shown) ( 0) ( 0) 4( 1)( 4800) 1 ( ) ± x = = 80 = or - 60 (rejected) d. 1 End of Year Examination Secondary Express Mathematics Syllabus 4016 Paper

EAST VIEW SECONDARY SCHOOL SECOND SEMESTRAL EXAMINATION 2017 SECONDARY ONE EXPRESS

EAST VIEW SECONDARY SCHOOL SECOND SEMESTRAL EXAMINATION 017 SECONDARY ONE EXPRESS CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS 4048/0 Paper 11 October 017 Total Marks: 50 1Hours15Minutes Additional Materials: