CHIJ ST JOSEPH S CONVENT PRELIMINARY EXAMINATION

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1 Index Number Class Name CHIJ ST JOSEPH S CONVENT PRELIMINARY EXAMINATION NA MATHEMATICS Paper 1 Secondary 4 Normal (Academic) NA 4045/01 Thursday, 4 August 016 hours Candidates answer on the Question Paper. No additional material is required. READ THESE INSTRUCTIONS FIRST Write your index number, class and name on all the work you hand in. Write in dark blue or black pen on both sides of the paper. Working in pencil will not be marked. You may use an HB pencil for any diagrams or graphs Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. Write your answers on the separate Answer Paper provided. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles, unless a different level of accuracy is specified in the question. The use of an approved scientific calculator is expected, where appropriate. For, use either your calculator value or 3.14, unless the question requires the answer in terms of. You are reminded of the need for clear presentation in your answers. 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 80. FOR EXAMINER S USE Total 80 This document consists of 16printed pages. Setter(s) :Mrs Lee Ann Gee [Turn over 91

2 Mathematical Formulae Compound interest r Total amount = P ) n ( Mensuration Curved surface area of a cone = rl Surface area of a sphere = 4r Volume of a cone = 1 3 r h Volume of a sphere = 4 r 3 3 Area of triangle ABC = 1 ab sin C Arc length = r, where is in radians Sector area = 1 r, where is in radians Trigonometry a sin A b sin B c sin C a b c bc cos A Statistics Mean = fx f Standard deviation = fx f fx ( ) f 9

3 3 Answer all questions. 1. Find the fraction which is exactly halfway between 9 and 5 9. For Examiner s Use Answer. []. It is given 8,,, 3. 7 (a) List, in ascending order, the above four numbers. (b) State the irrational numbers. Answer (a).. (b) [] x 3. (a) Simplify ( ) y (b)given that 4, giving your answers in positive indices k, find the value of k. Show your working clearly. Answer (a).. (b)k =...[] 93 [Turn over

4 4 4.Solve the following simultaneous equations x y 1, 3yx56. For Examiner s Use Show your working clearly. Answer x =, y =.. [3] 94

5 5 5. The temperature at 0800 is 3Cand the temperature at 1400 is1 C. (a) Find the difference between the two temperatures. (b) Assuming the temperature rises at a steady rate, find (i) the temperature at 100, (ii) the time, in 4-hour notation, when the temperature is 10.5 C. [Turn over For Examiner s Use Answer (a)..... C (bi) C (bii).. 6. Written as the product of its prime factors, (a) Write 360 as the product of its prime factors (b) Find the lowest common multiple of 108 and 360. Give your answer as the product of its prime factors. (c) Find the smallest positive integer n such that 108n is a perfect cube. Answer (a) [] (b)..... [] (c)n =.. [Turn over 95

6 6 7.A map is drawn to a scale of 1 : (a)find the actual distance, in kilometres, represented by 6 cm on the map. (b)a city covers an area of 900 km. Find, in square centimetres, the area representing the city on the map. For Examiner s Use Answer (a)..km[] (b)...cm [] 8. It is estimated that by 060, the population of the world will be (a) can be written as x billion. Find x. (b) The population of the world in 000 was increase in the population of the world from 000 to , find the estimated percentage Answer (a) x =... (b)...%[] 96 [Turn over

7 7 9. There are three baskets, a green one, a red one and a yellow one, holding a total of ten eggs.the green basket has one more egg in it than the red basket. The red basket has three fewer eggs than the yellow basket.how many eggs are in each basket? For Examiner s Use Answer... eggs in green basket.. eggs in red basket. eggs in yellow basket [] 10. Simplify (a) 8 x( x 1), (b) 1 x3 x 9. Answer (a) (b) [] [Turn over 97

8 11. It is given that x (a) Find p and q. (b) Hence,solve x 8 10x3 can be expressed in the form 10x3 0. ( x p) q. For Examiner s Use Answer (a)p =, q =. [] (b) x =. or.. [] 1.(a) A lady bought a painting and sold it at a profit of 350% several years later. Given that the selling price is $5, find the price the lady paid. (b) Mary invested $5 000 at 6% simple interest per annum. Calculate the accumulated amount she received at the end of 8 years. Answer (a) $ [] (b)$...[3] 98 [Turn over

9 13. Factorise completely (a) 16x y, (b) 3 hk ( 1) 5(1 k), 9 For Examiner s Use (c) x 10x 1. Answer(a).. [] (b).. [] (c) [] [Turn over 99

10 (a) Gail explored PulauUbin Island by riding a bicycle. She was travelling at 4.5 m/s. Find her speed in kilometres per hour. (b) A plane travelled from Changi Airport, Singapore to Sydney Airport, Australia. The flight took 7 hours and 40 minutes. When the local time in Changi is 6.00 am, the local time in Sydney is 8.00 am. (i) The plane left Changi at 8.45 am local time. What was the local time in Sydney when it arrived? (ii) The plane travelled a total distance of 6305km. Find the average speed, in kilometres per hour, of the plane. For Examiner s Use Answer(a).. km/h [] (bi).. (bii).km/h[] [Turn over 100

11 11 15.The diagram shows a kite, ABCD, where AD CD 8 cm, DAB 130, and AB BC. (a) Write down the length of AC. (b) Find ABC. D (c) Find the length of AB. 8 cm 60 8 cm A 130 C B For Examiner s Use Answer(a)... cm (b)..... [] (c)...cm [] [Turn over 101

12 16.In the diagram, ABCD is a quadrilateral. 1 For Examiner s Use A B D C (a) Contruct the perpendicular bisector of AD. (b) Construct the bisector of angle ADC. (c) MeasureAT given that point T is the intersection of the perpendicular bisector of AD and bisector of angle ADC. Answer(c).cm [Turn over 10

13 (a) A regular polygon has interior angles of 168. Find the number of sides of the polygon. (b)a 7-sided polygon has 6 interior angles of 130. Find the remaining interior angle. For Examiner s Use Answer (a)...sides[] (b). [] [Turn over 103

14 18.In the diagram, P, Q and R are points on the circumference of the circle. PQ 5 cm, 14 For Examiner s Use 1 cm R Q 5 cm 13 cm QR = 1 cm and PR = 13 cm. (a) Find P PQR. Show your working clearly. (b) Find the shaded area. Answer (a). [] (b).cm [3] [Turn over 104

15 19.Tammy collated the sizes of the 9 pairs of shoes sold in a week. The bar chart summarises the results. 15 For Examiner s Use Number of pairs of shoes sold in various sizes Shoe size Number of pairs of shoes (a) Complete the table. Shoe size Number of pairs of shoes (b)find the mode. (c) Find the median. (d) Find the mean. (e) Explain why the mean is not a good measure of average in this case. Answer (b)... (c)..... (d)..... [] (e) [Turn over 105

16 16 0. (a) In the diagram, the coordinates of A are (0, 5) and that of B are (6, ). Calculate the lengthab. (b) Draw the line y x1on the same axes and hence find the coordinates of the point where y x1 crosses line AB. (c) Find the equation of the line AB. y A B x Answer(a)... units [] (b)(...,.. ) [] (c). [] END OF PAPER 106

Index Number Class Name CHIJ ST JOSEPH S CONVENT PRELIMINARY EXAMINATION NA MATHEMATICS Paper Secondary 4 Normal (Academic) NA 4045/0 Monday, 15August 016 hours Additional Material: Writing Paper

17 Index Number Class Name CHIJ ST JOSEPH S CONVENT PRELIMINARY EXAMINATION NA MATHEMATICS Paper Secondary 4 Normal (Academic) NA 4045/0 Monday, 15August 016 hours Additional Material: Writing Paper Graph Paper (1 sheet) READ THESE INSTRUCTIONS FIRST Write your index number, class and name on all the work you hand in. Section A Answer all questions. Section B Answer one question. Write in dark blue or black pen. Do not use staples, paper clips highlighters, glue or correction fluid. All working must be shown clearly. Omission of essential working or units may result in loss of marks. Working in pencil will not be marked. You may use a soft pencil for any diagrams or graphs. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, the answer should be given to three significant figures. Answers in degree should be given to one decimal place. For, use either your calculator value or 3.14, 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. FOR EXAMINER S USE 60 This document consists of 9 printed pages. 107

18 Setter(s) : Mrs Joyce Lynn Hong Compound Interest Mathematical Formulae Total amount = r P1 100 n Mensuration Curved surface area of a cone = rl Surface area of a sphere = 4r 1 Volume of a cone = r h Volume of a sphere = r 3 Area of triangle ABC = 1 absin C Arc length = r, where is in radians Sector area = 1 r, where is in radians Trigonometry a sin A b sin B c sin C a b c bc cos A Statistics Mean = fx f Standard deviation = fx f fx f 108

19 3 Section A (5 marks) Answer all the questions in this section. 1. Given that P is inversely proportional to r and that P = 4 when r = 3, find (a) the equation connecting P and r, (b) the values of r when P = 9. []. Amy travels from Singapore to Malaysia. She exchanged S$5000 into Malaysian Ringgit when the exchange rate was S$1= RM$3.05. (a) Find the amount of money that Amy exchanged in Malaysian Ringgit. While in Malaysia, she spends RM$6800. On her return, she decided to exchange the remaining Malaysia Ringgit into Singapore dollars when the exchange rate was $1 = RM$.96. (b)find the amount of money that Amy left in Singapore dollars. With the remaining Singapore dollars, Amy invested at.5% per year compound interest for 3 years. (c) Find the compound interest that Amy earned at the end of 3 years in Singapore dollars, giving your answer correct to the nearest cent. [] [] 3. E D 4 cm 5.5 cm 36 A B 7cm C In the figure, BCDE is a quadrilateral such that BCE 90, BC = 7 cm, CE =4cm and DCE 36. (a) Find BE. (b) By giving your answer in fraction and in the lowest term, find the value of (i) tan BEC, (ii) cos ABE. (c) Calculate the area of quadrilateral BCDE. [] [3] [Turn over 109

20 4 4. The diagram shows the speed-time graph of a moving particle. Speed (m/s) m (a) What is the acceleration of the particle at time t = 15 s? (b) Find the speed when t = 8 s. (c) Given that the total distance travelled is 900 m, (i) show that m= 30, (ii) findthe average speed of the particle. Time (s) [] [] 5. P Q 6 O 10 S 18 R PQRS is a trapezium and PS = QR. The diagonals PR and QS meet at O. (a) Give a reason why (i) POQ ROS, (ii) QPR PRS. (b) Triangles POQ and ROS are similar. OP = 6 cm, OR = 10 cm and RS = 18 cm. Calculate PQ. (c) Write down two triangles that are congruent. [] 110

21 5 6. The diagram shows a solid formed by removing a cone from a cylinder. h 16 cm 0 cm 1 cm The cylinder and the cone have a common radius of 1 cm. The slant height of the cone is 16 cm and the height of the cylinder is 0 cm. Take Calculate (a) the height, h, of the cone, (b) the curved surface area of the cone, (c) the volume of the solid. [] [3] 7. Mr Tan bought some crabs and prawns from the market. (a) He bought x kilograms of crabs for $10. Write down an expression, in terms of x, for the cost of 1 kilogram of crabs. He spent the same amount of money on prawns as crabs. He received 6 kilograms more prawns than crabs. (b) Write down an expression, in terms of x, for the cost of 1 kilogram of prawns. (c) The cost of 1 kilogram of crabs is $4.0 more than the cost of 1 kilogram of prawns.write down an equation in terms of x and show that it reduces to 7x 4x (d) Solve this equation 7x 4x [3] [] [Turn over 111

22 8. Mabel usessquares to make a series of pattern. The first three patterns are as shown below. 6 Pattern 1 Pattern Pattern 3 The number of squares used in the above patterns are tabulated in the table shown below. Pattern Number (n) Number of grey squares(g) Number of white squares(w) a b Total number of squares (T) (a) Write down the values of a and b. (b) Write down an equation connecting n and g. (c) Write down an equation connecting n and w. (d) Express T in terms of n. (e) Hence or otherwise, find the pattern number that uses a total of 14 squares. [] 11

23 7 9. Answer the whole of the question on a single sheet of graph paper. 1 4 for x 4. x y p (a) The table shows some values of the graph y xx 3 (i) Find the value of p, leaving your answer in 1 decimal place. (ii) Using a scale of cm to represent 1 unit on both axes where x 4 and 1 1 y 9, draw the graph of y xx x x (b) Use your graph to solve (c) By drawing a tangent, find the gradient of the graph at x =. [3] [] [Turn over 113

24 8 Section B (8 marks) Answer one question from this section. Each question carries 8 marks. 10. (a) In the diagram, P, Q and R are points on level ground. QT is a vertical pole. It is given that PQ = 104 m, QR = 10 m, PQR 11 and the angle of elevation of T from P is 8. T Q m R m P Find (i) the distance PR, (ii) PRQ, (iii) the height of the pole. [] [] (b) The diagram, which shows the sector XOY of a circle with centre O, represents a piece of card. X 6 cm.4 radians O Y The radius of the sector is 6 cm and XOY =.4 radians. (i) Calculate the length of arc XY. (ii) The card is used to make a hollow cone by joining edges OX and OY. Calculate the radius of the base of the cone. [] 114

25 11. The table summarises the marks of the 00 students of schoolx in the last Science examination. 9 Mark (x) 0 x x 0 0 x x x 50 Frequency (a) Calculate the estimates of the mean and standard deviation of these marks. The students of SchoolY sat for the same examination. For schooly, the mean mark was 5.3 and the standard deviation was (b) Which school had better marks? Give a reason for your answer. (c) Which school is more consistent in the marks? Give a reason for your answer. (d) One student is chosen at random in school X. Find the probability that the student chosen has the mark that is less than 0. (e) Two students are chosen at random in school X without replacement. Given that a student attains a Grade A if he scores more than 40 marks, find the probability that both students chosen have attained Grade Afor the Science examination. [3] [] END OF PAPER [Turn over 115

26 116

27 Marking Scheme 016 Sec 4NA Prelim EMath Paper 1Setter: Mrs Lee Ann Gee Test Item Marking Point Mark awarded Remarks 1 5 ( ) a 8=4, , , , zero mark In ascending order:,, 3, 8 7 b, 3, Deduct one mark for each wrong answer seen. 3a x 4 y 4 ( ) ( ) y x 8 y 4 16 x xy 3b 8 k Convert 7 to 3 5 k 3 3 If trial and error nd showed working, award up to marks. k 5 If totally no working, award zero. 4 x y 1, (1) OR 3 y x 56. () Substitute x or y into the other eqn e.g. sub. y = 1 Eqn 1 :4 4y y 68 x x.5 y 17 5a 1 ( 3) 15 5bi 6 hours, increase by 15C 4 hours, increase by 4 15=10C 6 Ans: ( 3)

28 Test Item Marking Point Mark awarded Remarks 5bii Increase = 10.5 ( 3) 13.5C Increase by 15 C, took 6 hours If 13:4 or 134h, no mark. Question stated 4 hour notation. increase by 13.5C Time = 134 6a =5.4 hours B 6b LCM = B Give your answer as the product of its prime factors. So no mark is awarded arde d if 1080 without any prime factors seen. en. Award if is seen but final ans is If o.e., no mark. 6c n = 7a Map : Actual distance 1cm : 3 km 6cm : 18 km Answer: 18 km 7b Map area : Actual area a 1cm : 9 km ecf If 1cm : cm, 100 cm : 900 km award full marks if completely correct else zero mark. 8a or

29 Test Item Marking Point Mark awarded Remarks 8b % % Accept 67.8% 9 Red basket = n eggs Green basket = n+1 eggs Yellow basket = n+3 eggs Total eggs = 10, so n + (n+1) + (n+3) = 10 3n + 4 = 10 3n = 6 n = So, green basket - 3eggs red basket - eggs yellow basket - 5 eggs B Allow for one correct ans 10a 8 x ( x 1) 7x1 10b 1 1 x 3 x 9 x 3 ( x 3)( x3) ( 3)( 3) ( x 3) 1 ( x 3)( x 3) x 5 ( x 3)( x3) ( x 3) 1 Award if x 9 ( x 9) 1( x 3) ( x3)( x 9) If, no ( 3)( 9) but award B if completely correct. 11a x 10x3 x 10 x( ) ( ) 3 ( x 5) 8 x 5 Accept, award x 9 10 p, not accepted 3 119

30 Test Item Marking Point Mark awarded Remarks p = 5, q 8, 11b x 10x3 0 ( x 5) 80 x 5 8 x 1a 450% $5 8 5 x 0.9 or Lose if not to 3 s.f. Hence, so no other method accepted. 100% $ $5 1b Simple Interest 100 $400 Acc amount = $ a 16 x y (4 x ) y (4 x y )(4 x y ) 13b 3 hk ( 1) 5(1 k ) 3 hk ( 1) 5( k 1) ( k 1)(3 h 5) Allow B OR 3 h (1 k ) 5(1k) (1 k )( 3 h5) 13c x 10 x 1 ( x )( x 3) B Award if (x 4)( x 3) or ( x )( x6 14a 4.5 m km 1 s 1 h km/h 14bi 8 h 45 min + 7 h 40 min = 16 h 5 min Arrival time = 4.5 pm in local time in Singapore Arrival time = 6.5 pm in local time in Sydney Award if ( x 5 x 6) Not 6:5, not 18:5, not 185h. Accept

31 Test Item Marking Point Mark awarded Remarks 14bii 6305 km 7 h km/h 3 15a AC = 8 cm 15b ABC ( sum of quad.) 15c 4* cos 70 AB AB 11.7 cm Accept 8 ( to 3 sf). Deduct 1 mark if without working, but allow. *ecf (their AC) divided by Other methods: AB 8 sin 30 sin 0 AB 8 or *ecf par sin*70 sin*40 16 See attached. Lose 1 mark if angle bisector and perpendicular bisector are correct but not labelled as (a) and (b) in diagram. 17a One ext. angle = No. of sides Accept better ( n ) n or 17b Sum of interior angles = (7 ) Remaining int. angle = a cos PQR (5)(1) PQR 90 OR } PQ QR PR No no, should not assume angle in semicircle straightaway. 5 11

32 Test Item Marking Point Mark awarded Remarks 18b Area of triangle = 1 1 5=30 13 Area of circle = ( ) 13 Shaded area = ( ) ecf 19a 7, 8, 5, 1 19b Mode = 7 19c Median = 6 19d 4(1) 5(7) 6(7) 7(8) 8(5) 9(1) Mean Allow low B 19e The mean is not an integer (or a whole number). OR There is no shoe size that is Must write in complete sentences. ence s. Not accurate is not accepted unless clearly elaborated. 0a length AB (0 6) (5 ) = b Draw the line y x 1. (4, 3) 0c Gradient y x 5 o.e. Accept 3 5. Do not penalize if did not label. 6 1

33 Ms Joyce Lynn Hong Marking Scheme 016 Sec 4NA EMath Prelim Paper Test Item Marking point Mark Awarded Remarks 1 (3m) (5m) 3 (6m) k (a) (i) P r k 4 3 k P r 36 (b) r 9 r (a) $1= RM$3.05 $5000 = = RM$1550 (b) Amount left (RM) = = RM $8450 Amount left (SGD) = = S$ (c) A $ Compound Interest = $ $ $19.50 (a) ( BE ) 4 7 BE 5 cm 7 (b) (i) tan BEC 4 7 (b)(ii) cos ABE 5 (c) Area of Triangle of BCE 3 (ECF) (ECF) = 84 cm Area of Triangle of DCE sin cm Area of quadrilateral BCDE = = cm CHIJ SJC Sec 4NA Prelim Math Paper

34 Ms Joyce Lynn Hong Test Item Marking point Mark Awarded Remarks 4 (5m) (a) 0 m/s (b) Gradient = = 4 m/s x = 4 x 3 m/s For (b), students may use similar triangles to find the speed at t= 8s. 5 (5m) 1 (c) (i) ( ( m 15) (o.e.) 0 ( m 15) 900 m m 30 (ii) Average Speed = 900 = 30 m/s 30 (a) (i) POQ ROS ( ( vert. opp s ) (ii) QPR PRS ( ( alt. s) (b) 6 PQ (6m) 6 PQ 18 = 10.8 cm 10 (c) Any pair: PSQ QRP or POS QOR or PRS QSR (a) Height of the cone = cm (b) Curved surface area of cone = (1)(16) cm (c) Volume of cylinder = Volume of cone : For any 1 correct volume = Volume of container cm 3 CHIJ SJC Sec 4NA Prelim Math Paper

35 Ms Joyce Lynn Hong Test Item Marking point Mark Awarded Remarks 7 (7m) (a) 10 x (b) 10 x 6 8 (6m) 9 (7m) (c) (i) x x 6 10( x6) 10x 1 xx x( ( 6) x( xx ( 6) 5 1 xx ( 6) 70(5) 1x 16x x 4x (4) 4(7)( 100) (d) x (7) = or = = 10.4 or = (reject) (a) a = 18 b = 34 (b) g n (c) w = 4n + (d) (e) n 4 n 14 n 4n ( n 14)( n 10) 0 n = 10 or n = -14 (rejected) ed) n = 10 (a) p 8.1 (b) Correct points and scale (1m) Smooth curve (1m) Label axes and curve (1m) (ECF) (ECF) G3 Accept if student reject ect one of the ans or did not reject. No working,? For (e), student must reject -14. (c) x = , x = 0& x = (c) Draw tangent. Gradient =.5 10% (Accept.05 to.475) CHIJ SJC Sec 4NA Prelim Math Paper

36 Ms Joyce Lynn Hong Test Item Marking point Mark Awarded Remarks 10 (8m) 11 (8 m) (a) (i) By the cosine rule, PR ( cos 11) PR m (correct to 3 sig. fig.) (ii) By the sine rule, sin11 sin PRQ PRQ (correct to 1 d.p.) (iii) TQ tan8 104 TQ 14.6 (b) (i) Arc length XY = cm (ii) r 14.4 r.9 cm (a) Mean marks for School X 5(17) 15(38) 5(48) 35(53) 45(44) = Standard deviation for School ol X 1.5 (correct to 3 sig. fig.) (b) Since the mean marks of school ol X is higher than school Y, school ol X has better er results. (c) Since the standard deviation of the number of school Y is lower than school X, the performance of school Y more consistent. stent. (d) P (the mark of the student is less than 0) (o.e.) 40 (d) P (the mark of both students > 0) (o.e.) 9950 (ECF) (ECF) M ( B CHIJ SJC Sec 4NA Prelim Math Paper

37 Ms Joyce Lynn Hong CHIJ SJC Sec 4NA Prelim Math Paper

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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: