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: Writing Paper (4 sheets) and Graph Paper (1 sheet) READ THESE INSTRUCTIONS FIRST Write your name, class and index number on all your answer sheets to be handed in. Write in dark blue or black pen. You may use a soft pencil for any diagrams, graphs or rough working. 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. For, use either your calculator value or 3.14, unless the question requires the answer in terms of. 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. For Examiner s Use This paper consists of 6 printed pages (including the cover page) 50 Setter: Mdm Humairah 170
Mathematical Formulae Compound interest n r Total amount = P 1 100 Mensuration Curved surface area of a cone = rl Surface area of a sphere = Volume of a cone = Volume of a sphere = Area of triangle ABC 1 4 r 3 rh 4 3 r 3 1 absin Arc length = r, where is in radians Sector area = 1 C r, where is in radians Trigonometry a b c sin A sin B sin C a b c bccosa Statistics Mean = fx f Standard deviation = fx f fx f 171
1 The cash price of a new car is $175 000. 3 Answer all the questions. (a) Sarah buys the car on hire purchase. She pays a deposit of one fifth of the cash price. She then pays $1300 monthly for 10 years. What is the total amount that Sarah pays for the car? [3] The original value of the car is its cash price of $175 000. Each year the value of the car decreases by 10% of its value at the start of the year. At the end of three years, Sarah decides to sell the car. Calculate the overall percentage reduction in the value of the car compared with its original value. [3] Marcus, Ali and Tan shared a sum of money in the ratio 11 : 4 : 1. (a) Given that Ali received $4.80 more than Tan, find the sum of money shared by the three of them. [] Marcus distributed part of his money equally to Ali and Tan and was left with $.60. Find the new ratio of Marcus s money to Ali s money to Tan s money. [3] 17
4 3 There are 16 adults and 10 children going to the Singapore Flyer. You are required to book taxis for them. Below is the taxi seating capacity given to you. At least one adult must accompany the children. Source: https://www.cdgtaxi.com.sg/commuters_seating_capacity.mvn?cid=56 (a) What is the minimum number of taxis you need? Show all your working clearly. [3] There is a change of number of people going to the Singapore Flyer. An additional 4 adults and children would like to go too. How many more taxis do you need to book? [] 4 Two different sizes of cylindrical fruit cans are shown below. The small can has a diameter of 1 cm and a height of 13 cm. The prices of the fruit cans are given on the respective cans. LARGE SMALL $4.80 13 cm $18.80 11 310 cm 3 1 cm (a) Find the volume of the small can. [] (c) Which size of canned fruit gives the better value? Show all the working clearly of can. [3] What is the maximum number of small cans that can fit into a rectangular packaging of size 7 cm by 4 cm and height of 39 cm? [3] 173
5 5 There are (k 3) peaches in a box. There are 3 more apples than peaches and twice as many oranges as peaches in the same box. (a) Express the number of apples in term of k. [1] Express the number of oranges in term of k. [1] (c) If there are a total of 35 fruits in the box, how many peaches are there in the box? [3] (d) If the cost of a peach, an apple and an orange is $1.10, $0.0 and $0.50 respectively, what is the cost of one box of fruits? [3] (e) How many numbers of boxes of fruits can May purchase with $4? [] 6 An aeroplane travelled a distance of 1130 km from Singapore to Jakarta. For the first x hour of its journey, the aeroplane travelled at a constant speed of 350 km/h. The speed of the aeroplane was increased by 80 km/h for the remaining x hour of its journey. (a) Write down the total distance travelled for the first x hour of its journey, in terms of x. [1] (c) (d) Write down the distance travelled by the aeroplane in the remaining x hour of its journey, in terms of x. [] Find the value of x. Hence, find the total time, in hours, taken for the whole journey. [3] Find the average speed, in km/h, for the whole journey, correct to decimal places. [] 174
6 7 Answer the whole of this question on a sheet of graph paper. The variables x and y are connected by the equation y x. Some corresponding values of x and y, are given in the table below. x 1 0 1 y p 4 q (a) Calculate the value of p and of q. [] Using a scale of cm to 1 unit for the y-axis and 4 cm to 1 unit for the x-axis, draw the graph y x for x. [3] (c) Using your graph, find the value of x when y 3. 5. [1] (d) On the same axes, draw the line x = 1. 5. Find the coordinates of the point of intersection of the two lines. [] --- End of Paper --- 175
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3 1 (a) Consider the following numbers. Answer all the questions. 64,, 11, 1., 79, 5 Write down the prime number. 79 Answer (a) [1] By rounding each number to 1 significant figure, estimate the value of You must show your working clearly. 51.76.65 3.95. 300 3 3 [ M 1] Answer [] The first four terms m of a sequence q ence are 1, 15, 18, 1 50 (a) Write down the 6 th term. 7 Answer (a) 6 th term = [1] Write i down d the h general lterm, Tn for f the h sequence. 3n + 9 Answer Tn =..... [1] 177
4 3 When written as the product of their prime factors, 3 p 3 n, 3 q 5 13, 3 r 5 7. Find (a) the value of the n if the cube root of p is 3, 6 Answer (a) n = [1] the LCM of q and r, giving your answer as the product u t of its prime factors, r 5 7 13 3 3 Answer [1] (c) the greatest number b that will divide q and r exactly. Answer (c) [1] 5 178
5 4 (a) Jordan took two tests. In a second test, Jordan scored 18 marks. The second test mark is an improvement of 0% of the first test mark. Find Jordan s first test mark. 18 1. [ M 1] 15 Answer (a) marks [] Convert 56 m/s to km/h. 01.6 Answer km/h [1] (c) Given that h t the rate of exchange between Euro and Singapore dollars is 1 = S$1.59. Find the amount u of Euro dollars one can receive from S$300. Give your answer to decimal places. 188.70 Answer (c) Euros [1] 179
6 b b 4ac 5 Given that x, a find the value of x when a =4,b = and c = 3. Give your answer to 3 decimal places. 44 3 4 x [ M1] 1.151 =.... Answer r x =.. [] 6 In the diagram below, AB // CD // EF. ABC 4 and CEF C F 136. Find (a) BCD, Answer (a) 4 o BCD = [1] DCE, Answer 44 o DCE = [1] (c) the reflex BCE. 74 o Answer (c) reflex BCE.. [1] 180
7 7 In the trapezium ABCD, AB // DC, AD is perpendicular to DC, AB = 14 cm, BC = 18 cm, CD = 6 cm and AD = 15 cm. A 14 cm B 15 cm 18 cm D Find the area of trapezium ABCD. 1 14 6 15 1 M 6 cm C 300 Answer e cm [] 8 Solve x 10 4 and show the solution l on on a number line. x 6 xx 3 [ M1] x 3 [ M1] x 3 3 [A1] 3 0 x [3] 181
8 9 (a) Using the line segment given below, AC, construct a triangle ABC, such that BC = 10 cm and BAC = 40. A C [] On the same diagram, construct the angle a bisector of ACB. [1] (c) construct the perpendicular bisector of AC. [1] 18
9 10 (a) Factorise 8cd cd completely. cd (4 d ) Answer (a)....... [1] Simplify 3 3(x ( 3) ). 3 6x 9 [ M 1] 1 6x Answer............. [] x x (c) Simplify 1 3. 3 4x 3x 9 [ M 1] 6 x 11 6 Answer A e (c)....... [] _ 11 (a) Simplify 4 x x5 4 x4 completely. x x 4 x 5 x x4 x x 5 [ M1] x x x x 5 4 Answer (a)....... [] 183
10 Simplify 8x x 5 7 7 7 x x x x7 x7 8x 5 x 7 x [ M1] completely. Answer....... [] _ 1 (a) Express 35 m in cm. x x 4 7 7 5 350 000 Answer (a)........ cm [1] The ratios of a : b and a : c are given g below. a : b = :3 a : c = 3:5 : 5 Find the ratio a of a : b : c. 6 : 9 : 10 [B] Answer... :... :... [] 184
11 13 The diagram below shows a straight line. y 16 14 1 10 8 6 4 0 4 6 8 10 1 14 16 x (a) Find the gradient of this straight line. 0.5 05 Answer (a) gradient =..... [1] ( ) Write down the equation q of this straight i line in the form y mx c, where m is the gradient a of the line, and c is its y-intercept. 0.5x + 8 Answer y =........ [1] End of Paper 185
EAST VIEW SECONDARY SCHOOL SECOND SEMESTRAL EXAMINATION 017 SECONDARY ONE EXPRESS CANDIDATE NAME CLASS MARKING SCHEME INDEX NUMBER MATHEMATICS 4048/0 Paper 13 October 017 Total Marks: 50 1Hours15Minutes 15 Additional Materials: Writing Paper (4 sheets) and Graph Paper (1 sheet) et) READ THESE INSTRUCTIONS FIRST Write your name, class and index number on all your answer sheets h et s to be handed in. Write in dark blue or black pen. You may use a soft pencil for any diagrams, r graphs or rough o working. Do not use staples, paper clips, highlighters, glue or correction r ction fluid. Answer all questions. If f working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. Calculators ators should be used where h appropriate. pria If f the degree of accuracy acy is not specified ed in the question, and if the answer is not exact, give the answer to three significant figures. s Give answers in degrees to one decimal place. For, use either your calculator ator value or 3.14, unless the question requires the answer in i terms of. 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. For Examiner s Use This paper consists of 6 printed pages (including the cover page) 50 Setter: Mdm Humairah 186
Mathematical Formulae Compound interest n r Total amount = P 1 100 Mensuration Curved surface area of a cone = rl Surface area of a sphere = 4 r 1 Volume of a cone = 3 rh 3 rh 4 Volume of a sphere = 3 r Area of triangle ABC 3 1 absin C Arc length = r, where is in radians 1 Sector area = r, where is in radi ans r, where is in radians Trigonometry a b c sin A sin B sin C a b c bc cos A a b c bccosa Statistics Mean = fx f Standard deviation = fx f fx f 187
1 The cash price of a new car is $175 000. 3 Answer all the questions. (a) Sarah buys the car on hire purchase. She pays a deposit of one fifth of the cash price. She then pays $1300 monthly for 10 years. What is the total amount that Sarah pays for the car? [3] The original value of the car is its cash price of $175 000. Each year the value of the car decreases by 10% of its value at the start of the year. At the end of three y years,, Sarah decides to sell the car. Calculate the overall percentage reduction in the value of the car compared with its original value. [3] S/N Answer Mark Marker r Report 1(a) 1 Deposit = $ 175000 = $35000 5 Total monthly for 10 years = $ 1300 1 10 $ 156000 Total amount that Sarah pays for the car $ 35000 $156000 $191000 [A1] [ 1 At first year = $175000 At second year = $ 175000 0.9 $ 157500 At third year = $ 157500 0.9 $ 141750 Reduction price = $ 175000 $141750 $ 3350 Percentage reduction = 100% 191 9 % 175000 [A1] 188
4 Marcus, Ali and Tan shared a sum of money in the ratio 11 : 4 : 1. (a) Given that Ali received $4.80 more than Tan, find the sum of money shared by the three of them. [] Marcus distributed part of his money equally to Ali and Tan and was left with $.60. Find the new ratio of Marcus s money to Ali s money to Tan s money. [3] S/N Answer Mark Marker Reportp (a) Marcus : Ali : Tan 11 : 4 : 1 4-1 = 3 3 units = $4.80 1 unit = $ 4.80 3 $1. 60 11+4+1 = 16 16 units = $ 1.60 16 $5. 60 [A1] [ The sum of money shared by the three of them is $5.60. 5 At first, Marcus = $ 1.60 11 $17. 60 $17.60 $.60 $15.00 $15.00 $7.50 Ali and Tan received $7.50 each. Ali = ($ 1.60 4) $7.50 $13. 90 Tan = $ 1.60 $7.50 $9. 10 Marcus : Ali : Tan.60 : 13.90 : 9.10 6 : 139 : 91 [A1] 189
5 3 There are 16 adults and 10 children going to the Singapore Flyer. You are required to book taxis for them. Below is the taxi seating capacity given to you. At least one adult must accompany the children. (a) What is the minimum number of taxis you need? Show all your working clearly. [3] There is a change of number of people ple going to the Singapore Flyer. 4 adults and children would like to go too. How many a y more taxis do you need to book? [] S/N Answer Mark Marker Report 3(a) Note: We cannot take one child only as we do not know how the seating capacity for one child to how many adults. Child cannot go alone must be accompany comp any by an adult. Child Adult Taxi 4 1 1 4 1 1 3 1 0 4 1 0 4 1 0 3 1 10 16 6 [B3] or 6 is the minimum number of taxi needed. 190
Child Adult Taxi 3 1 3 1 3 1 3 1 3 1 0 1 1 10 16 6 6 is the minimum number of taxi needed. or Child Adult Taxi 3 1 3 1 3 1 3 1 1 1 1 1 10 16 6 6 is the minimum number of taxi needed. e ed. 6 3 Child Adult Taxi 4 1 1 4 1 1 3 1 0 4 1 0 4 1 0 4 1 3 1 1 0 7 7 6 = 1 1 more taxi needed. eded. or Child Adult Taxi 3 1 3 1 3 1 3 1 3 1 3 1 0 1 1 0 7 7 6 = 1 [B] 191
7 1 more taxi needed. or Child Adult Taxi 3 1 3 1 3 1 3 1 3 1 3 1 0 1 1 0 7 7 6 = 1 1 more taxi needed. 19
8 4 Two different sizes of cylindrical fruit cans are shown below. The small can has a diameter of 1 cm and a height of 13 cm. The prices of the fruit cans are given on the respective cans. LARGE SMALL $4.80 13 cm $18.80 11 310 cm 3 1 cm (a) Find the volume of the small can. [] Which size of canned fruit gives the better value? Show all the working clearly of can. [3] (c) What is the maximum number of small cans that can fit into a rectangular packaging of size 7 cm by 4 cm and height of 39 cm? [3] S/N Answer Mark M Marker Report 4(a) Volume of the small can = r h = (6) 13 = 1470.65 cm 3 = 1470 cm 3 [A1] 4 Small can per cm 3 = $ $4.80 1470.65 5 $0. $ 00364717 7 7 Large can per cm 3 = $ 18.808 0 11310 $0. 0016645 6 45 Large can gives the better value based on per cm 3. [A1] 4(c) 7 1 6 4 1 39 13 3 6 3 = 36 36 cans is the maximum number to fit into a rectangular packaging. k i [B] [A1] 193
9 5 There are (k 3) peaches in a box. There are 3 more apples than peaches and twice as many oranges as peaches in the same box. (a) Express the number of apples in term of k. [1] Express the number of oranges in term of k. [1] (c) If there are a total of 35 fruits in the box, how many peaches are there in the box? [3] (d)( ) If the cost of a p peach,, an apple and an orange g is $1.10,, $0.0 and $0.50 respectively, what is the cost of one box of fruits? [3] (e) How many numbers of boxes of fruits can May purchase with $4? [] S/N Answer Mark Marker Report 5(a) peaches = ( k 3) k 6 apples = ( k 3) 3 k 6 3 k 3 [B1] 5 oranges = (k 6) 4 k 1 [B1] [ 5(c) ( k 6) ( k 3) (4 k 1) 35 k 6 k 3 4 k 1 35 8 k 1 35 8 k 35 1 8 k 56 k 56 8 k 7 peaches = k 6 (7) 6 8 [A1] 5(d) apples = k 3 (7) 3 11 oranges = 4 k 1 4(7) 1 16 total cost for one box = 8 (1.10) 11(0.0) 16(0.50) $19. 00 [A1] 5(e) $ 4.00 $19.00 4 19 number of boxes that May is able to purchase with $4. [A1] 194
10 6 An aeroplane travelled a distance of 1130 km from Singapore to Jakarta. For the first x hour of its journey, the aeroplane travelled at a constant speed of 350 km/h. The speed of the aeroplane was increased by 80 km/h for the remaining x hour of its journey. (a) Write down the total distance travelled for the first x hour of its journey, in terms of x. [1] (c) (d) x Write down the distance travelled by the aeroplane in the hour of its journey, in terms of x. [] Find the value of x. Hence, find the total time, in hours, taken for the whole journey. [3] Find the average speed, in km/h, for the whole journey, correct e to decimal places. [] S/N Answer Mark r Marker Report 6(a) First part of journey Speed = 350 km/h Time taken = x hour Total distance travelled = 350x km [B1] 6 Second part of journey Speed = 350 + 80 = 430 km/h Time taken = x/ hour 6(c) 1 Total distance travelled = 430 x 15 x km [A1] 350x 15 x 1130 565 x 1130 x 1 1 x x ()) 3 Total time taken for the whole journey = 3 hours 6(d) Average speed for the whole journey 1130 3 376 km/h 3 = 376.67 km/h [A1] [A1] 195
11 7 Answer the whole of this question on a sheet of graph paper. The variables x and y are connected by the equation y x. Some corresponding values of x and y, are given in the table below. x 1 0 1 y p 4 q (a) Calculate the value of p and of q. [] Using a scale of cm to 1 unit for the y-axis and 4 cm to 1 unit for the x-axis, draw the graph y x for x. [3] (c) Using your graph, find the value of x when y 3. 5. [1] (d) On the same axes, draw the line x = 1. 5. Find the coordinates or d of the point o of intersection of the two lines. [] --- End of Paper --- 196
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