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1 1 Evaluate Answer all the questions. (a) , [B1] (b) ( ) ( ). Give your answer in standard form [B1] Answer (a). [1] (b). [1]. An express train travelled 645 km in 7 hours 55 minutes to arrives at its destination at 06 1 h on Monday. Find (a) the time and day at which the train started its journey, 17, Sunday [B1] (b) the average speed of the train, giving your answer in km/h, correct to 1 decimal place km/h [B1] Answer (a) [1] (b).km/h [1] [Turn Over

2 4 The diameter of a circular micro-organism is 1.95 nanometres. (a) Express the radius of the micro-organism, in centimetres, giving your answer in standard form [B1] (b) Find the area of the micro-organism, in square centimetres, giving your answer in standard form [B1] Answer (a). cm [1] (b).. cm [] 4 y is inversely proportional to the square of x. It is given that y = 6 for a certain value of x. When this value of x is doubled, find (a) an expression connecting y, x and k, k y [B1] x (b) the value of y, 1.5 [B1] (c) the percentage decrease in the value of y. 75% [B1] Answer (a). [1] (b). [1] (c). [1]

3 5 (a) Simplify y x 0 5 y x 0 = = x x 9 [M1] [A1] (b) Given that 7 k 15, find the value of k. 7 k k k = [M1] [A1] Answer (a) [] (b) k =.....[] 6 The cost of unleaded petrol is $x per litre while the cost of leaded petrol is 10 percent more per litre. Find an expression for the total cost of buying y litres of unleaded petrol and z litres of leaded petrol. 1 litre $x y litres ---- $xy [M1] 1 litre $1.1x z litres $1.1xz Total = $ xy + 1.1xz [A1] Answer. [] [Turn over

4 6 7 The figure consists of a trapezium and a semi-circle. The trapezium has parallel sides of length 4y and 6y and a height of h. h 4y 6y (a) Show that the area, A, of the whole figure is given by the formula A 5hy y. (a) 4y 6y 1 A h (y) 5yh y [M1] [A1] (b) Rearranging the formula to express h in terms of A, y and π. [] A 5hy y 5hy y A [M1] A y h [A1] 5y Answer: (b)... []

5 7 8 (a) Factorise completely 6m 8km mn 4kn m(m n) 4k(m n) [M1] ( m n)(m 4k) [A1] (b) Simplify 0 p (p 1) 4 0p (9 p 6p 1) 4 [M1] p 1 p 6 [A1] Answer: (a).[] (b).[] 9 (a) (i) Solve the inequality x 6 (ii) Hence, write down the smallest integer x which satisfies x 6. (i) 1 x 1.5 or 1 [B1] (ii) 1 [B1] (b) Solve the simultaneous equations. x y 11 x 5 4y (b) From (1), x 11 y () Subst. () into (), (11 y) 5 4y [M1] x [A1] y 4 [A1] Answer: (a)(i) [1] (ii) [1] (b) x =. y =.....[] [Turn over

6 8 10 (a) On the Venn Diagram shown in the answer space, shade the region ' representing ( P Q) R. Answer: (a) P Q E R [1] (b) E = {x : x is an integer, 10 x 4} A = {x : 15 x 1} B = {x : x is an odd number} C = {x : x is a prime number} Find ' (i) n( A B) (ii) n( A C) (b)(i) 4 [B1] (ii) 5 [B1] Answer: (b)(i) [1] (ii).[1]

7 9 11 The following table records the number of notes of denomination of $, $10 and $50 in each of the three cashier s cash register. Denomination $ $5 $10 Mary Jane Shirley 10 8 (a) (a) Using the above table, form a matrix P and evaluate P [M1] [A1] 90 Answer: (a)...[] (b) Explain what your answer to (a) represents. Answer: (b) (b) The elements represent the total amount of money in each cashier s cash register. [B1] 1 In a particular class, 5% of them are boys and 1 are girls. Find the total number of students in the class. 75 % [M1] 100 % /75 x 100 = 8 [A1] Answer:...[] [Turn over

8 10 1 (a) (i) Express 980 as the product of its prime factors. (ii) Given that 980 k is a perfect cube, write down the smallest possible value of k. (iii) Find the highest common factor of 980 and 784. i) 5 7 [B1] ii) 50 iii) 196 [B1] [B1] (b) Two schools situated next to each other start their first lessons at The duration of each period in the first school is 48 minutes and that of the second school is 6 minutes. The school bells of both schools ring at the beginning of each period. At what time will the bells ring at the same time again after 0740? Using LCM [M1] LCM = 144 mins, hrs [A1] Answer: (a)(i) [1] (ii) [1] (iii) [1] (b) []

9 11 14 The figure below shows an equilateral triangle ABC and arc BC with radius AB. Given that AB = 9 cm, show that the perimeter of the shaded area is 9 cm. [] Arc length BC = r = 9 cm. BC = 9 cm [M1] [M1] Therefore perimeter = 9 cm. [A1] 15 In the diagram, ABD is a right-angled triangle with point C on the line BD. AB = x, BC = y, CD = z. Find in terms of x, y and/or z, (a) tan ADB, (b) cos ACB, (c) cos ACD. a) tan ADB = y x z [B1] b) AC = x y [M1] cos ACB = x y y [A1] c) cos ACD = y x y [B1] Answer: (a).[1] (b)..[] (c)..[1] [Turn over

10 1 16 The ages, in years of eleven members of the Senior Citizen Club are given below. 46, 5, 67, 65, 49, 56, 64, 78, 56, 60, 49 A box-and-whisker diagram is drawn to represent the data. 46 a b c 78 (a) Find the values of a, b and c. a = 49; b = 56; c = 65 [B1 x ] (b) Find, (i) the mean, (ii) the standard deviation of the ages of the members. Mean = 58.4 [B1] Standard Deviation = 9.14 [B1] Answer: (a) a =, b =, c =.[] (b)(i)..[1] (ii)..[1]

11 1 17 The diagram shows a regular octagon. Calculate the angles (a) x, (b) y, (c) z. A B z z H D z x C z G D D z F D y E D x (a) 60 0 x 45 (ext angles of polygons) [B1] 8 (b) (c) 45 y. 5 (ext angle = sum of interior opp angles) [B1] 15 ABF [M1] ABG 45 z [A1] Answer: (a).[1] (b)..[1] (c)..[] [Turn over

12 14 18 The diagram shows a solid cone which is divided horizontally into portions A, B and C in the ratio 1 : :. Find the numerical value of height of A (a) height of whole cone (b) volume volume of A of B (c) curved surface area of A : curved surface area of B : curved surface area of C. C units B units A 1 unit (a) height of A height of whole cone 1 [B1] 6 (b) (c) volume of A 1 1 volume of A B 7 [M1] volume of A 1 volume of B 6 [A1] area of A : area of A+B : area of A+B+C = 1 : 9 : 6 Area B = 8 units ; Area C = 7 units [M1] curved surface area of A : curved surface area of B : curved surface area of C. = 1 : 8 : 7 [A1] Answer: (a).[1] (b)..[] (c)..[]

13 15 19 A cyclist starts from rest and accelerates at a constant rate to a speed of 0m/s in 10 seconds. He then cycles at this constant speed for the next 0 seconds before decelerating uniformly to rest in another 0 seconds. (a) On the axes below, (i) draw the speed-time graph for his journey; (ii) draw the distance-time graph for his journey. (b) Find the acceleration of the cyclist in the first 10 seconds. (c) Find the average speed of the cyclist for the whole journey. (ai) (aii) d (m) t (s) (b) Acceleration = 0 ms (c) Average speed = 14m / s 50 Answer: (b).[1] (c)..[1] [Turn over

14 16 0 The diagram shows a triangle OPR with the point Q on PR and S on OR. (a) Show that SQ = 9 (b) Find (i) SQ OP (ii) area of triangle SQR area of triangle OPR (iii) area of triangle OQS area of triangle OQR (iv) the coordinates of R a) SQ SO OQ 6 9 = bi) 1 SQ 9 = = OP ii) area of triangle SQR 9 area of triangle OPR 5 iii) area of triangle OQS 5 area of triangle OQR 5 iv) OR 5 OS OR OS 0 0 R = (15, 0) 5 [B1] [B1] [B1] [B1] [M1] [1] [A1] Answer: (b)(i).[1] (ii)..[1] (iii)..[1] (iv)..[]

15 17 1 (a) The figure shows the graph of y ( x )( x b). Find the values of a, b and c. y - a c x When y = 0, ( x )( x b) 0 x or x b a and - - b b [B] (b) When x = 0, y ( )() 6 c 6 The diagram shows the graph of y x. On the same diagram, sketch and label the 1 graphs (i) y (ii) y x [] x 1 y x x y x - Answer: (a) a =.[1] b =.[1] c =.[1] End of Paper

16 Answer all the questions. 1 Evaluate (a). Give your answer to significant figures (b) ( ) ( ). Give your answer in standard form to significant figures. Answer (a). [1] (b). [1] An express train travelled 645 km in 7 hours 55 minutes to arrive at its destination at 06 1 h on Monday. Find (a) the time and day at which the train started its journey, (b) the average speed of the train, giving your answer in km/h, correct to 1 decimal place. Answer (a) [1] (b).km/h [1] [Turn Over

17 4 The diameter of a circular micro-organism is 1.95 nanometres. (a) Express the radius of the micro-organism, in centimetres, giving your answer in standard form. (b) Find the area of the micro-organism, in square centimetres, giving your answer in standard form. 4 y is inversely proportional to the square of x. (a) Find an expression connecting y, x and k, where k is a constant. Answer (a). cm [1] (b).. cm [] (b) It is given that y = 6 for a certain value of x. When this value of x is doubled, find (i) the value of y, (ii) the percentage decrease in the value of y. Answer (a). [1] (b)(i). [1] (ii). [1]

18 5 (a) Simplify y x 0 5 (b) Given that 7 k 15, find the value of k. Answer (a) [] (b) k =.....[] 6 The cost of unleaded petrol is $x per litre while the cost of leaded petrol is 10 percent more per litre. Find an expression for the total cost of buying y litres of unleaded petrol and z litres of leaded petrol. Answer. [] [Turn over

19 6 7 The figure consists of a trapezium and a semi-circle. The trapezium has parallel sides of length 4y and 6y and a height of h. h 4y 6y (a) Show that the area, A, of the whole figure is given by the formula A 5hy y. [] (b) Rearrange the formula to express h in terms of A, y and π. Answer: (b)... []

20 7 8 (a) Factorise completely 6m 8km mn 4kn (b) Simplify 0 p (p 1) 4 Answer: (a).[] (b).[] 9 (a) (i) Solve the inequality x 6 (ii) Hence, write down the smallest integer x which satisfies x 6. (b) Solve the simultaneous equations. x y 11 x 5 4y Answer: (a)(i) [1] (ii) [1] (b) x =. y =.....[] [Turn over

21 8 ' 10 (a) On the Venn Diagram shown in the answer space, shade the region representing( P Q) R. Answer: (a) P Q E R [1] (b) E = {x : x is an integer, 10 x 4} A = {x : 15 x 1} B = {x : x is an odd number} C = {x : x is a prime number} Find ' (i) n( A B) (ii) n( A C) Answer: (b)(i) [1] (ii).[1]

22 9 11 The following table records the number of notes of denomination of $, $10 and $50 in each of the three cashier s cash register. Denomination $ $5 $10 Mary Jane Shirley 10 8 (a) Using the above table, form a matrix P and evaluate P Answer: (a)...[] (b) Explain what your answer to (a) represents. Answer: (b).... [1] 1 In a particular class, 5% of them are boys and 1 are girls. Find the total number of students in the class. Answer:...[] [Turn over

23 10 1 (a) (i) Express 980 as the product of its prime factors. (ii) Given that 980 k is a perfect cube, write down the smallest possible value of k. (iii) Find the highest common factor of 980 and 784. (b) Two schools situated next to each other start their first lessons at The duration of each period in the first school is 48 minutes and that of the second school is 6 minutes. The school bells of both schools ring at the beginning of each period. At what time will the bells ring at the same time again after 0740? Answer: (a)(i) [1] (ii) [1] (iii) [1] (b) []

24 11 14 The figure below shows an equilateral triangle ABC and arc BC with radius AB. Given that AB = 9 cm, show that the perimeter of the shaded area is 9 cm. [] 15 In the diagram, ABD is a right-angled triangle with point C on the line BD. AB = x, BC = y, CD = z. Find in terms of x, y and/or z, (a) tan ADB, (b) cos ACB, (c) cos ACD. Answer: (a).[1] (b)..[] (c)..[1] [Turn over

25 1 16 The ages, in years of eleven members of the Senior Citizen Club are given below. 46, 5, 67, 65, 49, 56, 64, 78, 56, 60, 49 A box-and-whisker diagram is drawn to represent the data. 46 a b c 78 (a) Find the values of a, b and c. (b) Find, (i) the mean, (ii) the standard deviation of the ages of the members. Answer: (a) a =, b =, c =.[] (b)(i)..[1] (ii)..[1]

26 1 17 The diagram shows a regular octagon. Calculate the angles (a) x, (b) y, (c) z. A B z z H D z x C z G D D z F D y E D x Answer: (a).[1] (b)..[1] (c)..[] [Turn over

27 14 18 The diagram shows a solid cone which is divided horizontally into portions A, B and C in the ratio 1 : :. Find the numerical value of height of A (a) height of whole cone (b) volume volume of A of B (c) curved surface area of A : curved surface area of B : curved surface area of C. C units B units A 1 unit Answer: (a).[1] (b)..[] (c)..[]

28 15 19 A cyclist starts from rest and accelerates at a constant rate to a speed of 0m/s in 10 seconds. He then cycles at this constant speed for the next 0 seconds before decelerating uniformly to rest in another 0 seconds. (a) On the axes below, (i) draw the speed-time graph for his journey; (ii) draw the distance-time graph for his journey. (b) Find the acceleration of the cyclist in the first 10 seconds. (c) Find the average speed of the cyclist for the whole journey. v (m/s) d (m) t (s) [] t (s) [] Answer: (b).[1] (c)..[1] [Turn over

29 16 0 The diagram shows a triangle OPR with the point Q on PR and S on OR. (a) Show that SQ = 9 (b) Find SQ (i) OP area of triangle (ii) area of triangle (iii) (iv) area of triangle area of triangle SQR OPR the coordinates of R OQS OQR [1] Answer: (b)(i).[1] (ii)..[1] (iii)..[1] (iv)..[]

30 17 1 (a) The figure shows the graph of y ( x )( x b). Find the values of a, b and c. y - a c x (b) The diagram shows the graph of y x. On the same diagram, sketch and label the 1 graphs (i) y (ii) y x [] x y x Answer: (a) a =.[1] b =.[1] c =.[1] End of Paper

31 1 (a) ( m )( m ) m( m) ( m) m M1 A1 (b) 4 p p 1 p 1 4 p = ( p 1)( p 1) p 1 4 p ( p 1) = ( p 1)( p 1) ( p 1)( p 1) 4 p p = ( p 1)( p 1) p = ( p 1)( p 1) M1 M1 A1 (c) ( x )( x 1) 4 x 14x 0 0 M1 x 1.9 or x A1, A1. (a) (b) BC 80 BC = m = 5.7 m o 0 50 (0)(50) cos M1 A1 sin 80 M1 00 x = m = 9.5 m A1 0 x (c) Area of triangle = ½ (0)(50)sin80 M1 = 78.6 = 79 m A1. (a) M1 = US $ A1 5.5 (b)(i) Amt in US dollars = M1 = A1 (ii) M1 = A (c) Total amount = M1 = S$ A1 (d) ( ) ( ) = S$ M1 1

32 = 16.7% A1 4. (a) 156 B1 (b)(i) decreases by 4 B1 (ii) increases by 6 B1 (c) (x 8) + (x + ) + (x + 10) M (if all, M1 if any 1) = 4x + 4 A1 (d) 4x + 4 = 10 x = 9 M1 1, 9, 1, 9 A1 5. a)(i) 80 x (ii) x 5 (iii) 80 x 5 B1 x (b) x x ( x 5) 80x x( x 5) x( x 5) x( x 5) x 5x x 5x A1 M1 M1 (c) x or x 71.8( rejected ) A1, A1 (d) M =.11 h = h 19 min A1 6a. (i) OEF 90 ( tangent perpendicular to radius) B1 (ii) OEA 0 ( base angle of isosceles triangle) B1

33 (iii) AOE 180 (0) 140 ( isoceles ) ACE 140 (angle at the centre is twice 70 o angle at circumfere nce) M1 + A1 (iv) BDA EAF 0 (alt s, // lines) M1 BCA BDA 0 ( s in the same segment) A1 b Since BCE , M1 BE is a diameter of the circle. (right angle in semicircle). A1 7a. (i) Angle ABC = (0.5).14rad (SHOWN) B1 1 (ii) a) Area of sector ABD = r 1 = cm. B1 b) Area of triangle 1 = absin C 1 = (10)(10)sin. 14 = 4.075cm. M1 Area of shaded portion = = = 17.1 cm. ( sig. fig.) A1 c) AC = AB + BC (AB)(BC) cos ABC = (10)(10) cos.14rad = AC = cm = 17.6 cm B1 d) DC = = 7.55 cm Arc length BD = r = 10(0.5) = 5 cm M1 Perimeter = =.55 cm =.6 cm ( sig. fig.) A1 7b. i) angle ABD = 180 o 18 o = 16 o Angle ADB = 180 o 14 o 16 o = 4 o BD 0 ii) o 0 sin 14 sin 4 BD = 69.6 m = 69.4 m B1 M1 A1

34 iii) DC sin M1 DC = 1.4 m A a) i) Volume of cone = 0.5 (1.) M1 = 0.14 m Volume of cylinder = (0.5) (1.5) M1 = 1.178m Total volume = 1.49cm = 1.49 m A1 ii) Vol of water in cylinder = = 0.4 m M1 0.4 Height of water in cylinder = 0.08m (0.5) M1 Height of water = =.9 =.9 m A1 iii) h h h Height = = m M1 M1 A1 b) i) slant height = M1 = 1. m A1 ii) SA of cone = ( 0.5)(1.) m M1 SA of cylinder = (0.5)(1.5) m Total SA = 6.75 m A1 9. (a) a = -.96 b = -6. B1 x (b) graph M1 correct points M1 correct scale A1 smooth curve (c) gradient = - M1 tangent A1 answer (d) (i) x = 1.6 or x = 4. B1 (ii) y = 0. B1 4

35 1 1 (e) (i) x x x 1 0 y x x x 1 y 0 From graph, x = -.06 and 0.8 B1 (ii) 1 x x 9x x y x x x 1 & y x M1 From graph, x = -.4 or 0. A1 10a (i) Mark ( x ) 0 x 0 0 x x x x 100 Frequency B (ii) (a) 0 0/ / / / / 0 M1 400 = 54.5 A1 (b) Standard deviation = 18.7 (iii) The curve will have a steeper slope. B B1 10b (i) 6 1 8, B1 x (ii) (a) P(Both red) = P(RR) = B (b) P(one blue and one yellow) = P(BY or YB) = P(BY) = B (c) P(different colour) = 1 P(RR or BB or YY) = 1 M = A1 15 5

36 Answer all the questions. m 5m 6 1 (a) Simplify m m (b) Express, as a single fraction in its simplest form, 4 p p 1 p 1 [] [] (c) Solve ( x )( x 1) 4, giving your answers correct to decimal places. [] The points A, B and C are on a horizontal plane. The bearing of B from A is 057 o and the bearing of C from A is 17 o. The distance of AB = 0 m and AC = 50 m. Find (a) the length of BC, [] (b) the shortest distance between B and AC [] (c) the area of triangle ABC. [] [Turn over Canberra Secondary School O Level Preliminary Examinations Mathematics P Sec 4E/5NA

37 4 On nd January 006, Peter opened an account with UBO Bank. He exchanged S$5 000 for US dollars at the rate of US$1 = S$1.675 and deposited the whole sum of money in the bank. The bank agreed to pay 5.5% per annum compound interest. (a) Calculate the total amount of US dollars that Peter deposited on nd January 006. [] On nd January 009, Peter withdrew the whole sum including the interest from the bank and exchanged it back to Singapore dollars at a rate of US$1 = S$1.54. (b) Calculate the total amount of money that Peter received on nd January 009, (i) in US dollars, [] (ii) in Singapore dollars. [] On nd January 006, Dave deposited S$5 000 in POS Bank which paid.5% simple interest per annum. (c) Dave withdrew all his money from the bank on nd January 009. Calculate the total amount of money he received. [] (d) What is the difference in the amount of interest earned between Peter and Dave after they withdrew their savings from the two banks? Express this difference as a percentage of the total interest earned by Dave. [] Canberra Secondary School O Level Preliminary Examinations Mathematics P Sec 4E/5NA

38 5 4 The below array of 54 numbers, consisting of 6 rows and 9 columns, contains many diamonds of four numbers. Two of the diamonds are shown in the diagram (a) The sum of the numbers in one of the diamonds shown is 64. Write down the sum of the numbers in the other diamond. [1] (b) (i) When a diamond is shifted one column to the left, by how much is the sum of four numbers decreased? [1] (ii) When a diamond is shifted one row downwards, by how much is the sum of four numbers increased? [1] (c) If the number on the left of a diamond is x, write down expressions in terms of x for the other three numbers in the diamond. Hence, write down the sum of the numbers in the diamond in terms of x. [] (d) Find the four numbers in a diamond whose sum is 10. [] 5 Kate drove from Town A to Town B at an average speed of x km/h. The distance between the two towns is 80 km. the return journey, her average speed was 5 km/h faster. (a) Write an expression, in terms of x, for (i) the time taken, in hours, by Kate to travel from A to B, [1] (ii) her speed for the return journey from B to A, [1] (iii) the time taken, in hours, for the return journey. [1] (b) Given also that the return journey took 5 minutes less than the journey from A to B, from an equation in x, and show that it simplifies to x 5x [] (c) Solve the equation, giving your answers correct to decimal places. [] (d) Hence, find the total time Kate spent travelling between the two towns. Correct your answer(s) to the nearest minute. [] [Turn over Canberra Secondary School O Level Preliminary Examinations Mathematics P Sec 4E/5NA

39 6 6 A, B, C, D and E lie on the circumference of circle with centre O as shown. AE and BD are parallel to each other and line EFG is a tangent to the circle at E. B A 0 o O C D E F G Given that EAF 0, (a) calculate (i) OEF, [1] (ii) OEA, [1] (iii) ACE, [] (iv) BCA. [] (b) State whether BE is a diameter of the circle. State your reason(s) clearly. [] Canberra Secondary School O Level Preliminary Examinations Mathematics P Sec 4E/5NA

40 7 7 (a) The figure below shows an isosceles triangle ABC, where AB = BC = 10 cm and BAC = 0.5 radians. BD is an arc of a circle with its centre at A. (i) Show that ABC =.14 radians, [1] (ii) Find (a) the area of the sector ABD, [1] (b) the area of the shaded region, [] (c) the length AC, [1] (d) the perimeter of the shaded region. [] (b) A man standing at point A makes an angle of elevation of 14 o to the top of a tower CD. He then walks to point B and makes an angle of elevation of 18 o to the top of the tower. The length of AB is 0 m. Find (i) ADB, [1] (ii) length BD, [] (iii) height of the tower DC. [] [Turn over Canberra Secondary School O Level Preliminary Examinations Mathematics P Sec 4E/5NA

41 8 8 The figure below shows a cement mixer made up of an open cylinder and an inverted cone. The height of the cylinder is 1.5 m. The cone has a height of 1. m and base radius of 0.5 m. (a) Calculate (i) the volume of the mixer, [] (ii) the height of the water in the mixer if 1.5 m of water is poured into it. [] Hence, or otherwise, if 0.1 m of water is poured into the mixer instead, calculate the height of the water. [] (b) Calculate (i) the slant height of the cone, [] (ii) the total surface area of the mixer. [] Canberra Secondary School O Level Preliminary Examinations Mathematics P Sec 4E/5NA

42 9 9 Answer the whole of this question on a single sheet of graph paper. The table below gives some values of x and the corresponding values of y, correct to decimal places, 1 where y x x x 1. x y a b (a) Find the value of a and of b. [] (b) Using a scale of cm to represent 1 unit, draw a horizontal x-axis for x 5. Using a scale of 1cm to represent 1 unit, draw a vertical y-axis for 8 y. On your axes, plot the points given in the table and join them with a smooth curve. (c) By drawing a tangent, find the gradient of the curve at the point where x 0. [] (d) From your graph, find (i) the values of x when y 5. [1] [] (e) (ii) the value of y when x 8. [1] your graph to solve the equation 1 (i) x x x 1 0 [1] (ii) x x 9x x [] [Turn over Canberra Secondary School O Level Preliminary Examinations Mathematics P Sec 4E/5NA

43 10 10 (a) The cumulative frequency graph represents the examination marks of a group of 400 students No. of students Examination marks (i) Copy and complete the grouped frequency table of the examination marks. [] Mark ( x ) 0 x 0 0 x x x x 100 Frequency (ii) Using your grouped frequency table, calculate an estimate of (a) the mean examination marks of the group of 400 students, [] (b) the standard deviation. [] (iii) The marks scored by the same group of 400 students in another examination has the same median but a smaller standard deviation. Describe how the cumulative frequency curve will differ from the given curve. [1] Canberra Secondary School O Level Preliminary Examinations Mathematics P Sec 4E/5NA

44 11 (b) Ali has a box filled with 8 red discs, 4 blue discs and 6 yellow discs. Two discs are chosen at random, one after the other, without replacement. b a (i) Find the value of a and of b. [] (ii) Calculate the probability that (a) both discs are red, [1] (b) one disc is blue and the other is yellow, [1] (c) both discs are of a different colour. [] End of Paper Canberra Secondary School O Level Preliminary Examinations Mathematics P Sec 4E/5NA

Mathematical Formulae. Total amount = Curved surface area of a cone = rl. Surface area of a sphere = Volume of a cone = Volume of a sphere =

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