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Name : ( ) Class :

READ THESE INSTRUCTIONS FIRST Write your name, class and index number on all the work you hand in. Write in dark blue or black pen. 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.

For , use either your calculator value or 3.142, 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 the brackets [ ] at the end of each question or part question. The total number of marks for this paper is 80.

This question paper consists of 14 printed pages including this page.

COMMONWEALTH SECONDARY SCHOOL

PRELIMINARY EXAMINATION 2009

SECONDARY FOUR EXPRESS / FIVE NORMAL ACADEMIC

MATHEMATICS

Paper 1

Date : 27 August 2009

Candidates answer on the Question Paper.

4016/01

Time : 2 hours

0800 – 1000

80


Mathematical Formulae

Compound Interest

Total amount =

nr

P

1001

Mensuration

Curved surface area of a cone = πrl

Surface area of a sphere = 24 r

Volume of a cone = hr 2

3

1

Volume of a sphere = 3

3

4r

Area of triangle ABC = Cabsin2

1

Arc length = rθ, where θ is in radians

Sector area = 2

2

1r , where θ is in radians

Trigonometry

C

c

B

b

A

a

sinsinsin

a2 = b2 + c2 2bc cos A

Statistics

Mean = f

fx

Standard deviation =

22

f

fx

f

fx


Answer all the questions.

1 Rearrange the formulae y 5

x 23 y

to express y in terms of x.

Answer : [2]

2 Solve the equation 2x x3 6 12 . Answer : x = [2]

3 Factorize fully the expression 2 2 2 2ab 4a ab c 4ac . Answer : [3]


4 Mercury orbits around the Sun in 88 days, Venus does the same in 225 days and Earth

takes 360 days. The last time an eclipse occurred (when the Sun, Mercury, Venus and

Earth are set in a straight line) was in the year 1992.

By writing 88, 225 and 360 into the product of their prime factors, find the year in which

the next eclipse would occur on Earth. Answer : [3] 5 Mrs Cheah drove at 60kmh-1 for the first 1hour 20 minutes and 90kmh-1 for the rest of her

journey. If the whole journey took 2hours, find the exact value of the average speed of

Mrs Cheah’s journey, leaving your answer in ms-1. Answer : [3]

Sun

Mercury

Earth

Venus


6(a) In the Venn diagram, shade the region (A ' B) A . [1]

(b) Given that {x : x is an integer and 1 x p} , A {x : x is a multiple of 2} and

B {x : x is a multiple of 3} . If n A B 5 , find the largest and smallest possible

values of p.

Answer : largest p = , smallest p = [2]

7 Write out the largest prime number satisfying the inequality 12 2x 1 x 5

3 4 3

.

Answer : the largest prime number = [3]

BA


8 In one particular month, Hafizah gives her parents 15% of her salary, spends 5% on food,

1/5 on entertainment and 1/4 on rent. She uses the rest of her salary to invest in a

structured deposit that pays compound interest of 2% per year. Her rent is $1600.

(i) Find Hafizah’s salary.

(ii) Calculate the total interest she will receive in three years from her investment. Answer : (i) [1] (ii) [3] 9 The diagram shows a section of a regular 12-sided polygon which is cut from a circular

piece of paper of radius 5cm. All the vertices of the polygon lie on the circumference of

the circle. Find

(i) one interior angle of the polygon,

(ii) the amount of paper discarded, leaving your answer in terms of . Answer : (i) [1] (ii) [3]


10(i) Write the expression 2x 2x 3 into the form 2a(x h) k .

(ii) Hence sketch the graph of 2y x 2x 3 , showing clearly the turning point and

the x and y intercepts. [3]

Answer : (i) [2]


11 In the diagram, ABC 90 , AC = 29cm,

BD = 15cm, DC = 6cm and AD = y cm. Calculate

(i) the value of y,

(ii) the value of tan ADC, without solving for any angles.

Answer : (i) [2] (ii) [2] 12 The variables x, y and z are related. z varies directly as the square of x, y varies inversely

as the cube root of z, and when x = 1, y = 1 and z = 27.

(i) Find an expression for z in terms of x and y in terms of z.

(ii) Hence show that 2/3y x . [1]

Answer : (i) z = , y = [4]

6cm

29cm

15cm

y cm

C B

A

D


13 A piece of land on level ground is in the shape of an isosceles triangle ABC with the sides

AB = AC. The diagram, drawn to a scale of 1cm : 2m, shows the side AC.

Given that the bearing of B from A is 160,

(i) draw the triangle ABC and write down the length of BC in metres. [1]

(ii) A tree T is to be planted so that it is equidistant from points A and C and equidistant from

lines AC and BC. Construct the perpendicular bisector of AC and the angle bisector of

angle ACB and mark clearly with the point T the position of the tree. [3]

Answer : (i) BC = [1]

N

A

C


14 The table below shows the scores obtained when a die is thrown a number of times.

Score 1 2 3 4 5 6

No. of times 3 4 x 1 2 3

(i) Write down the maximum value of x if the modal score is 2.

(ii) Write down the minimum value of x if the median score is 3.

(iii) Find the median score if the mean score is 23/7.

Answer : (i) [1] (ii) [1] (iii) [3] 15 The equation of a line l is y – 2x + 6 = 0.

(i) Find the equation of the line parallel to line l and which passes through the point (1,-2) .

(ii) Line l cuts the y-axis at A and the x-axis at B and B is the midpoint of the line AC. Find

(a) the coordinates of the point C,

(b) the length of AC. Answer : (i) [2] (ii)a) [2] (ii)b) [2]


16 The price of a ticket in each category at the Night Safari is given below:

(i) The number of tickets sold on one weekend is given as follows.

Adult Senior Citizen Child

Saturday 52 85 125

Sunday 102 40 63

By putting the prices into a column matrix A and the number of tickets sold as matrix B,

find the matrix C given by C = BA and describe what is represented by the elements of C. (ii) To improve the revenue during weekends, two plans are proposed :

Plan 1 : Increase the price on Sunday only by 30%.

Plan 2 : Increase the price by 15% on each day.

A 1x2 matrix P is such that PC gives the revenue for the weekend under Plan 1. Another

1x2 matrix Q is such that QC gives the revenue for the weekend under Plan 2.

(a) Evaluate PC and QC.

(b) State which plan would be more profitable. Answer : (i) C = . C represents [2] (ii)a) PC = QC = . [2] (ii)b) [1]

,


17 Two open troughs X and Y are geometrically similar

prisms with 2 trapeziums and 3 rectangles making

up their sides.

The ratio of the sides of trough X to the sides of

trough Y is 1 : 4. If the capacity of the trough Y

is 1200 cm3, calculate

(i) the ratio of the surface area of X to Y.

(ii) the capacity of the trough X.

(iii) the depth d cm of trough Y. Answer : (i) [1] (ii) [2] (iii) [3]

12cm

8cm

d cm

5cm

X

Y


18 The diagram shows the speed time graph of

a cyclist over a period of T seconds.

The cyclist sees a stretch of wet road ahead

and slows down uniformly from 6m/s to 3m/s

in 20 seconds. He then progresses at constant

speed for 30 seconds, passing the stretch of

wet road, before gaining speed uniformly

to 6m/s at T seconds. (i) Given that the cyclist’s speed is 3.6m/s at t = 60s, find the value of T.

(ii) Find the average speed of the particle for the first 50 seconds.

(iii) On the axes in the answer space, sketch the corresponding distance-time graph

for the period of T seconds, indicating the values of distance travelled clearly.

Answer : (i) [2] (ii) [2] (iii) [2]

0

speed (m/s)

time (s)

6

3

20 50 T

0

distance (m)

time (s)20 50 T


19 In the diagram, OPQR is a parallelogram. M is the midpoint of OQ, N is the midpoint of

OM and L is the point on OR such that OL = 2LR.

(a) Given that OP a and OR b , express as simply as possible in terms of a and b,

(i) OM

(ii) NP

(iii) LM (b) Explain why NP and LM are parallel. (c) Find the following ratios.

(i) Area of OPN

Area of PNQ

(ii) Area of PNQ

Area of OML

Answer : (a)(i) [1] (ii) [1] (iii) [1] (b) [1] (c)(i) [1] (ii) [1]

End of Paper

L

N

M

P Q

RO

a

b


Answer Key

1) 23x 20

y(2 x)(2 x)

2) x = -1

3) a(b+2)(b-2)(1+c)(1-c) 4) 2047

5) 4

19 m / s9

6)a) 6)b) smallest p = 30 , largest p = 35 7) 5 8)i) $6400 ii) $137.11

9)i) 150 ii) 25 75 10) 2(x 1) 4

11)i) y = 25 ii) 1

13

12)i) 23

3z 27x , y

z

13) BC = 17.6m 14)i) 3 ii) 2 iii) 2.5 15)i) y = 2x – 4 ii) (6,6) , 13.4 units

16)i) 3029

C3177

ii) PC = $7159.10 , QC = $7136.90 , Plan 1 is more profitable

17)i) 1/16 ii) 18.75 iii) 6 18)i) T = 100 ii) 3.6

19ai) 1

(a b)2

ii) 1

(3a b)4

iii) 1

(3a b)6

b) 3

NP LM2

ci) 1/3 cii) 1

24

COMMONWEALTH SECONDARY SCHOOL PRELIMINARY EXAMINATION 2009

SECONDARY FOUR EXPRESS/FIVE NORMAL

MATHEMATICS 4016/02

Paper 2 27 August 2009

10 45 – 13 15 2 hours 30 minutes

Additional Materials: Writing Paper Graph Paper (1 sheet)

NAME: _____________________________ ( ) CLASS: ________

READ THESE INSTRUCTIONS FIRST

Write your name, index number and class on all the work you hand in.

Write in dark blue or black pen on both sides of the paper.

You may use a 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.

For , use either your calculator value or 3.142, 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.

The total of the marks for this paper is 100.

This question paper consists of 11 printed pages including the cover page.

2

CSS/Prelim2009/MATH/SEC4E5N/P2/AGS/Page 2 of 11

Mathematical Formulae

Compound Interest

Total amount = 1100

nr

P

Mensuration

Curved surface area of a cone = rl

Surface area of a sphere = 24 r

Volume of a cone = 21

3r h

Volume of a sphere = 34

3r

Area of triangle ABC = 1

sin2

ab C

Arc length = r , where is in radians

Sector area = 21

2r , where is in radians

Trigonometry

sin sin sin

a b c

A B C

2 2 2 2 cosa b c bc A

Statistics

Mean = fx

f

Standard deviation =

22fx fx

f f

3


Answer all the questions.

1 (a) National Petroleum Company (NPC) provides 3 different grades of petrol. The price per litre of each grade of petrol is as follows:

Petrol Grade Price per Litre ($)

Grade 92 1.687

Grade 95 1.767

Grade 98 1.870

(i) Mr Soh pumped 42 litres of Grade 98 petrol for his car.

Calculate the amount of money he paid for the petrol.

[1] (ii) Mr Soh’s car has a petrol consumption rate of 12.5 km

per litre. Calculate the distance his car can travel with $50 worth of Grade 98 petrol.

[2]

(iii) During a promotion month, the cost per litre of Grade 95

petrol was reduced by 15% but an instant rebate of $5 was given to car owners who pumped Grade 92 petrol. What is the maximum volume of Grade 92 petrol to be pumped before the total cost becomes more than the cost of pumping Grade 95 petrol? Give your answer in litres correct to 1 decimal place. [3]

(b) A shopkeeper sells two types of luxury handbags, Elegant and

Convenient. Elegant handbags cost $7500 a piece and Convenient handbags cost $240 less.

(i) Write down, in its simplest form, the ratio of the cost of

Elegant handbags to Convenient handbags. [1] (ii) Given that the shopkeeper sold an Elegant handbag at a

discount of 15% and a Convenient handbag at a discount of $50, calculate the total percentage discount given on the sale of the handbags. [2]

4


2 Each diagram in the sequence below is made up of a number of dots.

●

● ● ●

●

● ●

● ● ● ● ● ● ● ●

●

● ● ● ●

● ● ● ● ● ● ● ● ● ● ● ● ● ● ●

●

● ● ● ●

● ●

Diagram 1 Diagram 2 Diagram 3 Diagram 4

(a) Draw the next diagram in the sequence. [1] (b) The table shows the number of dots in each diagram.

Diagram 1 2 3 4 5 6

Number of dots 1 6 13 22 p q

Write down the values of p and of q . [2] (c) The formula for finding the number of dots in the n th diagram is

2An Bn C , where A , B and C are constants. Find the

values of A , B and of C .

[3] (d) Find the number of dots in Diagram 10. [1] (e) Which diagram has 253 dots? [2]

3 (a) (i) Simplify 2 2 2 26 9 5 45

6 3 2 6 3

a ab b a b

ac ad ac ad bc bd

.

[3]

(ii) Solve

3 54

2 1 3 1x x

.

[2] (b) A box contains several red discs and green discs. A disc is

randomly chosen and then placed back into the box and the process is repeated several times. The probability of choosing a red disc is p .

(i) Write down, in terms of p , the probability of choosing a

green disc. [1] (ii) The process was repeated 8 times. Find the probability

that (a) a red disc was chosen every time, [1]

(b) at least one green disc was chosen. [1]

5


4 In the diagram, 90ACB , 51ABC , 35BEC ,

103ACD , 4CD cm, 4.6BC cm and 7.3CE cm.

Calculate (a) CBE , [2] (b) the length of CA , [1] (c) the length of AD , [3] (d) the area of triangle BCE , [2] (e) the shortest distance from E to CB produced. [2]

6


5 An airplane is scheduled to fly to its destination 3500 km away. The speed of the airplane in still air is 600 km/h and the speed of wind, which is constant throughout, is x km/h. Due to a haze, the speed of the airplane in still air is reduced by 10%.

(a) Write down an expression, in terms of x , for the time taken by

the airplane, in hours, if it is flying in the direction of the wind.

[1] (b) Write down an expression, in terms of x , for the time taken by

the airplane, in hours, if it is flying against the wind.

[1] (c) The difference in arrival time is 1 hour and 10 minutes. Write

down an equation in terms of x , and show that it reduces to 2 6000 291600 0x x . [3]

(d) Solve the equation 2 6000 291600 0x x . [3] (e) Hence, find the time taken by the airplane, in hours and

minutes, if it is flying in the direction of the wind when there is no haze. [2]

7


6 In the diagram, O is the centre of the circle and points P , S , T and R lie on the circumference of the circle. The tangent at P meets RT produced at Q . TS PS , TQ SQ and 36TRP .

(a) Find

(i) reflex angle POT , [2] (ii) PTS , [2] (iii) PQS . [3] (b) Show that PS bisects QPT . [3]

8


7 (a) The diagram shows the cross-section of a swing in a children’s playground. The seat is suspended on a 1.8 m long rope. To oscillate the swing, the seat is pulled back to point A and released to swing an angle of 62° to point A ‘. The seat makes one complete oscillation when it moves from point A to point A’ and back to point A again.

(i) Calculate the distance moved by the swing seat from

point A to point A’. [2] (ii) Assuming that the swing oscillates regularly from point A

to point A’, find the speed of the swing, in metres per minute, if it makes 5 complete oscillations in 2 minutes. [2]

(b) The diagram shows the swing and a bench, 4 m away, in the

children’s playground. Both the bench seat and swing seat are at the same height above the ground.

(i) Calculate the angle of depression of the edge of the

bench seat from the top of the swing. [2] (ii) A bird flies from the edge of the bench seat to the top of

the swing. Calculate the distance the bird flies. [2]

A A’

1.8 m 62°

1.8 m

4 m

9


8 (a) A factory manufactures small decorative ornaments. Each decorative ornament is made up of two parts: a solid hemisphere with radius 7 cm and a solid cone with a height 10 cm, as shown in Diagram I.

Diagram I

(i) Calculate the volume of the hemisphere. [2] (ii) The volume of the hemisphere is 3 times the volume of

the cone. Find the base radius of the cone. [2] (iii) Given that the solid cone is made with a light plastic

material with a density of 0.9 g/cm3, find the mass of the material used for the cone. [2]

The two pieces are joined together to form the

decorative ornament as shown in Diagram II. (iv) Calculate the total external surface area of the ornament.

Diagram II [4] (b) Given that the area of the major sector is

98 cm2, find the value of and hence

calculate the perimeter of the major sector. [2]

7 cm 10 cm

6 cm rad.

10


9 The cumulative frequency curve below represents the daily wages of 80 male employees in a company.

Use the graph to estimate (a) the median daily wage, [1] (b) the interquartile range, [2] (c) the value of z such that 77.5% of the male employees have a

daily wage more than $ z . [2] The box-and-whisker diagram

represents the daily wages of 60 female employees in the same company.

(d) Find the median daily wage of the female employees and the

interquartile range. [3] (e) Compare and comment briefly on the daily wages of the male

and female employees in the company. [2] (f) Find the probability that an employee chosen at random from all

the employees has a daily wage less than or equal to $38. [2]

Daily Wages ($)

15 20 25 30 35 40 45 50 55 60 65

10

20

30

40

50

60

70

80

0

Cum

ula

tive F

req

uency

Daily Wages ($) 10 20 30 40 50 60 70

11


10 Answer the whole of this question on a sheet of graph paper.

The following table gives the corresponding values of x and y , which

are connected by the equation 5

2 9y xx

, correct to 1 decimal

place.

x 1 2 3 4 5 6 7 8 y 12 7.5 4.7 2.3 0 -2.2 p -6.4

(a) Calculate the value of p correct to 1 decimal place. [1] (b) Using a scale of 2 cm for 1 unit on the x -axis and 1 cm for 1

unit on the y -axis, draw the graph of 5

2 9y xx

for the

values of x in the range 1 8x .

[3] (c) Use your graph to find the value of y when 2.5x . [1]

(d) Use your graph to solve the equation 5

2 1xx

. [2]

(e) Find the coordinates of the point on the graph for which the

gradient of the curve is -4. [2] (f) By drawing a suitable straight line, solve the equation

24 6 5 0x x for 1 8x .

[3]

END OF PAPER

COMMONWEALTH SECONDARY SCHOOL PRELIMINARY EXAMINATION 2009

SECONDARY FOUR EXPRESS/FIVE NORMAL MATHEMATICS 4016/02

1 (a) (i) Amt. of money paid = $1.870 × 42 = $78.54

[B1]

(ii) Amt. of petrol = 50

1.870

≈ 26.73797 litres Dist. = 26.73797 × 12.5 ≈ 334 km

[M1]

[A1]

(iii) Let the max. volume be V litres.

1.687 5 0.85 1.767

1.687 5 1.50195

0.18505 5

27.0197

V V

V V

V

V

Max. volume is 27.0 litres.

[M1]

[A1] [A1]

(b) (i) Elegant handbags : Convenient handbags

= 7500 : 7260 = 125 : 121

[B1]

(ii) % discount =

0.15 7500 50100%

7500 7260

≈ 7.96%

[M1]

[A1]

2 (a)

● ● ● ● ● ● ● ● ●

● ● ● ● ● ● ●

● ● ● ● ●

● ● ●

●

● ●

● ●

● ● ● ●

[B1]

(b) 33p

46q

[B1] [B1]

(c) no. of dots = 2 2 1n n

= 2 2 2n n

2


1A 2B 2C

[B1] [B1] [B1]

(d) no. of dots = 210 2 10 2

= 118

[B1]

(e) 2 2 2 253n n

2 2 255 0n n

15 17 0n n

15n or 17n (N.A) Diagram 15 has 253 dots. (other methods are acceptable)

[M1]

[A1]

3 (a) (i) 2 2 2 26 9 5 45

6 3 2 6 3

a ab b a b

ac ad ac ad bc bd

23 2 3 2

3 2 5 3 3

a b a c d b c d

a c d a b a b

23 2 3

3 2 5 3 3

a b c d a b

a c d a b a b

3

15

a b

a

[M1]

[M1]

[A1]

(ii)

3 54

2 1 3 1x x

9 24 1 10x

24 1 1x

1

124

x

23

24x

[M1]

[A1]

(b) (i) P(choosing a green disc) = 1 p [B1]

(ii) (a) P(red disc chosen each time) = 8p [B1]

(b) P(at least one green disc chosen)

= 1 – P(red disc chosen each time)

= 81 p

[B1]

4 (a) By Sine Rule,

sin sin35

7.3 4.6

CBE

[M1]

3


180 65.538659

114.46134

114.5

CBE

[A1]

(b) tan514.6

CA

5.6805269

5.68 cm

CA

[B1]

(c) By Cosine Rule,

2 2 25.6805269 4 2 5.6805269 (4)cos103AD

7.647948

7.65 cm

AD

[M2]

[A1] (d) 180 35 114.46134 ( s sum of )BCE

30.53866

Area of 1

4.6 7.3 sin30.538662

BCE

2

8.5313285

8.53 cm

[M1]

[A1]

(e) 1

4.6 shortest dist. 8.53132852

Shortest dist. 3.70927 3.71 cm

[M1]

[A1]

5

(a) Speed of plane = 90

600100

= 540 km/h

Time taken (with wind) =

3500h

540 x

[B1]

(b) Time taken (against wind) =

3500h

540 x

[B1]

(c)

3500 3500 101

540 540 60x x

3000 30001

540 540x x

3000 540 3000 540 540 540x x x x

21620000 3000 1620000 3000 291600x x x

2 6000 291600 0x x (Shown)

[M1]

[M1]

[A1]

(d) 2 6000 291600 0x x

4


26000 6000 4 1 291600

2 1x

48.21259 or 6048.212 (N.A.) 48.2

[M1]

[A1] [A1]

(e) Time taken =

3500

600 48.21259

5.399 h 5 h 24 min

[M1]

[A1]

6 (a) (i) 36 2 ( at ctr. = 2 at circumference)TOP

72 Reflex 360 72 ( s at a pt.)POT

288

[M1]

[A1]

(ii) 180 36 (opp. s of cyclic quad.)TSP

144

180 144

(base of isos. )2

PTS

18

[M1]

[A1]

(iii) 90 ( in a semicircle)PTR

180 90 18 ( s on a st. line)QTS

72

180 2 72 ( s sum of isos. )SQT

36 90 (tangent rad.)QPR

180 90 36 ( s sum of )PQR

54

54 36PQS

18

[M1]

[M1]

[A1]

(b) 18 (isos. )SPT

180 72 (base of isos. )

2TPO

54 90 54 18QPS

18

Since 18QPS SPT , PS bisects QPT .

[M1]

[M1]

[A1]

7

(a) (i) dist. moved = 62

2 1.8360

1.947787

1.95 m

[M1]

[A1]

5


(ii) No. of oscillations in 1 min = 2.5 Dist. travelled in 1 min = 2.5 1.95 2 9.7389 9.74 m Speed is 9.74 m/min.

[M1]

[A1] (b) (i) Let the angle of depression be a .

1.8

tan4

a

24.2277a

24.2 Angle of depression is 24.2 .

[M1]

[A1]

(ii) 2 2 2dist. 4 1.8 (by Pythagoras' Thm.)

dist. 4.39 m

[M1] [A1]

8

(a) (i) Vol. of hemisphere = 31 4

72 3

718.3775201

3718 cm

[M1]

[A1]

(ii) Let the base radius of the cone be cmr .

21

10 3 718.37752013

r

Base radius of cone is 4.78 cm.

[M1]

[A1]

(iii) Mass = 1

0.9 718.37752013

215.5132 216 g

[M1]

[A1]

(iv) Let the slanted height of the cone be cml .

2 2 210 4.7819 (by Pythagoras' Thm.)l

11.0845l

Total external surface area

= 2 2

3 7 4.7819 11.0845 4.7819

700.171587

2700 cm

[M1]

[M2]

[A1]

4.781910357

4.78

r

(b) 21

6 982

4

5 rad.9

[M1]

6


Perimeter of major sector =

46 5 2 6

9

2

44 cm3

[A1]

9 (a) Median daily wage ≈ $43 [B1] (b) Interquartile range ≈ $49 – $36

= $13 [M1] [A1]

(c) 77.5% of the male employees = 22.5

80100

= 18 z ≈ 35

[M1] [A1]

(d) Median daily wage ≈ $38

Interquartile range ≈ $46 – $18 = $28

[B1] [M1] [A1]

(e) The median wage of males ($43) is higher than that of females

($38). The interquartile range for wage of males (13) is smaller than that of females (28) and thus, the wage of males is less widespread as compared to that of females.

[B1]

[B1]

(f) P(wage less than or equal to $38) = 26 30

140

2

5

[M1]

[A1]

7


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