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__________________________________________________________________________ This question paper consists of 18 printed pages

Candidate Name _______________________________________

FUHUA SECONDARY SCHOOL

Secondary Four Express / Five Normal Academic / Four NA (TT)

Preliminary Examination 2010 Fuhua Secondary Fuhua Secondary Fuhua Secondary Fuhua Secondary Fuhua Secondary Fuhua Secondary Fuhua Secondary

Fuhua Secondary Fuhua Secondary Fuhua Secondary Fuhua Secondary Fuhua Secondary Fuhua Secondary Fuhua Secondary

Fuhua Secondary Fuhua Secondary Fuhua Secondary Fuhua Secondary Fuhua Secondary Fuhua Secondary Fuhua Secondary

MATHEMATICS 4016/1

PAPER 1

DATE 3 Sept 2010

TIME 0750 - 0950 DURATION 2 Hours

INSTRUCTIONS TO CANDIDATES

Answer all questions.

Write your answers and working on the space provided in the question paper.

You may use a soft pencil for any diagrams or graphs.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of

angles in degrees, unless a different level of accuracy is specified in the question.

The number of marks is given in brackets [ ] at the end of each question or part question.

The total number of marks for this paper is 80.

The use of an electronic calculator is expected, where appropriate.

You are reminded of the need for clear presentation in your answers.

PARENT'S SIGNATURE FOR EXAMINER’S USE Highest Mark

Lowest Mark

Setter: Mdm Sharon Yee

Class

Index Number

E/NA

80

___________________________________________________________________________________________________ FSS/Prelim2010/EM_1EXP/4016/1

2

MATHEMATICAL FORMULAE

Compound Interest

Total amount = P nr)

1001(

Mensuration

Curved surface area of cone = rl

Surface area of a sphere = 4 r2

Volume of a cone = hr 2

3

1

Volume of sphere = 3

3

4r

Area of triangle ABC = Cabsin2

1

Arc length = radiansin is where, r

Sector area = radiansin is where,2

1 2 r

Trigonometry

C

c

B

b

A

a

sinsinsin

Abccba cos2222

Statistics

Mean =

f

fx

Standard Deviation =

22

f

fx

f

fx

FSS/Prelim2010/EM_1EXP/4016/1 [Turn over

3

Answer all the questions.

1 (a) Express the value 23 103.410056.0 to 3 significant figures in

standard form.

(b) Find the value of 22

3

103.18.1

1048.6

.

Answer (a) …………………………[1]

(b)…………………………..[1]

_____________________________________________________________________________

2 Find the value of x and y when

(a) ,3

1327 612

x

x

(b) y

7

497

73

.

Answer (a) …………………………[1]

(b)…………………………..[1]

___________________________________________________________________________________________________ FSS/Prelim2010/EM_1EXP/4016/1

4

3 (a) It is known that the temperature at the top of a mountain is – 8° C and the

temperature at the foot of the mountain is 12°C. A mountaineer finds that all his

water bottles freezes over (0 °c) at an altitude of x m. Given that the temperature

changed uniformly with height, find the height of the mountain in terms of x.

(b) A factory has 30 packers. Each packer can load 6

1 of a box in 9 minutes.

How many boxes can be loaded in 1.5 hours by all 30 packers?

Answer (a) …………………..…….[1]

(b) ……………………..…..[1]

_____________________________________________________________________________

4 A train travelling at a speed of 120 km/h overtakes another train on another track that is

moving 96 km/h in the same direction. A passenger in the slower train observes that it

took the faster train 1 minute to completely pass him. What is the length of the faster

train in metres?

Answer …………………….m [2]


5

5 The equation of a straight line is 2x + 3y = 6.

(a) Find the gradient of the line.

(b) Given that the point ( h, 4 ) lies on the line, find the value of h.

Answer (a) ………………………....[1]

(b) ……………………….....[1]

_____________________________________________________________________________

6 The diagram shows a semi-circle inside a sector of radius 12 cm and angle AOB is 150°.

Calculate the perimeter of the shaded region. Give your answer in the form ba .

Answer …..………………………….[2]

O

A B

12 cm

150°

___________________________________________________________________________________________________ FSS/Prelim2010/EM_1EXP/4016/1

6

7 The number of goals scored by a football team, Tiger United, during the S-League 2010

is illustrated in the table below.

No.of

goals

1 2 3 4 5

No.of

matches

2 3 n 1 5

(a) State the largest possible value of n if the modal number of goals scored is 5.

(b) State the least possible value of n if the median score is 3.

(c) Calculate the value of n if the mean number of goals scored is 7

23 .

Answer (a)..………..……………[1]

(b) ..……….…..…….... [1]

(c)..…….…..……………[1]

_____________________________________________________________________________

8 An actual distance of 60 km is represented by 12 cm on a map. Calculate

(a) the scale of the map in the form of 1 : n,

(b) the area of a plot of land, in cm2 , on the map if the actual area of the plot of land

is 75 km2.

Answer (a) ……………....…...…….[1]

(b) ……………………...…..[2]


7

A

B

C

D

60

30

E

13 cm

55 cm

9 ABCD represents a wooden plank drilled onto the wall, as shown in the diagram. From

B, the angle of depression of a point C is 30 . From C, the angle of depression of a

point E on the ground is 60 . Given that BC is 13 cm, CD is

55 cm, and 90ABC BCD , find

(a) how much higher is B than C above the ground,

(b) the distance of DE.

Answer (a) ……………………..…..[1]

(b) ………………………….[2]

_____________________________________________________________________________

10 A gift shop sells three different hampers for Valentine’s day.

Hamper A contains 3 bottles of wine and 5 boxes of chocolates.

Hamper B contains 2 bottles of wine, 1 box of chocolate and 12 stalks of roses.

Hamper C contains 1 bottle of wine and 24 stalks of roses.

The price of a bottle of wine is $18, a box of chocolate is $7 and a dozen of roses is $60.

(a) Evaluate the cost price of each type of hamper by using multiplication of

matrices.

(b) The shop intends to make a profit of 15% on each Hamper A, 20% on each

Hamper B and 30% on each Hamper C. Evaluate the selling price of each type of

hamper by using multiplication of matrices.

Answer (a) ………………………………………………………………………………..........[1]

(b) …………………………..[2]

___________________________________________________________________________________________________ FSS/Prelim2010/EM_1EXP/4016/1

8

11 (a) All pupils in a class were asked if they have a fire extinguisher (denoted by E) or

a first-aid box (denoted by B) at home. Express in statement for the notation

7)( BEn .

(b) Given that {x : x is a positive integer less than 8 }, A = {x : x < 6}, and

B = {x : x2 – 2x – 3 = 0}. List the elements of

(i) B ,

(ii) BA ' .

Answer (a) ………………………………………………………………………………………

…………………………………………………………………………………….[1]

(bi)………………………..[1]

(bii)………………………..[1]

_____________________________________________________________________________

12 A rectangular box has dimensions 20 cm by 8 cm by 5 cm. Metal spherical balls are

packed neatly into the box in layers. Each ball is of radius 2 cm.

(a) Find the largest number of balls that can be put into the box.

(b) Find the amount of empty space that is left after putting in the largest number

of balls.

Answer (a) ………………….…….[1]

(b) ………………….……..[2]


9

13 (a) Given that y varies directly as (x - 2)2 and that if y = 5 when x = 7, find the

positive value of x when y = 20.

(b) Given that p varies as qr, write down the value of r if p and q are the sides of

a rectangle of given area.

Answer (a) …………………..…….[2]

(b) ………………………....[1]

_____________________________________________________________________________

14 (a) Given that 1232

xx

and 2

85

4

12

yy, find the range of values of x

and of y.

(b) Hence, find the smallest possible value of x y2 2 , given that both x and y are

integers.

Answer (a) …………………..…….[3]

(b) ………………………....[1]

___________________________________________________________________________________________________ FSS/Prelim2010/EM_1EXP/4016/1

10

15 The readings of the air pollution index (API) of a town in a period of eight days is shown

below where x is a constant.

API: 68 77 80 70 47 65 53 x

(a) Determine the possible values of x if the range of the data is 35.

(b) Using the larger value of the x found in (a), draw a box and whisker plot

for the data.

Answer (a) …………………..…….[2]

Answer (b) [1]


11

16 (a) The numbers 180 and 576, written as the products of the prime numbers,

are 180 = 2 5322 , 576 = 2 26 3

Find

(i) the largest integer which is a factor of both 180 and 576,

(ii) the smallest positive integer value of n for which 180n is a multiple of

576.

(b) The following lunch menu shows the dishes that Chef Kook can come up with.

Starter Main Course Dessert

Cream of Mushroom Beef Steak Brownie

Lobster Bisque Salmon Fillet Crème Brulee

Caeser Salad Fish and Chips Tiramisu

Prawn Salad Lamp Chop Cheesecake

Seafood Pasta Apple Crumble

Chicken and Ribs Combo

One the first day, Chef Kook served cream of mushroom, beef steak and brownie.

On each day that follows, he replaced each part of the meal by the next item on

the list. For instance, if the menu on one day was prawn salad, lamb chop and

cheesecake, then next day's menu would be cream of mushroom, seafood pasta

and apple crumble.

How many days would pass before Chef Kook serves cream of mushroom, beef

steak and brownie again?

Answer (ai) ………...……………….[1]

(aii) …………….………..….[1]

(b) ………………...........…..[2]

___________________________________________________________________________________________________ FSS/Prelim2010/EM_1EXP/4016/1

12

17 (a) (i) Simplify )2)(2(2 babaa .

(ii) Using your answer in part (a), write down the value of

12342 – 1244 1224.

(b) Given that 06946 bcacba and3

2c , find the value of

b

a.

Answer (ai) ………...………….…….[1]

(aii) …………………..…..….[1]

(b) ………………............…..[2]


13

18 (a) (i) Sketch the graph of y = x

1 .

(ii) Write down the equation of the line of symmetry of y = x

1 .

(b) (i) Sketch the graph of y = .1)1( 2 x

(ii) Write down the coordinates of the minimum point of the curve.

Answer (ai)

[1]

(aii) ……….…………………..[1]

Answer (bi)

[1]

(bii) …………………………..[1]

y

x

x

y

___________________________________________________________________________________________________ FSS/Prelim2010/EM_1EXP/4016/1

14

19 P, Q and R are three vertices of a regular polygon and the reflex angle 200PQR .

(a) Find the exterior angle of the polygon.

(b) Calculate the number of sides of the polygon.

(c) X is a point on QR and S lies on PX produced. Given that angle PSR = 160,

explain why P, Q, R and S lie on a circle.

Answer (a) …………………….….[1]

(b) ………………………...[2]

(c) …………………………………………………………………… ………………….…..

…………………………………………………………………………………….……...

………………………………………………………………………………….……...[2]

200

P

Q

R


15

20 The diagram below shows the speed–time graph of a car journey from Town A to

Town B.

(a) Find the speed v km/h if the acceleration at 70 minutes is 60 km/h2.

(b) Find the average speed for the whole journey.

(c) Draw the distance-time graph of the car for the whole journey.

Answer (a) …………………...km/h [1]

(b) ………..………….km/h [2]

(c) [2]

0 30 50 80 100

v

60

Time (mins)

Speed (km/h)

30 50 100 130

Time (mins)

Distance (km)

___________________________________________________________________________________________________ FSS/Prelim2010/EM_1EXP/4016/1

16

21 In the diagram, 090

PSRSPQ , QU = 6 cm and RU = 3 cm. The point R is the

reflection of T in the line PS and QT intersects PS at U.

(a) State and prove the triangle which is congruent to triangle RSU.

(b) Calculate the numerical values of the ratios

(i) QPUofArea

TSUofArea

(ii) PQRSTrapeziumofArea

USTofArea

Answer (a) ………...….…………….[3]

(bi) …….……….…..……….[1]

(bii) ..….…………...........…..[2]

P Q

RST

U

3

6

P Q

RST

U

3

6


17

22 In the diagram given below, AB is parallel to DC and 4

3DC AB .

E is a point on BD of ∆ABD such that1

4DE DB . Given that AB = 3a and

AD = b.

A

b

E

D C

Ba3

(a) Find

(i) DB

(ii) AE

(iii) BC

(b) Explain why BC is parallel to AE

(c) Giving your answer as a fraction in its lowest terms, find the value of

(i) Area of

Area of

CBD

ABD

(ii) Area of

Area of

CBD

ABCD

Answer (ai) ………...……………….[1]

(aii) ……………………...….[1]

(aiii)……………………...….[1]

(b) ………………………………………………………………...…………………..[1]

(ci) …….……….………..….[1]

(cii) ..….………………...…..[1]

___________________________________________________________________________________________________ FSS/Prelim2010/EM_1EXP/4016/1

18

23 A developer bought a triangular piece of land, ABC, where AB = 85 m,

AC = 105 m and BAC = 85.

(a) (i) Using a scale of 1 cm to represent 10 metres, construct an accurate

scale drawing of the plan of the land, with AC as the horizontal base. [1]

(ii) Measure and write down the length of BC in metres.

(b) The developer intends to build a house H on the land.

The house H is on a bearing of 060° from A and on a bearing of 290° from C.

Find and label the position of house H. [2]

(c) The developer intends to build a children’s playground on the land at

location P which is equidistant from A, B and C. By constructing perpendicular

bisectors, find and label the position of P. [2]

Answer (aii)………....……………….[1]


19

Answer

1a 5.60 x 10 1b 11.8

2a 7

3 2b

3

22

3a x3

5 3b 50

4 400

5a 3

2 5b h = 9

6 16 + 12

7a n = 4 7b n = 2 7c n = 3

8a 1 : 500 000 8b 3

9a 6.5 9b 55

10a Hamper A = $89, B = $103, C = $138

10b Hamper A = $102.35, B = $123.60, C = $179.40

11a There are 7 pupils with fire extinguisher only

bi {1, 2, 4, 5, 6, 7}

bii {3, 6, 7}

12a 10 12b 465

13a x = 12 13b r = -1

14a -6 < x < 9, y > 8

12 14b 9

15a 45, 82

16ai 36 ii 16 b 60

17ai 4b2 ii 100 b 3

2

18aii y = x or y = -x bii (1, -1)

19a 20° b 18

20a 90 b 52.5

21bi 4

1 ii

9

1

22ai 3a – b ii 4

3(a + b) b AEBC

4

3

ci 3

4 ii

7

4

23ai 129m

FSS/Prelim2010/EM_4EN5N/4016/2 FSS/Prelim2010/EM_4EN5N/4016/2

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Page 3

1 (a) Simplify pqqp

pp

1052010

105 2

. [3]

(b) Given that zyx

111 ,

express x in terms of y and z [2]

(c) (i) Factorise 532 2 xx . [1]

(ii) Hence solve the equation 2253 xx . [2]

2

9.2m

38B A

C D

A quadrilateral ABCD is divided into 2 triangles by a diagonal AC.

Given that AC = CD, AC = 9.2m, angle ACB is a right angle and angle BAC = 38°,

calculate

(a) BC, [2]

(b) BD, [2]

(c) AD, [2]

(d) the area of quadrilateral ABCD, [3]

(e) the perimeter of quadrilateral ABCD. [2]


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Page 4

3 (a) Andy deposits $10 000 in Bank A which offers a simple interest rate of 5%

per annum. Bill deposits the same amount of money in Bank B which offers

a 3.5% per annum compound interest rate that is compounded monthly.

(Give all your answers to the nearest cent)

(i) Find the total amount of interest Andy receives after 15 months. [1]

(ii) Find the total amount of interest Bill receives after 15 months. [1]

(iii) By finding the total amount that each will receive after 30 months,

state who has made the better choice.

[3]

(b) A builder works 10 hours a day for 6 days a week. He receives a daily wage

of $88 for his work.

(i) Find his hourly wage and weekly wage for his work. [2]

(ii) If the builder is paid an extra 50% for overtime work, how much

overtime must he work in order to earn $594 a week?

Express your final answer in hours and minutes. [2]


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Page 5

4 For a system of N nodes, C connections are drawn to link each node to every other node.

Node Connection

N = 6N = 5

N = 4N = 3N = 2

(a) Complete the diagram for N = 6 on your answer paper. [1]

(b) Using the diagram above, count the number of connections for each

diagram and complete the table below on your answer sheet.

Nodes (N) Connections (CN)

N = 2 C2 = 1

N = 3 C3 = 3

N = 4 C4 = 6

N = 5 C5 = ?

N = 6 C6 = ?

[2]

(c) Given that CN )1(2

NN

,

(i) Find the number of connections for a system of 15 Nodes. [1]

(ii) How many nodes are there in a system that have 351 possible

connections? [3]

(iii) Show that CN – CN-1 = N – 1 [2]


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Page 6

5 A car travels from town A to town B at an average speed of k km/h and returns

from town B to town A at an average speed of 15k km/h. Given that the

distance between town A and town B is 360 km and that the average speed of the

entire journey is 60 km/h,

(a) Find the total time taken for the entire journey. [1]

(b) Find an expression in terms of k for the time taken from town A to town B

and from town B to town A.

[2]

(c) Show that k can be expressed in an equation, and that it simplifies to

0450452 kk

[3]

(d) Solve 0450452 kk [3]


[Turn over]

Page 7

6

32

F

E

A

C

O D

B

The diagram shows a semicircle, ABCD, with centre O.

The chord BC is parallel to diameter AD. The chords BD and AC intersect at E.

Angle ADB = 32°

(a) Find

(i) angle ABD, [1]

(ii) angle DBC, [1]

(iii) reflex angle AOC, [1]

(iv) angle CED, [1]

(v) angle COD. [1]

(b) Hence, show that triangles EFC and OFD are similar. [2]


[Turn over]

Page 8

7 (a)

The diagram above shows a triangular field ABC.

AB = 45m, BC = 28m and angle ABC is a right angle.

Calculate

(i) angle BAC [1]

(ii) length AC [1]

A pole AD is planted perpendicular to the ground such that the angle of

elevation of D from B is 40°.

Calculate

(iii) the height of the pole [1]

(iv) the angle of elevation of D from C [1]

(v) the area of triangle BDC. [4]

(b)

The diagram above shows a square EFGH of side 8cm. Arc EG and Arc

FH are drawn with a radius of 8cm from centers H and E respectively.

28m45m

AC

B

D


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Page 9

Find the area of the shaded region. [3]

8 (a)

5m

8m

3m

A grain silo is built with a cylinder as the base and a cone, of equal radius, for a roof.

The cylinder has a diameter of 8m and height 3m.

The cone has a slant height of 5m.

(i) Calculate the total volume of the silo [3]

(ii) If 1 tin of paint is able to paint 13m2 of surface, how many tins are

needed to paint the surface area of the silo?

[4]

(b)

A bowl is shaped as a hemi-sphere of radius 10cm and capped with a circular lid on

top.

Workers use these bowls to transport grain to fill the silos.

Calculate

(i) the surface area of the bowl inclusive of the lid [2]

(ii) the volume of the bowl. [2]


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Page 10

(iii) the number of grain-filled bowls needed to fill the silo. [1]

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

9 The variables x and y are connected by the equation )63(12

1 23 xxxy .

Some corresponding values of x and y , correct to 2 decimal places, are given in

the table below.

0 1 2 3 4 5 6

0 -0.67 -1.33 -1.5 -0.67 p q

(a) Calculate the value of p and q. [2]

(b) Using a scale of 2cm to represent 1 unit on each axis, draw a horizontal

x -axis for 60 x and a vertical y -axis for 62 y .

(c) On your axes, plot the points given in the table and join them with a smooth

curve.

[3]

(d) By drawing a tangent, find the gradient of the curve at the point (4, -0.67).

[2]

(e) Use your graph to find the smallest value of y in the range 60 x and

the x value for when it occurs.

[2]

(f) Use your graph to find two solutions of 01263 23 xxx in the range

60 x .

[3]


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Page 11

10

Time (min)

The diagram above is the cumulative frequency curve for the daily time spent

surfing Facebook of 250 students.

(a) Use the graph to find

(i) the median time spent surfing Facebook, [1]

(ii) the number of students who spend more than 20mins a day surfing

Facebook,

[1]

(iii) the 90th percentile, [1]

(iv) the interquatile range. [1]

(b) A second group of students have a higher median and a larger standard

deviation. Describe how the cumulative frequency graph will differ from

this given curve.

[2]

Cu

mu

lative fre

qu

ency


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Page 12

11 A bag contains 3 green balls, 2 blue balls and 1 red ball.

Two balls are drawn at random, one after the other, from the bag with

replacement.

(a) Draw a possibility tree diagram to show the probability outcome of the

draw.

[2]

(b) Find, as a fraction in its simplest form, the probability that

(i) both balls are green, [1]

(ii) neither ball is red, [1]

(iii) neither ball is green, [1]

(iv) at least one ball is blue. [1]

END OF PAPER

1a

q

p

qp

pp

pqqp

pp

pqqp

pp

2

)2)(21(

)21(

)242(5

)21(5

1052010

105 2

1b

zy

yzx

yz

zy

yzx

zyx

111

111

1ci) )1)(52( xx

1cii)

0)1)(52(

0532 2

xx

xx

x = -1, 2.5

2(a)

BC = 9.2 tan38

= 7.187

≈7.19m

(b) BD² = 7.187² + 9.2² - 2(7.187)(9.2)cos 128

BD² = 217.709

BD = 14.75 ≈ 14.8m

(c) AD² = 9.2² + 9.2² - 2(9.2)(9.2) cos 38

= 35.885

AD = 5.990 ≈ 5.99m

2(d) Area of triangle ABC = 0.5(BC)(9.2) = 33.06

Area of triangle ACD = 0.5(9.2)(9.2)sin 38 = 26.05

Area of quad = 33.06 + 26.05 = 59.11 ≈ 59.1 m²

(e) AB = 9.2/cos38 = 11.67

Perimeter = 7.187 + 5.990 + 11.67 + 9.2 = 34.05 ≈ 34.1 m

[1]

[1]

[1]

[1]

[1]

[1] [1]

[1]

[1]

[1]

[1]

[1]

[1]

[1]

[1]

[1]

[1]

[1]

[1]

3(a)(i) 10625$))05.0(12

151(10000

$625.00

(a)(ii) 40.10439$)035.1(10000 12/15

$439.40

We use the method below

).2(55.446$

54.10446$)12/035.01(10000 15

pd

(a)(iii) 11250$))05.0(12

301(10000

2 Methods, we go with 2nd.

10.10898$)035.1(10000 12/30

03.10913$)12/035.01(10000 30

Andy Made the better choice

3(b)(i) hourly wage = $88 /10 = $8.80

weekly wage = $88 X 6 = $528

3(b)(ii) $594 - $528 = $66

$66/($8.80 x 150%) = 5

= 5hr

4(a)

4(b) C5 = 10, C6 = 15

4(c)(i) C15 = 15/2 (15 – 1)

= 105

(c)(ii) 3512

)1(

NN

N2 – N – 702 = 0

(N-27)(N+26) = 0

N = 27, -26 (rej)

4(c)(iii)

)(1

)2(2

1

)11(2

1

2

)1(1

shownN

NNN

NNNN

CC NN

[1]

[1]

[1]

[1]

[2]

[1]

[1]

[1]

[1]

[1]

[1]

[1]

[1]

[1]

[1]

[1]

5(a) h1260

2360

(b) from town A to B: k

360h

from town B to A: 15

360

kh

(c)

045045

)15)((12360)15(360

1215

360360

2

kk

kkkk

kk

(d)

4.53

)(423.8,42.53

25.9562

45

2

)450(44545

045045

2

2

rej

k

kk

6a(i) 90ABD (Rt Ang. In

Semicircle)

(ii) 32DBC (Alt Ang.)

(iii)

244

)9032(2

2 ABCAOC

(iv)

64

3232

32 BDA

BCEEBCCED

(v)

64

322

2

2

BCA

OACCOD

(b)

)(~

32

64

AAOFDEFC

FDOECF

FODCEF

[1]

[1]

[1]

[1]

[1]

[1]

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[1]

[1]

[1]

[1] [1]

[1]

[1] [1]

[1]

7a(i)

9.31

89.31

45

28tan 1BAC

(ii) mAC 532845 22

(iii) Pole Height = 45tan 40 = 37.75

≈37.8m

(iv)

5.35

46.35

53

75.37tan 1DCA

7(v)

2

21

2221

22

22

822

4.822

sin

45.25

2

28cos

06.6575.3753

73.5875.3745

m

BDCDCBDArea

DCBD

DCBDBDC

mDC

mBD

7(b) Area of minor segment

797.53163

32

60sin)8(2

1)8(

6

1 22

Area of sector =

75.163

16)8(

12

1 2

Shaded area = 2(16.75 – 5.797)

= 21.90 ≈ 21.9cm2

[1]

[1]

[1]

[1]

[1] [1]

[1]

[1]

[1]

[1]

[1]

8(a)(i) Total Volume

3

2222

201061929.201

)3)(4()45)(4(3

1

m

(ii) Total surface area

49.1882.138

1644

))4(()3)(4(2)5)(4(

)(2

2

2

or

rrhrl

Paint required

1113

44

tins

or 1513

60

tins

8(b)(i) Surface area of bowl

2

2

2

22

942

4.942

300)10(3

2

cm

cm

rr

(ii)Volume of bowl

3

33

2090

395.2094

)10(3

2

3

2

cm

r

(iii) Number of bowls needed

)(96000

395.2094929,061,201

395.2094061929.201

33

33

exactbowls

cmcm

cmm

[1]

[1]

[1]

[1] Gave marks as long

as they used 5s.f or more

in their calc

[1]

[1]

[1] [1]

[1]

[1]

[1]

[1]

9(a) p = 5/3, q = 6 --- [2]

(c) Axes/Origin unlabelled -1 mark

Equation not labelled -1 mark

Curve not smooth, curve hairy, not 2B pencil -1 mark

[3 if eqn drawn correctly]

(d) tangent drawn correctly --- [1]

gradient = 1.5 (Accept 1.3 ≤ gradient ≤ 1.7) --- [1]

(e) turning point = (2.73, -1.53) --- [1 mark for ordinate, 1 mark for abscissa]

(Accept 2.6 ≤ x ≤ 2.9, -1.5 ≤ y ≤ -1.6)

(f) 112

63 23

xxx

(Plot y = -1) --- [1]

x = 1.45, 3.75 (accept 1.4 ≤ x ≤ 1.5 and 3.6 ≤ x ≤ 3.8) --- [2]

10a) (i)(a)Median time = 19.7min

(Accept 19.5 to 20.0)

(b) 250 – 130 = 120 students

(accept 115 – 125)

(c) 26.75min (accept 26.5 – 27)

(d) Interquatile range = 23.25 - 16.5

= 6.75min (accept 6.0 – 7.5)

The curve will be shifted to the

right/lower and would be steeper

initially and at the end/gentler in the

middle.

(b)(ii)

Red

Blue

Green

1

6

1

3

1

2

1

21

3

1

6

Green

Blue

Red

1

2

1

31

6

Green

Blue

Red

Red

Blue

Green

1

6

1

3

1

2

a. 4

1

2

1

2

1

b. 36

25

6

5

6

5

c. 4

1

2

1

2

1

d. 9

5

3

2

3

21

[2]

[1]

[1]

[1]

[1]

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[2]

FUHUA SECONDARY SCHOOL E/NA - WordPress.com · Compound Interest Total amount = P r)n 100 (1...

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