1
HIHS Prelim 2011
Sec 4 Exp 5 N(A) Paper 1 [Turn over
2
HIHS Prelim 2011
Sec 4 Exp 5 N(A) Paper 1 [Turn over
3
HIHS Prelim 2011
Sec 4 Exp 5 N(A) Paper 1 [Turn over
Answer all questions.
1 (a) Find the fraction that is exactly between 11
5 and
11
6.
(b) Express %2
1105 as a fraction in its simplest form.
Ans: (a) ……………………….….……. [1]
(b)
……………………….….…….
[1]
2 Calculate
71.4
7
6)2.3(129
2
5.13
.
Give your answer correct to 4 decimal places.
Ans: ……………………….….……. [2]
3 Simplify 2
27
3
)( 36
3
5 y
x
xy
.
Ans: ……………………….….……. [2]
4
HIHS Prelim 2011
Sec 4 Exp 5 N(A) Paper 1 [Turn over
4 In the construction of a ship, an alloy of copper, iron and titanium is used.
Every 130 kg of iron is mixed with 20 kg of copper, and every 100 kg of iron is mixed with 15 kg of
titanium. Assuming that the ratio of copper to iron to titanium in the alloy is represented by the
ratio x : y : z, find the ratio x : y : z.
Ans: ……… : ……… : ……… [2]
5 If the height of a triangle is decreased by 20% while its area remained unchanged, find the percentage
change in the length of the base.
Ans: ……………………………% [2]
5
HIHS Prelim 2011
Sec 4 Exp 5 N(A) Paper 1 [Turn over
6 List the integer values of such that 53
154
x.
Ans: x = ………………………… [3]
7 It is given that 22 532300 , when expressed as a product of its prime factors.
(a) Express 180 as a product of its prime factors.
(b) Find the largest integer that is a factor of both 180 and 300.
(c) Find the smallest integer value of x such that the lowest common multiple of 180, 300 and x
is 1800.
Ans: (a) ……………………………. [1]
(b)
……….……………….........
[1]
(c)
x = ……………………….…
[1]
6
HIHS Prelim 2011
Sec 4 Exp 5 N(A) Paper 1 [Turn over
8 Tap A takes 5 minutes to fill up a tank. It takes 4 minutes for tap A and tap B to fill up the same tank
together. Calculate the amount of time it would take for tap B to fill up the tank by itself.
Ans: ...…………..……………min [3]
9 (a) Shade in the diagram below the region representing )'(' ABB .
(b) Given that
x : x is an integer and 4 < x < 15}
P = { x : x is an even number}
Q = { x : x is a prime number }
Find
(i) )'( QPn ,
(ii) )'( QP .
[1]
(b)(i) …………..…………………. [1]
(b)(ii)
…………..………………….
[1]
A
ε
B
Ans: (a)
7
HIHS Prelim 2011
Sec 4 Exp 5 N(A) Paper 1 [Turn over
10 The diagram shows a circular disc, with centre O. An arrow is attached to the disc and pointed initially
to N.
A fair die is thrown and if 1, 2, 3, 4 or 5 is shown, the arrow is rotated 90° clockwise, otherwise, the
arrow is rotated 90° anti-clockwise.
Find the probability that the arrow is pointing to
(a) position E after one throw,
(b) position N after two throws.
(c) position S after three throws.
Ans: (a) ……………………….….……. [1]
(b)
……………………….….…….
[1]
(c)
…..……………………….…
[1]
11 A microchip is made up of transistors printed on one side.
Each transistor is a flat square of side 51 nanometres.
(a) Express 51 nanometres in metres.
(b) Find the surface area of each transistor in square meters.
(c) The microchip is in the shape of a square of side 0.102 cm.
Assuming that the surface of the microchip is completely filled with transistors, calculate the total
number of transistors on the microchip.
Express all your answers in standard form.
Ans: (a) ……………………….….…m [1]
(b)
..……………………….....m2
[1]
(c)
..………………………….…
[2]
N
E W O
S
8
HIHS Prelim 2011
Sec 4 Exp 5 N(A) Paper 1 [Turn over
12 The diagram below shows a right-angle triangle ABC.
(a) Using compasses and ruler only, construct the
(i) perpendicular bisector of AB,
(ii) bisector of angle ABC.
(b) (i) State the radius of the circle passing through A, B and C.
(ii) Explain your reason for the answer to part (b)(i).
Ans: (a)(i), (a)(ii)
Ans: (b)(i) …………..……………… cm [1]
(b)(ii)………………………………………………………………………………………...
………………………………………………………………………………………………
………………………………………………………………………………………………
[1]
A B
C
[2]
9
HIHS Prelim 2011
Sec 4 Exp 5 N(A) Paper 1 [Turn over
13 The prices of tickets for a KPOP concert is given below.
Child - $40; Adult - $80; Senior citizen - $65.
(a) Represent the information as a column matrix P.
(b) The number of tickets sold on one weekend can be represented by the matrix
Sunday
Saturday
30200315
25150200
Citizen
SeniorAdultChildren
N
Evalute the product NP.
(c) Explain what the matrix NP represents.
Ans: (a) ………..……………………. [1]
(b)
NP =…..……………….........
[2]
(c) …………………………………………………………………………………………..
..……….……………………………….……………………………………………………
[1]
10
HIHS Prelim 2011
Sec 4 Exp 5 N(A) Paper 1 [Turn over
14 (a) Simplify )1(
3
)1(3
2
xx
.
(b) Make v the subject of the formula
y
xvyx
2
.
Ans: (a) ……………………………. [2]
(b)
v = …………………….........
[2]
15 (a) Factorise 672 2 xx completely.
(b) Using your result from above, solve the equation 062118 2 yy .
Ans: (a) ……………………………. [2]
(b)
y = .………………...…….
[2]
11
HIHS Prelim 2011
Sec 4 Exp 5 N(A) Paper 1 [Turn over
16 The diagram shows the speed-time graph of a car.
(a) Calculate the distance travelled by the car when it was travelling at constant speed.
(b) Calculate the deceleration of the car at t = 37 min.
(c) Calculate the value of x if the average speed of the car in the last 25 minutes of the journey
was 53 km/h.
Ans: (a) .…………………………km [1]
(b)
……….………………km/h2
[1]
(c)
x = …………………...km/h
[2]
100 75 50 time (min)
40
x
100
Speed km/h
12
HIHS Prelim 2011
Sec 4 Exp 5 N(A) Paper 1 [Turn over
17 The marks obtained by the pupils in a mathematics test in two Secondary Three classes are shown in
the tables below.
Class A
Marks 45 – 49 50 – 54 55 – 59 60 – 64 65 – 69
No. of
pupils 2 3 8 23 6
Class B
Mean = 58 marks
Standard Deviation = 4 marks
(a) For Class A, calculate
(i) the mean,
(ii) the standard deviation.
(b) Compare and comment on the results of the two classes.
Ans: (a) ……………………………. [1]
(b)
……………………….........
[2]
(b) ..……….……………………………….………………………………………………...
..……….…………………………………………………………………………………..
[2]
13
HIHS Prelim 2011
Sec 4 Exp 5 N(A) Paper 1 [Turn over
18 (a) (i) Express 322 xx in the form bax 2)( , where a and b are integers.
(ii) Hence state the coordinates of the turning point of 322 xxy .
Indicate if the turning point is a maximum or minimum point.
(b) The point (1,1) has been marked on the each diagram on the answer space.
On these diagrams, sketch the graphs of
(i) 3
1
yx ,
(ii) 13 xy .
Ans: (a)(i) ………………….……………. [1]
(a)(ii)
( .…. , ..… ) ;…..….......point
[2]
(b) (i)
(b) (ii)
x
y
x
y
[2]
14
HIHS Prelim 2011
Sec 4 Exp 5 N(A) Paper 1 [Turn over
19 A series of diagrams of shaded and unshaded squares is shown below.
Diagram Number of shaded squares
(S)
Number of unshaded squares
(U)
Total number of squares (T)
1 1 0 1
2 6 3 9
3 15 10 25
4 28 21 49
(a) Find the number of shaded squares in Diagram 5.
(b) Write down, in terms of n, the total number of squares in the nth diagram.
(c) Calculate the total number of squares in Diagram 13.
(d) Write down the equation connecting S, U and T.
(e) Is it possible for a diagram to have a total of 2024 squares?
Explain your answer.
Ans: (a) ……………………………... [1]
(b)
…………...……………........
[1]
(c)
…………...……………........
[1]
(d)
..…………………………….
[1]
(e) ………..……….…………………………………………………………………………
……………..……….………………………………………………………………………
[1]
v v v v
v v
v v v
v v v
v v v v
v v
v v v
v v v
v v v
v v v
v v v
v v v
v v v
v v v
v v v
v v v
v v v
v v v
v v v
v v v
v v v
Diagram 1 Diagram 2 Diagram 3 Diagram 4
15
HIHS Prelim 2011
Sec 4 Exp 5 N(A) Paper 1 [Turn over
20 In the diagram, the equation of the line AC is 03023 xy .
The length of the line BC is 10 units.
(a) Find the coordinates of A and C.
(b) State the coordinates of B.
(c) Find the area of triangle ABC.
(d) Find the length of the perpendicular from B to AC.
Ans: (a) A = ( ..… , ….. ), C = ( ….. , ..… ) [2]
(b)
B = ( ..… , ..… )
[1]
(c)
…………………………….units2
[1]
(d)
…………………………….units
[2]
y
x O B
A
C
16
HIHS Prelim 2011
Sec 4 Exp 5 N(A) Paper 1 [Turn over
21 In the diagram, ACE is a triangle and BCDF is a parallelogram.
AB = x cm, BC = 40 cm, CD = 10 cm and DE = 20 cm.
(a) Prove that triangle ABF is similar to triangle FDE.
(b) Find x.
(c) Find BCDF
ABF
ramparallelog of area
triangleof area.
Ans: (a) ...…….……………………………………………………………………………..
………………………………………………………………………………………………
………………………………………………………………………………………………
[2]
(b)
x = …………………….......
[1]
(c)
……….……………….........
[2]
40
10 20
x
F
E D
A
B
C
17
HIHS Prelim 2011
Sec 4 Exp 5 N(A) Paper 1 [Turn over
22 In the diagram, the points A, B, C, D, and E all lie on the circumference of a circle.
DE is parallel to CB.
Given that angle ACE = 40°, angle CBE = 65° and angle CED = 60°,find
(a) angle ABE,
(b) angle ACB,
(c) angle BEC,
(d) angle AED.
Ans: (a) ∠ABE =……………………° [1]
(b)
∠ACB =…………...………°
[1]
(c)
∠BEC =………………...…°
[1]
(d)
∠AED =……………...……°
[2]
-------------------------- End of Paper 1--------------------------
A
B
C
D
E
65°
60°
40°
18
HIHS Prelim 2011
Sec 4 Exp 5 N(A) Paper 1 [Turn over
Answers
Question Answer
1(a)
1(b)
200
111
2 –0.1145
3
2
78 yx
4 40 : 260 : 39
5 Percentage increase = 25%
6 x = -1, 0, 1
7(a) 7(b) 60
7(c) 8
8 x = 20 min
9(b)(i) 5
9(b)(ii) {9}
10(a)
10(b)
18
5
10(c) 0
11(a) 11(b) 1510601.2
11(c) 8104
13(a)
13(b)
30550
21625
13(c) It represent the amount collected from the sale of tickets on Saturday and Sunday respectively.
14(a)
)1(3
11
x
14(b)
x
yxyv
)(
15(a)
19
HIHS Prelim 2011
Sec 4 Exp 5 N(A) Paper 1 [Turn over
15(b)
16(a)
16(b)
16(c) 66 km/h
17(a)(i) 60.3 marks or marks
17(a)(ii) 4.84 marks
17(b) Class A performed better as the mean marks was higher while the marks of the students had a lower spread in class B.
18(a)(i) 18(a)(ii) (1 , 2)
minimum point
19(a) 45
19(b) 19(c) 625
19(d) S + U = T
19(e) It is not possible as the number of squares should be a square term.
20(a) C = (-15 , 0)
20(b) B = (-5 , 0)
20(c) Area =
20(d) 5.55
21(a) ∠FAB = ∠EFD (corresponding angles) ∠AFB = ∠FED (corresponding angles, FB // DC) ΔABF = ΔFDE (AA property)
21(b) x = 20
21(c) Ratio =
22(a) ∠ABE = ∠ACE = 40o (∠s in the same segment)
22(b) ∠ACB = 60 o – 40o = 20o (alternate angles)
22(c) 180 o – 65 o – 60o = 55o (∠s in a triangle)
22(d) 135o
PRELIMINARY EXAMINATION 2011 SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC)
MATHEMATICS 4016/02 Paper 2
Name : _________________________ Date : 4 Aug 2011 Register No : _________________________ Duration : 2 h 30 min Class : _________________________
Additional Materials needed: 6 sheets of writing papers 1 sheet of graph paper
Instructions to Candidates
Write your index number and name on all the work you hand in. Write in dark blue or black pen. 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 . The number of marks is given in brackets [ ] at the end of each question or part question. The total marks for this paper is 100.
Setter: Mrs Chang Poh Joo
This paper consists of 12 printed pages, inclusive of this cover page.
HOLY INNOCENTS’ HIGH SCHOOL
2
Holy Innocents’ High School Preliminary Examination 2011
Secondary Four Express / Five Normal (Academic) Mathematics Paper 2
Mathematical Formulae
Compound interest
Total amount
nr
P
1001
Geometry and Measurement
Curved surface area of a cone rl
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 r , where is in radians
Sector area 2
2
1r , where is in radians
Trigonometry
C
c
B
b
A
a
sinsinsin
Abccba cos2222
Statistics
Mean
f
fx
Standard deviation
22
f
fx
f
fx
3
Holy Innocents’ High School Preliminary Examination 2011
Secondary Four Express / Five Normal (Academic) Mathematics Paper 2
Answer all the questions
1 The diagram shows a park ABCDE.
Given that angle BAE = angle BEC = 90o, angle BCE = 47o, AE = 30 m, BE = 52 m,
CD = 98 m.
(a) Calculate
(i) BC, [2]
(ii) the perimeter of the park. [3]
(b) C is due south of E.
Calculate the bearing of A from B. [3]
2 (a) Amos changed $3 600 Singapore dollars (S$) into Australian dollars (A$) for
his trip to Perth. Upon returning, he has A$68 left.
Given that the exchange rate is A$1 to S$1.25, calculate the amount he spent
for this trip, in Singapore dollars. [2]
(b) The cash price of a sofa set is $4 380. Basil paid for it by hire purchase, with downpayment of 15% and the remaining
amount over 18 equal monthly instalments, with interest charged at a flat rate of
5% per annum.
Find
(i) the interest charged by the hire purchase scheme, [2]
(ii) the amount of each instalment. [2]
(c) Cathy invested a sum of money in a bank at 6 % per annum compounded every half-yearly.
She received an interest of $11 798.38 at the end of 3 years.
Calculate the sum of money invested. [3]
A
C
B
D
E
30 52
98
47o 25o
4
Holy Innocents’ High School Preliminary Examination 2011
Secondary Four Express / Five Normal (Academic) Mathematics Paper 2
3 (a) If x – y = 2 and x + y = – 2, find the value of 2222 2 yxyxyx . [2]
(b) Given that 4
32
yx
xy, find the value of
y
x. [2]
(c) A solid cone is cut into 2 parts, A and B, by a plane parallel to the base.
The heights of A and B are in the ratio 2 : 3. The volume of cone A is V cm3.
(i) Express the total volume of A and B in terms of V. [1]
(ii) If the volume of B is 245 cm3, calculate the volume of A. [2] (iii) If the base area of A is 30 cm2, calculate the base area of the
original cone. [2]
A
B
5
Holy Innocents’ High School Preliminary Examination 2011
Secondary Four Express / Five Normal (Academic) Mathematics Paper 2
4 In the diagram, OABC is a parallelogram.
D is the mid-point of BC.
It is given that
OA = a and
OC = c.
E is the point on OC such that 5OE = 2OC.
F is the point on OD such that
FDOF2
1.
(a) Express, as simply as possible, in terms of a and/or c,
(i)
EC , [1]
(ii)
OD , [1]
(iii)
OF [1]
(b) Show that
FEAE 6 . [3]
(c) Given that the coordinates of F is (4, 2) and
12
3AE .
(i) Calculate
AE . [1]
(ii) Find the coordinates of E. [2]
(iii) Find the value of t, given that the vector
t
5.4 is parallel to
AE . [2]
A
O
B
C
F
E
a
c
D
6
Holy Innocents’ High School Preliminary Examination 2011
Secondary Four Express / Five Normal (Academic) Mathematics Paper 2
5 (a) The diagram shows part of a regular polygon ABCDEF… , which has nine sides.
BC and ED are produced to meet at P.
(i) Show that angle PDC = 40o. [1]
Calculate
(ii) angle DCE, [1]
(iii) angle BCE, [1]
(iv) angle BEF. [1]
(b) GHJK is a quadrilateral. (i) Angle HGK= u o, angle GHJ= v o.
If GHJK is a parallelogram, write down the relationship between u and v.
[1]
(ii) Angle GJK= x o, angle JGK= y o.
If GHJK is a rhombus, write down the relationship between x and y.
[1]
(c) In triangle PQR, PQ = PR.
QX bisects angle PQR and RY bisects angle QRP.
Prove that triangles PQX and PRY are congruent. [3]
A
B
C
D
E
F
P
O
P
Y
Q
X R
7
Holy Innocents’ High School Preliminary Examination 2011
Secondary Four Express / Five Normal (Academic) Mathematics Paper 2
6 The Adventure Society chartered an air-conditioned bus for $1500 to take a group of x
members to Malaysia for a trekking trip.
It was agreed that each member of the group would pay an equal share of this transport
fee.
(a) Write down an expression, in terms of x, for the amount of transport fee each member of the group had to pay. [1]
On the day of departure, three members of the group could not make it for the trip.
The Adventure Society decided that it would contribute $140 from its funds and that the
balance of the transport fee was to be shared equally by the remaining members.
(b) Write down an expression, in terms of x, for the transport fee that each remaining
member had to pay after the three members had withdrawn from the trip. [1]
(c) If each of the remaining members had to pay an additional $6 in order to cover the
transport fee, form an equation in x and show that it reduces to
3x2 + 61x – 2250 = 0. [3]
(d) Solve the equation 3x2 + 61x – 2250 = 0, giving the answers correct to three decimal places. [3]
(e) Hence find the transport fee that each member had to pay if all the members were present for the trip. [1]
8
Holy Innocents’ High School Preliminary Examination 2011
Secondary Four Express / Five Normal (Academic) Mathematics Paper 2
7. The diagram below shows four points A, B, C and D on a piece of horizontal land.
It is given that AB = 22 m, AD = 33 m, BC = 24 m, angle BDC = 38o and
angle CBD = 54o.
Calculate
(a) BD, [3]
(b) angle .ABD [4]
(c) A tower TB stands vertically at B.
Given that the angle of elevation of T from A is 30o, find
(i) the height of the tower. [2]
(ii) the angle of depression of D from T. [2]
A
B
C
22
54o
D
33
24
38o
9
Holy Innocents’ High School Preliminary Examination 2011
Secondary Four Express / Five Normal (Academic) Mathematics Paper 2
8 A cylindrical container with radius 30 cm and length 80 cm is partially filled with water.
Diagram I shows the cross-section of the container where the shaded area represents the
area in contact with water.
Angle AOB = 2.8 radians.
Diagram II shows the side view of the container.
(a) Find the area of the shaded region in Diagram I. [3]
(b) Find the volume of water in the cylindrical container. [1]
(c) Find the total surface area of container that is in contact with the water. [4]
The major sector AOBP in Diagram I is used to make a cone by joining
the edges OA and OB.
(d) Calculate the radius of the base of the cone. [2]
(e) Find the volume of the cone. [2]
A
O
B
a
B
2.8 rad 30 30
Diagram I
A B
O
Diagram II
80 cm
P
Q
10
Holy Innocents’ High School Preliminary Examination 2011
Secondary Four Express / Five Normal (Academic) Mathematics Paper 2
9 Answer the whole of this question on a sheet of graph paper.
In a particular week, a tailor makes a profit of $y when he produces x shirts, where the
variables x and y are connected by the equation
xxy 10020310
1.
The table below shows the profit the tailor makes when he produces different number of
shirts.
(a) Suggest a reason for y = –200 when x = 0. [1]
(b) Calculate the value of p. [1]
(c) Using a scale of 2 cm to represent 10 shirts, draw a horizontal axis for 0 ≤ x ≤ 80.
Using a scale of 2 cm to represent $100, draw a vertical axis for –200 ≤ y ≤ 700.
On your axes, plot the points given in the table and join them with a
smooth curve. [3]
(d) Use your graph to estimate
(i) the profit made when 25 shirts are produced. [1]
(ii) the maximum possible profit of the tailor in a week, and the
corresponding profit per shirt when the profit is maximum. [2]
(iii) the gradient of the curve at the point where the number of shirts
produced is 40. [2]
(e) By drawing a suitable straight line, find the two values of x for which the average
profit per shirt is $9. [2]
Number of
shirts (x) 0 10 20 30 40 50 60 70 80
Profit ($y) –200 90 320 490 600 650 640 570 p
11
Holy Innocents’ High School Preliminary Examination 2011
Secondary Four Express / Five Normal (Academic) Mathematics Paper 2
Cum
ula
tive
Fre
quen
cy
20 40 60 80 100
200
400
600
800
1000
0
Wages
10 The cumulative frequency graph shows the distribution of weekly wages of 800 workers
in Company A.
(a) Find
(i) the median wage, [1]
(ii) the interquartile range, [2]
(iii) the thirtieth percentile wage. [1]
(b) 15% of the workers earn more than $w. Find w. [1]
(c) If two workers are selected at random, find the probability that one worker
selected earns not more than $60 and the other earns more than $80. [2]
(d) If the company decides to increase the wages of each of the workers by 10%,
describe how the cumulative frequency curve will differ from the given curve.
[1]
12
Holy Innocents’ High School Preliminary Examination 2011
Secondary Four Express / Five Normal (Academic) Mathematics Paper 2
(e) The weekly wages of 800 people in Company C is represented by the box and
whisker diagram below.
Wages
Compare the wages of the workers from Company A and C in two different ways.
[2]
~~ End of Paper 2 ~~
20 40 60 80 100 120
13
Holy Innocents’ High School Preliminary Examination 2011
Secondary Four Express / Five Normal (Academic) Mathematics Paper 2
HIHS Prelim Exam 2011
Sec 4 Express Mathematics Paper 2
1a (i)
1a (ii)
1b
2a
2b(i)
2b(ii)
2c
3a
3b
3c(i)
3c(ii)
3c(iii)
4a(i)
4a(ii)
4a (iii)
4b
71.1 m
330 m
305.2o
S$3 515
$279.23
$222.35
$60 800.00
or $60 816.39
– 16
5
V8
125
16.8 cm3
187.5 cm2
c5
3
ca 2
1
ca3
1
6
1
cac
OEFOFE
5
2
6
1
3
1
ca15
1
6
1
ca
OEAOAE
5
2
)15
1
6
1(6 ca
FE6
FEAE 6
4c(i)
4c(ii)
4c(iii)
5a(ii)
5a(iii)
5a(iv)
5b(i)
5b(ii)
5c
6a
6b
6d
6e
7a
7b
7c(i)
7c(ii)
8a
8b
8c
8d
8e
9a
9b
9d(i)
9d(ii)
9d(iii)
9e
12.4 units
E = (4.5, 0)
t = –18
20o
120o
100o
u + v = 180
x = y
RPYQPX (common angle) [1 m]
PRYPQX ( PRQPQR are
base angles of isosceles triangle, base
angle bisected) [1 m]
PQ = PR (given)
∆PQX is congruent to ∆PRY (ASA)
[B1 for length & case]
x
50
3
1360
x
x = 19.046 or x = – 39.379 (rejected)
$78.76 or $78.95
39.0 m
57.8o
12.7 m
18.1o
1720 cm2
137 000 cm3
11 800 cm2
16.6 cm
7230 cm3
starting cost (rental of machine,
materials cost etc)
440
$410
profit = $660
profit per shirt = 45.12$53
660
gradient = 8 ± 1
x = 10 ± 0.5 or x = 67 ± 0.5
14
Holy Innocents’ High School Preliminary Examination 2011
Secondary Four Express / Five Normal (Academic) Mathematics Paper 2
10a(i)
10a(ii)
10a(iii)
10b
10c
10d
10e
Median = $40
Q1 = 24, Q3 = 55, IQR = $31
P30 = $27
w = $62
799
66
The cumulative frequency curve will be less steep.
[Cumulative frequency curve will be stretched from x = 0 to x = 110.
i.e. cumulative frequency will reach 800 when wage = $110.]
Greater median for Company C. ($52)
Greater spread for Company C (IQR = 38)