0580 w10 QP 41
0580 w10 QP 41
0580 w10 QP 41
w
ap
eP
e
tr
.X
w
om
.c
s
er
*7157806085*
0580/41
MATHEMATICS
October/November 2010
Paper 4 (Extended)
2 hours 30 minutes
Candidates answer on the Question Paper.
Additional Materials:
Electronic calculator
Mathematical tables (optional)
Geometrical instruments
Tracing paper (optional)
[Turn over
2
1
(a) In 2008 the total number of tickets sold for an athletics meeting was 3136.
The ratio child tickets sold : adult tickets sold = 17 : 32.
For
Examiner's
Use
Answer(a)(i)
[2]
(ii) Child tickets cost $2 each and adult tickets cost $4.50 each.
Show that the total amount received from the sale of the tickets in 2008 was $11 392.
Answer(a)(ii)
[2]
(b) In 2009 the amount received from the sale of tickets for the athletics meeting was $12 748.
Calculate the percentage increase in the amount received from 2008 to 2009.
Answer(b)
[3]
(c) In 2008 the amount of $11 392 was 28% more than the amount received in 2007.
Calculate how much was received in 2007.
Answer(c) $
UCLES 2010
0580/41/O/N/10
[3]
3
2
(a)
For
Examiner's
Use
y
5
4
3
2
A
1
5
1
2
3
4
5
[2]
(ii) Draw the image when triangle A is rotated through 90U anticlockwise about the origin.
Label the image C.
[2]
(iii) Describe fully the single transformation which maps triangle B onto triangle C.
Answer(a)(iii)
[2]
0 1
(b) Rotation through 90U anticlockwise about the origin is represented by the matrix M =
.
1 0
(i) Find M1, the inverse of matrix M.
Answer(b)(i) M =
[2]
(ii) Describe fully the single transformation represented by the matrix M1.
Answer(b)(ii)
UCLES 2010
[2]
0580/41/O/N/10
[Turn over
4
3
For
Examiner's
Use
Wall
NOT TO
SCALE
x
Enclosure
[2]
(b) Factorise completely 72x 2x2.
Answer(b)
[2]
10
310
520
15
20
25
30
550
360
35
[3]
(d) Draw the graph of A = 72x 2x2 for 0 Y x Y 35 on the grid opposite.
UCLES 2010
0580/41/O/N/10
5
A
For
Examiner's
Use
700
600
500
400
300
200
100
10
15
20
25
30
35
[4]
or x =
[2]
m2
[1]
Answer(f)
UCLES 2010
0580/41/O/N/10
[2]
[Turn over
6
4
For
Examiner's
Use
NOT TO
SCALE
4m
1.5 m
2m
Answer(a)
m2
[6]
[4]
UCLES 2010
0580/41/O/N/10
7
(ii)
For
Examiner's
Use
NOT TO
SCALE
0.5 m
Answer(b)(ii)
[3]
litres
[1]
[2]
Answer(c)(i)
(ii) The water drains from the tank at a rate of 1800 litres per minute.
Calculate the time, in minutes and seconds, taken to empty the tank.
Answer(c)(ii)
UCLES 2010
0580/41/O/N/10
min
[Turn over
8
5
The cumulative frequency table shows the distribution of heights, h centimetres, of 200 students.
For
Examiner's
Use
Height (h cm)
Cumulative frequency
10
50
95
115
145
180
200
(a) Draw a cumulative frequency diagram to show the information in the table.
200
160
120
Cumulative
frequency
80
40
0
130
140
150
160
170
180
190
Height (h cm)
[4]
(b) Use your diagram to find
(i) the median,
Answer(b)(i)
cm
[1]
Answer(b)(ii)
cm
[1]
Answer(b)(iii)
cm
[1]
UCLES 2010
0580/41/O/N/10
[1]
9
(ii) One of the 200 students is chosen at random and then a second student is chosen at random
from the remaining students.
For
Examiner's
Use
Calculate the probability that one has a height greater than 170 cm and the other has a
height of 140 cm or less.
Give your answer as a fraction.
Answer(c)(ii)
[3]
(d) (i) Complete this frequency table which shows the distribution of the heights of the 200
students.
Height (h cm)
Frequency
10
40
45
20
[2]
(ii) Complete this histogram to show the distribution of the heights of the 200 students.
6
Frequency
3
density
0
130
140
150
160
170
180
190
Height (h cm)
[3]
UCLES 2010
0580/41/O/N/10
[Turn over
10
6
(a)
For
Examiner's
Use
A
P
19.5 cm
16.5 cm
11 cm
NOT TO
SCALE
Answer(a)(i) PQ =
cm [2]
Answer(a)(ii) BC =
cm [3]
UCLES 2010
0580/41/O/N/10
[2]
11
(iv) The toy boat is mathematically similar to a real boat.
The length of the real boat is 32 times the length of the toy boat.
The fuel tank in the toy boat holds 0.02 litres of diesel.
For
Examiner's
Use
Calculate how many litres of diesel the fuel tank of the real boat holds.
litres
Answer(a)(iv)
[2]
(b)
E
F
32
143
NOT TO
SCALE
67 m
105 m
70
D
The diagram shows a field DEFG, in the shape of a quadrilateral, with a footpath along the
diagonal DF.
DF = 105 m and FG = 67 m.
Angle EDF = 70U, angle EFD = 32U and angle DFG = 143U.
(i) Calculate DG.
Answer(b)(i) DG =
[4]
Answer(b)(ii) EF =
[4]
UCLES 2010
0580/41/O/N/10
[Turn over
12
7
(a)
For
Examiner's
Use
A
y
NOT TO
SCALE
B
62
w
O
z
C
because
[2]
x=
because
[2]
y=
because
[2]
z=
because
[2]
(b)
y
B (4,4)
NOT TO
SCALE
A (2,1)
x
as a column vector.
Answer(b)(i)
UCLES 2010
0580/41/O/N/10
[1]
13
(ii)
0
= .
7
Work out
For
Examiner's
Use
as a column vector.
Answer(b)(ii)
[2]
(c)
R
NOT TO
SCALE
r
P
Q
t
= r and
= t.
P is on RT such that RP : PT = 2 : 1.
2
Q is on OT such that OQ = OT.
3
Write the following in terms of r and/or t.
Simplify your answers where possible.
(i)
Answer(c)(i)
[1]
Answer(c)(ii)
[2]
Answer(c)(iii)
[2]
(ii)
(iii)
(iv) Write down two conclusions you can make about the line segment QP.
Answer(c)(iv)
[2]
UCLES 2010
0580/41/O/N/10
[Turn over
14
8
g(x) = x2
f(x) = 2x 1
(a)
For
Examiner's
Use
Work out
(i) f(2),
Answer(a)(i)
[1]
Answer(a)(ii)
[1]
Answer(a)(iii) ff(x) =
[2]
Answer(a)(iv) f 1(x) =
[2]
(ii) g( 2),
or x =
Answer(a)(v) x =
[4]
(ii) y when x =
UCLES 2010
1
2
Answer(b)(i)
[2]
Answer(b)(ii) y =
[1]
0580/41/O/N/10
15
9
(a) The first five terms P1, P2, P3, P4 and P5 of a sequence are given below.
1
= 1 = P1
1+2
= 3 = P2
1+2+3
= 6 = P3
1+2+3+4
= 10 = P4
1+2+3+4+5
= 15 = P5
For
Examiner's
Use
(i) Write down the next term, P6, in the sequence 1, 3, 6, 10, 15
Answer(a)(i)
[1]
1
2
n(n + 1).
Answer(a)(iii)
[1]
Answer(a)(iv)
[1]
Answer(a)(v)
[1]
(vi) Use your answers to parts (iv) and (v) to find the sum of the numbers less than 150 which
are not multiples of 3.
Answer(a)(vi)
[1]
UCLES 2010
0580/41/O/N/10
[Turn over
16
(b) The first five terms, S1, S2, S3, S4 and S5 of a different sequence are given below.
(1 1)
= 1 = S1
(1 2) + (2 1)
= 4 = S2
(1 3) + (2 2) + (3 1)
= 10 = S3
(1 4) + (2 3) + (3 2) + (4 1)
= 20 = S4
(1 5) + (2 4) + (3 3) + (4 2) + (5 1)
= 35 = S5
For
Examiner's
Use
(i) Work out the next term, S6, in the sequence 1, 4, 10, 20, 35
Answer(b)(i)
[2]
1
6
Answer(b)(iii)
[1]
[1]
(d) Show by algebra that Sn Sn 1 = Pn .
[Pn =
1
2
n(n + 1)]
Answer(d)
[3]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
UCLES 2010
0580/41/O/N/10