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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
International General Certificate of Secondary Education
*5934015837*
0444/21
MATHEMATICS (US)
May/June 2012
Paper 2 (Extended)
1 hour 30 minutes
Candidates answer on the Question Paper.
Additional Materials:
Geometrical instruments
READ THESE INSTRUCTIONS FIRST
Write your Center number, candidate 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.
DO NOT WRITE IN ANY BARCODES.
Answer all questions.
CALCULATORS MUST NOT BE USED IN THIS PAPER.
All answers should be given in their simplest form.
If work is needed for any question it must be shown in the space provided.
The number of points is given in parentheses [ ] at the end of each question or part question.
The total of the points for this paper is 70.
This document consists of 15 printed pages and 1 blank page.
IB12 06_0444_21/5RP
© UCLES 2012
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2
Formula List
2
ax + bx + c = 0
For the equation
x=
_ b ± b2 _ 4ac
2a
Lateral surface area, A, of cylinder of radius r, height h.
A = 2πrh
Lateral surface area, A, of cone of radius r, sloping edge l.
A = πrl
Surface area, A, of sphere of radius r.
A = 4πr2
Volume, V, of pyramid, base area A, height h.
V=
Volume, V, of cone of radius r, height h.
V=
Volume, V, of sphere of radius r.
V=
1
3
Ah
1
3
4
3
πr2h
πr3
a
b
c
=
=
sin A sin B sin C
A
a2 = b2 + c2 – 2bc cos A
b
c
Area =
B
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a
C
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1
2
bc sin A
3
1
$1 = 0.619 pounds (£).
For
Examiner's
Use
The cost of a ticket to fly from New York to London is $300.
Work out the cost of this ticket in pounds.
Give your answer to the nearest pound.
2
Answer £
[2]
Answer(a)
[1]
Answer(b)
[1]
Answer
[2]
(a) Evaluate the value of 26.
(b) Work out 3–3 as a fraction.
3
Factor completely.
© UCLES 2012
15p2 + 24pt
0444/21/M/J/12
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4
4
For
Examiner's
Use
(2x + 1)2 + 7x O 3 = 4x2 + ax + b
Find the values of a and b.
Answer a =
Answer b =
5
[2]
P is the point (1, 4) and Q is the point (4, – 2).
T is the point on PQ so that PT : TQ = 2 : 1.
Find the co-ordinates of T.
You may use the grid below to help you.
Answer (
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,
) [2]
5
6
Simplify.
For
Examiner's
Use
(2 × 107) × (7 × 102)
Give your answer in scientific notation.
7
[2]
Answer y =
[2]
Solve the equation.
2
8
Answer
y O1=9
Leon scores the following marks in 5 tests.
8
4
8
y
9
His mean mark is 7.2.
Calculate the value of y.
Answer y =
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[2]
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6
9
r
3
For
Examiner's
Use
Find r when (5) = 125 .
Answer r =
[2]
10 Solve the system of linear equations.
x + 7y = 19
3x + 5y = 9
Answer x =
y=
[3]
5 9
11 Simplify 1 + .
6 10
Give your answer as a mixed number in its simplest form.
Answer
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[3]
7
12 An electrician repairs some machinery.
His total cost is a fixed amount of $40 plus $35 per hour.
For
Examiner's
Use
(a) Calculate the total cost when he works for 5 hours.
Answer(a) $
[1]
(b) (i) Find an expression, in terms of h, for the total cost, in dollars, when he works for h hours.
Answer(b)(i)
[1]
(ii) Find the value of h when the total cost is $390.
Answer(b)(ii) h =
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[1]
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8
13 (a) Find the slope of the line between (0, 2) and (2, 1).
For
Examiner's
Use
Answer(a)
[2]
(b) Write down the equation of the line passing through (0, 2) and (2, 1).
Answer(b)
[1]
Answer y =
[3]
14 y is inversely proportional to x2.
When x = 3, y = 2.
Find y when x = 5.
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9
15
For
Examiner's
Use
D
A
B
(a) The point C lies on AD and angle ABC = 67°.
Draw accurately the line BC.
[1]
(b) Using a straight edge and compass only, construct the perpendicular bisector of AB.
Show clearly all your construction arcs.
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[2]
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10
16
For
Examiner's
Use
y
7
6
5
4
3
2
1
–8
–7
–6
–5
–4
–3
–2
–1
0
x
1
2
3
4
5
6
7
–1
The region R contains points which satisfy the inequalities
y Y 1 x + 4,
2
y[3
and
x + y [ 6.
On the grid, label with the letter R the region which satisfies these inequalities.
You must shade the unwanted regions.
17 Solve for w.
c=
[3]
4 +w
w +3
Answer w =
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[4]
11
18
For
Examiner's
Use
y
NOT TO
SCALE
Q
0
x
P
l
The equation of the straight line, l, is y = 12 O 4x.
(a) Find the co-ordinates of P and Q.
Answer(a) P (
,
)
Q(
,
) [2]
(b) Find the equation of the line which is perpendicular to the line l and passes through the origin.
Answer(b)
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[2]
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12
19 (a)
For
Examiner's
Use
NOT TO
SCALE
10 cm
4 cm
The cone in the diagram has radius 4 cm and sloping edge 10 cm.
Show that the lateral surface area of the cone is 40π cm2.
Answer (a)
[1]
(b)
15 cm
10 cm
4 cm
4 cm
NOT TO
SCALE
The solid in the diagram is made up of a hemisphere, a cylinder and a cone, all of radius 4 cm.
The length of the cylinder is 15 cm.
The sloping edge of the cone is 10 cm.
The total surface area of the solid is kπ cm2.
Find the value of k.
Answer(b) k =
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[3]
13
20
S
For
Examiner's
Use
R
T
Q
t
O
P
p
O is the origin and OPQRST is a regular hexagon.
= p and
= t.
Find, in terms of p and t, in their simplest forms,
(a)
(b)
,
Answer(a)
=
[1]
Answer(b)
=
[2]
,
(c) the position vector of R.
Answer(c)
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[2]
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14
21
For
Examiner's
Use
R
NOT TO
SCALE
O
60°
P
5 cm
T
R and T are points on a circle, centre O, with radius 5 cm.
PR and PT are tangents to the circle and angle POT = 60°.
A thin rope of length l cm goes from P to R, around the major arc RT and then from T to P.
Explaining all your reasoning, show that l = 10 3 +
20π
3
.
Answer
[6]
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15
22 In this question, give all your answers as fractions.
For
Examiner's
Use
A box contains 3 red pencils, 2 blue pencils and 4 green pencils.
Raj chooses 2 pencils at random, without replacement.
Calculate the probability that
(a) they are both red,
Answer(a)
[2]
Answer(b)
[3]
Answer(c)
[3]
(b) they are both the same color,
(c) exactly one of the two pencils is green.
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BLANK PAGE
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© UCLES 2012
0444/21/M/J/12