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1380/3H
Edexcel GCSE
Mathematics (Linear) - 1380
Paper 3 (Non-Calculator)
Higher Tier
Monday 18 May 2009 - Afternoon
Time: 1 hour 45 minutes
Materials required [01' examination
Ruler graduated in centimetres and
millimetres, protractor, compasses,
pen, HB pencil, eraser.
Tracing paper may be used
Items included with question papel's
Nil
BLANK PAGE
Instructions to Candidates
In the boxes above, write your centre number, candidate number, your surname, initials and sil:,'Tlature,
Check that you have the con'ect question paper.
Answer ALL the questions. Write your answers in the spaces provided in this question paper.
You must NOT write on the formulae page.
Anything you write on the formulae Ilage will gain NO credit.
If you need more space to complete your answer to any question, use additional answer sheets.
Information for Candidates
The marks for individual questions and the parts of questions are shown in round brackets: e.g. (2). There are 26 questions in this question paper. The total mark for this paper is 100. There are 24 pages in this question paper. Any blank pages are indicated. Calculators must not be used. Advice to Candidates
Show all stages in any calculations. Work steadily through the paper. Do not spend too long on one question. If you cannot answer a question, leave it and attempt the next one. Retum at the end to those you have left out. Turn over
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GCSE Mathematics (Linear) 1380
Answer ALL TWENTY SIX questions. Fonnulae: Higher Tier
Write your answers in the spaces provided. You must not write on this formulae page.
Anything you write on this formulae I)age will gain NO credit
You must write down all stages in your working. You must NOT use a calculator. Volume of a prism
=
area of cross section
length
1.
The
day
table gives some information about how 100 children travelled to school one
Car
Walk
2_~
Boy
15
Girl
12­
Total
37
S
33
Other
Total
14
54
16
i+b
3_o
100
(a) Complete the two-way table.
Volume of sphere
Volume of cone
Surface area of sphere = 4n:r2
Curved surface area of cone = rr:rl
(3)
One of the children is picked at random.
(b) Write down the probability that this child walked to school that day.
The Quadratic Equation
In any triangle ABC
The solutions ofax 2 + bx +
C
where a
L----c:------"
Sine Rule
a
B
* 0, are given by
0
2.
(a) Simplify 4x
3y
2x
2a
(2)
Compasses cost c pence each, Rulers cost r pence each. h
sinB
(b) Write down an expression for the total cost, in pence, of2 compasses and 4 rulers.
Cosine Rule
Area of triangle =~ab
2
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3.
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(a) Complete the table of values for y = 4x ­ 3
4. P = 4k-IO
P = 50
I
x
Y
I
-2
I
-II
I
-1
1­
-
I
0
-3
I
1
I
I
2
5
I
3
I
b
(a) Work out the value of k.
9
\
'5C~
::
(2)
(b) On the grid, draw the graph of y = 4x ­ 3, for values of x from -2 to 3
(2)
y
y
=
4n - 3d
n=2 d=5 (b) Work out the value of y.
::; 3
l
x
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5.
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6.
y
Diagram NOT
accurately drawn
4x+ I
x
x
2x + 12
The diagram shows a rectangle. All the measurements are in centimetres. 4x + I
(a) Explain why
Rotate the shaded shape
clockwise about
(b) Solve
point O.
4x + I
~
2x
12
2x + 12
(2)
f'
~
x
(2)
(c) Use your answer to part (b) to work out the perimeter of the rectangle.
x
+(
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7.
Use the information that
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9.
322
x
Here are the plan and front elevation of a solid shape.
48 = 15456 to find the value of (a)
3.22
x
4.8
(1)
Plan
(b)
0.322
x
L~
Front Elevation
0.48
(a) On the grid below, draw the side elevation of the solid shape
(1)
(c)
15456 -:- 4.8
2
~'*
8.
2X2
(1)
= 72
of x
(a)
f
t
::3
(2)
.x.. ::;
(b) In the space below, draw a sketch of the solid shape
(2)
(b) Express 72 as a product of its prime factors.
L
(2)
3
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10. There are 40 litres of water in a barrel.
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11. The length of a line is 63 centimetres, correct to the nearest centimetre.
The water flows out of the barrel at a rate of 125 millilitres per second.
(a) Write down the least possible length of the line.
I litre = 1000 millilitres.
. ........... ""~ ....'.-""'.....,.:......... _.. centimetres
(1)
Work out the time it takes for the barrel to empty completely.
(b) Write down the greatest possible length of the line.
II>
..........= .. :-':, .......,"""............... centimetres
ti
12.
A
I"'..
\ C
ABC is a triangle
less
and
10
II
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13. Fred is
He wants
to take
survey of the magazines read
students.
)
14. Work out an estimate for the value of
a questionnaire.
6.8x 191
0.051
Design a suitable question that he could use to find out what types of magazine
students read.
/\..­
\
(2)
15. (al Write 64000 in standard fonn.
Fred 'I-lOw many magazines have you read'/' (I)
A lot
A few (b) Write 156
]0-7
in standard form.
(b) Design a better question. You should include some response boxes. 16. (a) Factorise fully
4x 2
6xy
")
.,:.
(b) Factorise
x 2 + 5x
6
.. c..}' ..."., ...'":':...
J)
(2)
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17. Lucy did a survey about the amounts of money spent by 120 men during their summer
holidays
The cumulative frequency table gives some information about the amounts of money
spent by the 120 men.
Cumulative frequency
Amount (£4) spent
O:(A
O:(A
Cumulative frequency
100
13
150
25
0:( A < 200
42
0:( A < 250
64
300
93
A
350
110
O:(A
400
120
O:(A
0
(a) On the grid, draw a cumulative frequency diagram.
(2)
(b)
your cumulative frequency diagram to estimate the median
£
(2)
A survey of the amounts of money spent by 200 women during their summer holidays
gave a median of £205
(c) Compare the amounts of money spent by the women with the amounts of money
the men.
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18.
19.
Diagram NOT
accurately
B
7
6
k·
+ .......:
41-~'"''''''';'''''''''''''''':''''''''''''''''''''''''''''-:';~''''''''''C'''''''''''''
.................,
3
D
2
I"".......... '............ ~.... "'.: ...... . The diagram shows a circle centre 0 A, 13 and C are points on the circumference. DCO is a straight line. DA is a tangent to the circle. Angle
x
36° (a) Work out the size of angle AOD
The diagram shows graphs of
y
2
and
2y
3x = 12 +2
Use the diagram to solve the simultaneous equations v
.. 2y
(2)
1
2
2
= 12 (b) (i) Work out the size of angle ABC
x ...... ~ ..___ .. y = .. __ ....c;~.... _..... ..
(ii) Give a reason for your
(1)
(b) Find an equation of the straight line which is parallel to the line
passes through the point (0, 4).
+ 2 and 2
+
.t"
17
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7
2
4
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20. (a) Solve the inequality
3t
22. A call centre receives 64 telephone caJls one morning. The table gives information about the lengths, in minutes, of these telephone calls t
I
12
Length (x) minutes
Frequency
-----­
0
5 <x::;;; 15
]0
15
x::;;; 30
24
30
x::;;; 40
20
40
x::;;; 45
(2)
(b) t is a whole number.
Write down the largest value of 1 that satisfies
31
t
4
x::;;; 5
+ 12
Draw a histogram for this information
When L
2, M-
Find the value of M when L
o
20
10
30
40
50
19
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23. In a game of chess, a player can either win, draw or lose.
24.
A
Diagram NOT
accurately drawn
The probability that Vishi wins any game of chess is 0.5 The probability that Vishi draws
game of chess is 0.3 Vishi plays 2 games of chess. (a) Complete the probability tree diagram
1st game 2nd game
Win
c
B
Win
ABC is an equilateral triangle. D
on Be. AD is perpendicular to Be. Draw
Prove that triangle ADe is congruent to triangle ADB.
Lose
Win
)
Draw ~-------------------- Draw
Lose
(3)
Win
Lose
(b) Hence, prove that BD
2
·ie
D
Draw
J. AB. De, Lose
t3
(2)
(b) Work out the probability that Vishi will win both games.
''''7
l)
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25.
1
1
1
II
v
f
-+-=­
11
=?~
- 2'
v =
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26.
y
y = f(x)
;
3.!.
;:::,
3
(a) Find the value off
3
-2
o
2
4
6
x
The curve with equationy = f(x) is translated so that the point at (0, 0) is mapped onto the
point (4, 0)_
-
~
(a) Find an equation of the translated curve
(3)
(b) Rearrange
1
1
1
II
v
f
-+-=­
::­
y
to make
11
the subject of the formula_
4
Give your answer in its simplest form.
~
\
21~-·-t,·-~~-~·--~-·-~·-,-----·-,--!-·+t-··"·----:-jf-~,
~-
~
v
\..-1..
The grid shows the graph ofy
=
cosxo for values ofx from 0 to 540
(b) On the grid, sketch the graph of y = 3 cos (2 x O) for values of x from 0 to 540
(2)
IQ2,6
(Total 4 marks)
TOTAL FOR PAPER: 100 MARKS
END
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