Name
Class
For Edexcel GCSE
Mathematics
Unit 3 : Number, Algebra, Geometry 2 (Calculator)
Higher Tier
Paper F
Time : 1 hour 45 minutes
Total Marks
You must have:
Ruler, protractor, compasses, pen, pencil, eraser, calculator.
Instructions and Information
•
•
•
•
•
•
Write your name in the box at the top of the page.
Answer all the questions in the spaces provided.
The total mark for this paper is 80.
The marks for each question are shown in brackets.
Calculators may be used.
If your calculator does not have a  button, take the value of
 to be 3.142 unless the question instructs otherwise.
• Questions labelled with an asterisk (*) are ones where the
quality of your written communication will be assessed.
Advice
•
•
•
•
Read each question carefully before you start to answer it.
Keep an eye on the time.
Try to answer every question.
Check your answers if you have time at the end.
Written by Shaun Armstrong
Only to be copied for use in the purchaser's school or college
2012 EHF Unit 3 Page 1
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GCSE Mathematics
Formulae: Higher Tier
You must not write on this formulae page.
Volume of prism = area of cross section × length
Area of trapezium =
1
2
(a + b)h
a
h
cross
section
leng
th
b
4
1
Volume of sphere = 3 πr3
Surface area of sphere = 4πr2
Volume of cone = 3 πr2h
Curved surface area of cone = πrl
r
l
h
r
In any triangle ABC
The Quadratic Equation
The solutions of ax2 + bx + c = 0
where a ≠ 0, are given by
C
a
b
A
Sine Rule
c
x=
B
a
b
c
=
=
sin A
sin B
sin C
Cosine Rule a2 = b2 + c2 – 2bc cos A
Area of triangle =
1
2
ab sin C
2012 EHF Unit 3 Page 2
© Churchill Maths Limited
−b± b2−4 ac 
2a
Answer ALL questions.
Write your answers in the spaces provided.
You must write down all stages in your working.
1
(a)
Calculate the square root of 20.25
(1)
………………………………
(b)
Calculate the reciprocal of 3.2
(1)
………………………………
(c)
Calculate
 8.2 − 2.95
0.038
giving your answer correct to 3 significant figures.
(3)
………………………………
(Total for Question 1 is 5 marks)
2
Solve
(a)
2n – 3 = 8
(2)
n = ……………………………
(b)
3(r + 12) = 7r
(3)
r = ……………………………
(Total for Question 2 is 5 marks)
2012 EHF Unit 3 Page 3
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3
8 cm
Diagram NOT
accurately drawn
10 cm
The diagram shows a paperweight in the shape of a cylinder.
The paperweight is packed in a box in the shape of a cube of side 16 cm.
The space between the paperweight and the sides of the box is filled with polystyrene.
Work out the volume of polystyrene in the box.
Give the units with your answer.
………………………………
(Total for Question 3 is 5 marks)
2012 EHF Unit 3 Page 4
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4
(a)
Expand
2y(3y – 8)
(2)
………………………………
* (b)
Make a the subject of the following.
a – 3r = r(a + 1)
(4)
………………………………
(Total for Question 4 is 6 marks)
2012 EHF Unit 3 Page 5
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5
Graph A
h
h
Graph B
h
t
Graph D
t
h
h
Graph C
t
Graph E
Graph F
h
t
t
t
Water is poured at a constant rate into three vases.
Write down the letter of the graph above which could show how the height of the water
in the vase, h, changes with time, t, for each vase.
(a)
(1)
Graph …………………………
(b)
(1)
Graph …………………………
(c)
(1)
Graph …………………………
(Total for Question 5 is 3 marks)
2012 EHF Unit 3 Page 6
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6
Scale: 1 cm represents 2 m
The scale drawing represents Mr. Singh's lawn which is rectangular.
There is a length of hose with holes in it running along one diagonal.
When water is pumped into the hose it acts as a sprinkler.
Any part of his lawn within 5 m of the hose gets watered.
(a)
Shade the regions of his lawn which do not get watered.
(2)
Ms. Hale has a rectangular lawn measuring 4 m by 7 m.
She would like to water it in the same way as Mr. Singh.
(b)
Calculate the length of a diagonal of her lawn.
(2)
…………………………… m
(Total for Question 6 is 4 marks)
2012 EHF Unit 3 Page 7
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*7
Tahir only uses his phone for calls.
The rest of the time his phone is on standby.
One full charge of his phone's battery lasts for 4 hours of calls or 90 hours on standby.
Tahir's phone is fully charged at 9 am on Monday.
By the time this charge runs out he has made 1 hour and 20 minutes of calls.
At what time on what day does the charge run out?
Show your working.
……………………………………………………………………………………
(Total for Question 7 is 5 marks)
2012 EHF Unit 3 Page 8
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*8
Diagram NOT
accurately drawn
x cm
(x + 2) cm
x cm
The diagram shows a cuboid.
The volume of the cuboid is 250 cm3.
Use a trial and improvement method to find the value of x correct to 1 decimal place.
Show all your working.
x = ……………………………
(Total for Question 8 is 5 marks)
2012 EHF Unit 3 Page 9
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9
y
5
4
A
3
2
1
–6
–5
–4
–3
–2
–1
O
–1
1
2
3
4
5
6
x
–2
–3
–4
–5
Triangle A is shown on the grid.
(a)
Reflect triangle A in the y-axis.
Label the image B.
(2)
(b)
Translate triangle A using the vector
Label the image C.
−36  .
(2)
(c)
Rotate triangle A 180º about the point (0, 0).
Label the image D.
(2)
(d)
Enlarge triangle A by scale factor 2 with centre of enlargement (–1, 5).
Label the image E.
(3)
(Total for Question 9 is 9 marks)
2012 EHF Unit 3 Page 10
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10
goal line
ball
The diagram shows an overhead view of the position of a football and the goal line.
The ball is kicked so that it travels along a path perpendicular to the goal line.
Construct the path the ball travels along using a ruler and a pair of compasses.
Leave in your construction lines.
(Total for Question 10 is 3 marks)
11
(a)
m2 – 9
Factorise
(1)
………………………………
(b)
Solve
3a2 – 10a – 8 = 0
(3)
………………………………
(Total for Question 11 is 4 marks)
2012 EHF Unit 3 Page 11
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12
B
Diagram NOT
accurately drawn
D
2.5 m
22º
C
28º
A
The diagram shows a vertical pole AB.
The point C is on the ground such that AC is horizontal.
A box is attached to the pole at D, 2.5 m above A.
Angle ACD = 28º.
Angle BCD = 22º.
Work out the distance BD.
……………………………… m
(Total for Question 12 is 5 marks)
2012 EHF Unit 3 Page 12
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13
A vet spends two hours giving health checks to cats and dogs.
In that time, she sees 15 animals.
It takes her 7 minutes to check each cat and 10 minutes to check each dog.
Let c be the number of cats she sees and d be the number of dogs she sees.
(a)
Write down two equations involving c and d.
(2)
………………………………………… and …………………………………………
(b)
Solve your equations simultaneously to find the values of c and d.
(3)
c = ………………………………
d = ………………………………
(Total for Question 13 is 5 marks)
2012 EHF Unit 3 Page 13
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14
Prove that
0.0 6̇ =
1
15
(Total for Question 14 is 2 marks)
15
Three years ago, Anton had £1200 in his savings account correct to the nearest £100.
The account paid compound interest of 4% per year correct to one significant figure.
Anton hasn't made any withdrawals.
Work out the smallest amount that could be in his account now.
£ ………………………………
(Total for Question 15 is 4 marks)
2012 EHF Unit 3 Page 14
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16
Diagram NOT
accurately drawn
A child draws a tractor with circular wheels.
On the drawing, the radius of the rear wheel is 2 cm more than the radius of the front
wheel.
The area of the rear wheel is 2.25 times the area of the front wheel.
Find the radius of the rear wheel on the drawing.
……………………………… cm
(Total for Question 16 is 5 marks)
2012 EHF Unit 3 Page 15
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*17
X
Diagram NOT
accurately drawn
8 cm
6 cm
Y
The diagram shows a prism of height 8 cm.
The cross-section of the prism is a regular hexagon of side length 6 cm.
The vertices X and Y are shown on the diagram.
Calculate the length XY.
……………………………… cm
(Total for Question 17 is 5 marks)
TOTAL FOR PAPER IS 80 MARKS
2012 EHF Unit 3 Page 16
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