Download GCSE Mathematics (Specification B) Foundation Question

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General Certificate of Secondary Education
Foundation Tier
June 2011
Mark
3
4–5
6 –7
Mathematics (Modular)
(Specification B)
Module 5
43055/2F
8–9
10 –11
F
Paper 2 Calculator
12 – 13
14 – 15
16 –17
Friday 10 June 2011
9.00 am to 10.15 am
18 – 19
For this paper you must have:
l
a calculator
l
mathematical instruments.
TOTAL
Time allowed
l 1 hour 15 minutes
Instructions
l Use black ink or black ball-point pen. Draw diagrams in pencil.
l Fill in the boxes at the top of this page.
l Answer all questions.
l You must answer the questions in the spaces provided. Do not write
outside the box around each page or on blank pages.
l Use a calculator where appropriate.
l Do all rough work in this book.
l If your calculator does not have a π button, take the value of π to be 3.14
unless another value is given in the question.
Information
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 70.
l You may ask for more answer paper, graph paper and tracing paper.
These must be tagged securely to this answer booklet.
Advice
l In all calculations, show clearly how you work out your answer.
WMP/Jun11/43055/2F
43055/2F
2
Formulae Sheet: Foundation Tier
You may need to use the following formulae:
a
Area of trapezium = 1– (a + b)h
h
2
b
Volume of prism = area of cross-section × length
crosssection
h
lengt
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3
Answer all questions in the spaces provided.
1 (a)
Write a number to make each statement correct.
1 (a) (i)
5 metres = ............................................ centimetres
(1 mark)
3 kilograms = ................................................. grams
(1 mark)
1 (a) (ii)
1 (b)
Write a word to make this statement correct.
2000 millilitres = 2 .....................................................
2
(1 mark)
Angle x is shown on the diagram.
x
2 (a)
2 (b)
What type of angle is x?
Answer ......................................................................
(1 mark)
Answer ........................................................ degrees
(1 mark)
Measure angle x.
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4
3
Here is a cuboid.
3 (a)
How many faces does the cuboid have?
Answer ......................................................................
3 (b)
The cuboid is cut in half to make this shape.
3 (b) (i)
How many rectangular faces does this shape have?
Answer ......................................................................
(1 mark)
(1 mark)
3 (b) (ii) How many triangular faces does this shape have?
Answer ......................................................................
(1 mark)
3 (b) (iii) How many vertices does this shape have?
Answer ......................................................................
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(1 mark)
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5
4 (a)
Jack is thinking of a number.
The number is
between 10 and 20
The number is
odd
The number is
a multiple of 3
What is the number?
............................................................................................................................................
............................................................................................................................................
Answer ......................................................................
4 (b)
(2 marks)
Nima is thinking of a number.
The number is
greater than 1
The number is
a factor of 20
The number is
a square number
What is the number?
............................................................................................................................................
............................................................................................................................................
Answer ......................................................................
(2 marks)
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6
5
The cost of hiring a bicycle is given by the formula
Cost in pounds = Number of days × 6 + 12
5 (a)
Work out the cost of hiring a bicycle for three days.
............................................................................................................................................
............................................................................................................................................
Answer £ ....................................................................
5 (b)
(2 marks)
Ruby hires a bicycle.
The cost is £96.
For how many days does she hire the bicycle?
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
Answer ......................................................................
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(2 marks)
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7
6
These patterns are made using circles.
Pattern 1
6 (a)
Pattern 2
Pattern 3
Draw Pattern 4.
(1 mark)
6 (b)
Fill in the missing entries in the table.
Pattern number
1
2
3
Number of shaded circles
2
3
4
Number of unshaded circles
2
4
6
Total number of circles
4
7
10
4
5
(2 marks)
6 (c)
It is not possible to make one of the patterns with a total of 29 circles.
Give a reason why.
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
(1 mark)
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7 (a)
Do not write
outside the
box
AB and AD are straight lines.
y
B
4
3
2
1
A
D
0
0
7 (a) (i)
1
2
3
4
5
6
x
Write down the coordinates of A.
Answer
( ................. , ................. )
(1 mark)
7 (a) (ii) Write down the coordinates of the midpoint of the line AD.
Answer
( ................. , ................. )
(1 mark)
7 (a) (iii) ABCD is a parallelogram.
Complete the diagram.
(1 mark)
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9
7 (b)
EF is a straight line.
y
7
6
F
5
4
3
2
1
E
0
0
7 (b) (i)
1
2
3
4
5
6
7
8
9
10
11
12
x
Measure the length of the line EF.
Answer ................................................................ cm
(1 mark)
7 (b) (ii) Lines EH and FG are parallel to the x-axis.
EFGH is a rhombus.
Complete the diagram.
(2 marks)
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10
8 (a)
Draw a triangle on the grid that has an angle of 90° and two equal sides.
(2 marks)
8 (b)
Which two of the following describe the triangle in part (a)?
Circle your answers.
Pythagoras
right-angled
scalene
isosceles
equilateral
congruent
(2 marks)
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11
9 (a)
c and d are positive numbers.
They are not equal.
Tick a box to show whether each statement is true or false.
True
False
c+d=d+c
c–d=d–c
c×d=d×c
c÷d=d÷c
(3 marks)
9 (b) (i)
Circle the expression that is twice as big as n.
2n
n+2
n
2
n2
(1 mark)
9 (b) (ii) Circle the expression that is 5 less than n.
n
5
n+5
n–5
5–n
(1 mark)
9 (c)
Write down two cube numbers that have a difference of 19.
............................................................................................................................................
............................................................................................................................................
Answer ............................... and ................................
(2 marks)
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10 (a)
ABC is a straight line.
D
Not drawn
accurately
37°
y
x
46°
A
10 (a) (i)
E
52°
B
C
Work out the value of angle DBE, marked x on the diagram.
............................................................................................................................................
............................................................................................................................................
Answer ........................................................ degrees
(2 marks)
10 (a) (ii) Work out the value of angle DEB, marked y on the diagram.
............................................................................................................................................
............................................................................................................................................
Answer ........................................................ degrees
10 (b)
(2 marks)
This is a regular pentagon.
Not drawn accurately
w
Work out the value of an exterior angle, marked w on the diagram.
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
Answer ........................................................ degrees
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(2 marks)
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13
11
Enlarge shape A by scale factor 3.
A
(2 marks)
Turn over for the next question
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14
12 (a)
Here is a sequence.
1
8
22
......
To find the next term the rule is
add 3 and multiply by 2
Work out the next term in the sequence.
............................................................................................................................................
Answer ......................................................................
12 (b)
(1 mark)
Here is a different sequence.
1
76
......
To find the next term the rule is
add 3 and multiply by n
Work out the value of n.
............................................................................................................................................
............................................................................................................................................
Answer ......................................................................
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(2 marks)
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15
13 (a)
Simplify fully
6x + 5y + 4x – 3y
............................................................................................................................................
Answer ......................................................................
13 (b)
Solve
(2 marks)
9c – 3 = 4c + 1
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
Answer c = ................................................................
14
(3 marks)
The cost of a taxi journey is made up of two parts.
£3.50 for any distance up to 1 kilometre
30p for every 100 metres after the first kilometre
How much will a taxi journey of 3 kilometres cost?
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
Answer £ ...................................................................
(3 marks)
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16
15
In this diagram, all lengths are in centimetres.
2
2
6
Not drawn
accurately
6
h
h
4
8
The area of the shape is 56 cm2.
Work out the length marked h in the diagram.
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
Answer ................................................................ cm
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(3 marks)
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17
16
Here is a right-angled triangle.
17 cm
x
Not drawn
to accurately
Not
accurately
15 cm
Work out the value of x.
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
Answer ................................................................ cm
(3 marks)
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18
17
Use trial and improvement to find a solution to the equation
x3 + 6x = 29
Continue the table of results.
Give your solution to 1 decimal place.
x
x3 + 6x
Comment
2
20
Too small
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
Answer x = .................................................................
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(4 marks)
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19
18
Here is a triangular prism.
4 cm
20 cm
6 cm
Work out the volume of the prism.
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
Answer ............................................................... cm3
(3 marks)
END OF QUESTIONS
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