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General Certificate of Secondary Education
Foundation Tier
November 2011
Mark
3
4 –5
6 –7
Mathematics
(Specification A)
4306/2F
10 –11
Paper 2 Calculator
Monday 14 November 2011
8 –9
9.00 am to 10.30 am
F
12 –13
14 –15
16 –17
18 –19
For this paper you must have:
l
mathematical instruments
l
a calculator.
20 –21
22 –23
24
Time allowed
l 1 hour 30 minutes
TOTAL
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 Do all rough work in this book. Cross through any work you do not
want to be marked.
Information
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 100
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.
(NOV1143062F01)
WMP/Nov11/4306/2F
4306/2F
2
Formulae Sheet: Foundation Tier
a
1
h
Area of trapezium = 2– (a + b)h
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 and C are points on a grid.
y
7
6
C
5
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3
2
A
1
0
0
1 (a)
1
2
3
4
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6
7
x
Write down the coordinates of point A.
Answer ( .............. , ................)
1 (b)
Plot the point B (1, 3).
1 (c)
Draw the triangle ABC.
(1 mark)
(1 mark)
What type of triangle is ABC?
Circle the correct answer.
scalene
isosceles
equilateral
(1 mark)
3
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4
2
In the diagram, each middle number is the sum of the two numbers at the nearest
corners.
5
11
3
7
4
Fill in the missing numbers on the diagram.
3 (a)
(3 marks)
Write down all the factors of 35
............................................................................................................................................
............................................................................................................................................
Answer ......................................................................
3 (b)
(2 marks)
Shafiq is thinking of a number.
The number is less than 30
The number is a multiple of 8
The number has a factor of 3
What is the number?
............................................................................................................................................
............................................................................................................................................
Answer ......................................................................
(04)
(2 marks)
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5
4 (a)
This clock shows the time 7 o’clock.
12
9
3
6
After the minute hand has turned through 360º, what time will the clock show?
Answer ......................................................................
4 (b)
(1 mark)
This clock shows the time 3 o’clock.
12
9
3
6
After the hour hand has turned through 90º, what time will the clock show?
Answer ......................................................................
4 (c)
(1 mark)
Complete the table to show the time in words and on a digital clock.
Time in words
Time on a digital clock
Half past seven
07.30
Quarter past eight
10.20
(2 marks)
11
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6
5
The graph shows the monthly rainfall at a holiday resort.
90
80
70
60
Monthly
rainfall
in mm
50
40
30
20
10
0
Jan
Feb Mar Apr May Jun
Jul
Aug Sep Oct Nov Dec
Month
5 (a) (i)
Which month has the highest rainfall?
............................................................................................................................................
Answer ......................................................................
(1 mark)
5 (a) (ii) What is the rainfall in that month?
............................................................................................................................................
Answer ............................................................... mm
5 (b)
(1 mark)
What is the range of the monthly rainfall?
............................................................................................................................................
Answer ............................................................... mm
(06)
(1 mark)
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7
5 (c)
The graph shows the average temperature each month at the same holiday resort.
35
30
25
Average
temperature
in degrees
Celsius
(oC)
20
15
10
5
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug Sep
Oct
Nov Dec
Month
Julia is going on holiday.
She would like an average temperature of 20 ºC and as little rainfall as possible.
Which month should she choose?
Give a reason for your answer.
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
(2 marks)
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5
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6
This question uses centimetre grids.
6 (a)
On this grid, draw a square of area 4 cm2.
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(1 mark)
6 (b)
Work out the area of this shape.
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Answer ............................................................... cm2
(08)
(1 mark)
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9
6 (c)
Work out the area of this square.
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Answer ............................................................... cm2
6 (d)
(1 mark)
Show that this square has an area of 8 cm2.
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(1 mark)
4
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7 (a)
Abigail has two 5p coins, one 50p coin and some 20p coins.
Altogether, she has £1.40
How many 20p coins does she have?
............................................................................................................................................
............................................................................................................................................
Answer ......................................................................
7 (b)
(2 marks)
Matthew has two 10p coins, ten 20p coins and two 50p coins.
Write down all the possible ways of making £1.80 using his coins.
One way has been done for you.
You do not have to use all the coins each time.
Number of 10p coins
Number of 20p coins
Number of 50p coins
2
3
2
(3 marks)
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11
8
8 (a)
Students take an examination that has two different papers.
Each paper is marked out of 100
The marks for the two papers are added together.
The table shows the grade given for each total mark.
Total mark for the two papers
Grade
133 or more
Distinction
82 to 132
Merit
30 to 81
Pass
Here are Ben’s marks.
Paper 1
36
Paper 2
41
What is Ben’s grade?
............................................................................................................................................
Answer ......................................................................
8 (b)
(1 mark)
Sara gets 46 on Paper 1.
What is the minimum mark she needs on Paper 2 for a Merit grade?
............................................................................................................................................
............................................................................................................................................
Answer ......................................................................
(2 marks)
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8
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9 (a)
Write down the next term in the sequence
1
9 (b)
5
9
(1 mark)
..............
Patterns with dots are shown.
The patterns form a sequence.
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pattern 1
pattern 2
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pattern 3
pattern 4
Draw pattern 4
(1 mark)
9 (c)
Complete the table of results.
Pattern number
1
2
3
Number of dots
1
5
9
4
5
(1 mark)
9 (d)
The rule for the number of dots is
number of dots = 4 × pattern number – 3
9 (d) (i)
Work out the number of dots in pattern number 10
............................................................................................................................................
Answer ......................................................................
(1 mark)
9 (d) (ii) Work out the pattern number when the number of dots is 77
............................................................................................................................................
............................................................................................................................................
Answer ......................................................................
(12)
(1 mark)
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10 (a)
Round 2837 to the nearest hundred.
............................................................................................................................................
Answer ......................................................................
10 (b)
(1 mark)
Write a number in the box so that the statement is true.
rounded to the nearest ten is 60
(1 mark)
11 (a)
What is the order of rotational symmetry of this shape?
Answer ......................................................................
11 (b)
(1 mark)
Draw in all the lines of symmetry of this shape.
(1 mark)
11 (c)
How many lines of symmetry does this shape have?
Answer ......................................................................
(1 mark)
10
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14
12
Here is a cuboid.
Not drawn
accurately
2 cm
3 cm
4 cm
Complete the net of the cuboid on the grid below.
(3 marks)
(14)
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15
13
Calculate the mean of these six numbers.
11
13
15
18
20
25
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
Answer ......................................................................
14 (a)
2r + 3s
Find the value of
(3 marks)
when r = 7 and s = 5
............................................................................................................................................
............................................................................................................................................
Answer ......................................................................
14 (b)
14 (b) (i)
(2 marks)
Solve the equations
w + 6 = 11
............................................................................................................................................
Answer w = ................................................................
14 (b) (ii)
(1 mark)
5x – 4 = 31
............................................................................................................................................
Answer x = .................................................................
14 (b) (iii)
(2 marks)
y
–=7
9
............................................................................................................................................
Answer y = .................................................................
(1 mark)
12
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16
15
Here are two ways of buying music downloads.
£14.95 per month
All downloads free
Minimum contract two years
79p for
each track
Jake estimates that he will download 500 tracks over the next two years.
Which is the cheaper option for Jake?
Tick a box.
Each track separately
Two-year contract
You must show all your working.
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
(4 marks)
0.7
––––
0.32
16
Use your calculator to work out
16 (a)
Write down all the figures on your calculator display.
Answer ......................................................................
16 (b)
Round your answer to two decimal places.
Answer ......................................................................
(16)
(1 mark)
(1 mark)
WMP/Nov11/4306/2F
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17
17
This shape is made from three squares.
Not drawn
accurately
The perimeter of the shape is 32 cm.
How long is a side of one of the squares?
............................................................................................................................................
............................................................................................................................................
(2 marks)
Answer ................................................................ cm
18
This is the rainfall, in mm, for each month at a holiday resort.
25
18 (a)
40
50
60
80
55
40
20
40
60
40
35
What is the mode of the data?
............................................................................................................................................
Answer ............................................................... mm
18 (b)
A month is chosen at random.
18 (b) (i)
What is the probability the rainfall for that month is 40 mm?
(1 mark)
............................................................................................................................................
Answer ......................................................................
(2 marks)
18 (b) (ii) What is the probability the rainfall for that month is not 40 mm?
............................................................................................................................................
Answer ......................................................................
(1 mark)
12
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18
19 (a)
ABC is a right-angled triangle.
Angle CAB is 51º.
C
Not drawn
accurately
51°
A
B
Work out the size of angle ABC.
............................................................................................................................................
............................................................................................................................................
Answer ........................................................ degrees
19 (b)
(2 marks)
PQRS is a quadrilateral.
PQT is a straight line.
S
92°
Not drawn
accurately
R
140°
x
46°
P
Q
T
Work out the size of angle x.
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
Answer ........................................................ degrees
(18)
(3 marks)
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19
20
All workers in a company are given a pay rise of 2.5%.
What is the new salary of a manager who earns £34 600 per year?
............................................................................................................................................
............................................................................................................................................
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Answer £ ...................................................................
21
(3 marks)
Here is some information about a group of 40 teenagers.
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There are 4 more boys than girls.
One-third of the girls are vegetarians.
Use this information to complete the two-way table.
Boys
Girls
Total
Vegetarian
10
Non-vegetarian
30
Total
40
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
(3 marks)
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22
Julia has a ‘pay as you go’ contract for her mobile phone.
Voice calls cost 7p per minute.
Texts cost 10p each.
22 (a)
In August, Julia paid £15
She made 120 minutes of voice calls.
How many texts did she send?
............................................................................................................................................
............................................................................................................................................
Answer ......................................................................
22 (b)
(2 marks)
In September, Julia made 140 minutes of voice calls.
She sent twice the number of texts that she sent in August.
How much did she pay that month?
............................................................................................................................................
............................................................................................................................................
Answer £ ...................................................................
23
(2 marks)
This shape is symmetrical.
Not drawn
accurately
13 cm
11 cm
14 cm
Work out the area of the shape.
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
Answer ............................................................... cm2
(20)
(3 marks)
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21
24 (a)
The diagram shows a regular hexagon.
a
24 (a) (i)
Show clearly why angle a = 60 º.
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
(1 mark)
24 (a) (ii) Work out the sum of the interior angles of a hexagon.
............................................................................................................................................
............................................................................................................................................
Answer ........................................................ degrees
24 (b)
(2 marks)
P, Q, R and S are four vertices of a regular polygon.
Each exterior angle is 18 º.
P
S
18°
Q
Not drawn
accurately
R
Work out the number of sides of the polygon.
............................................................................................................................................
............................................................................................................................................
Answer ......................................................................
(2 marks)
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22
25
Expand and simplify
4(2x + 1) – 3(x – 4)
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
Answer ......................................................................
26 (a)
(2 marks)
Two numbers a and b are less than 15
The Least Common Multiple (LCM) of a and b is 24
Give one possible pair for the two numbers, a and b.
............................................................................................................................................
............................................................................................................................................
Answer a ......................... and b .............................
26 (b)
(2 marks)
Two numbers x and y are between 10 and 20
The Highest Common Factor (HCF) of x and y is 3
Give one possible pair for the two numbers, x and y.
............................................................................................................................................
............................................................................................................................................
Answer x ......................... and y .............................
(22)
(2 marks)
WMP/Nov11/4306/2F
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23
27
A home-made four-sided spinner is known to be biased.
2
1
3
4
The table shows the probabilities of getting each score.
27 (a)
Score
1
2
3
4
Probability
1
––
10
3
––
10
7
––
20
1
–
4
What is the probability of landing on a 1 or a 2?
............................................................................................................................................
............................................................................................................................................
Answer ......................................................................
27 (b)
(1 mark)
The spinner is spun 400 times.
How many times would you expect it to land on a 3?
............................................................................................................................................
............................................................................................................................................
Answer ......................................................................
(2 marks)
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9
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24
28
y = x2 – x – 3
The graph of
is shown on the grid.
y
4
3
2
1
–3
–2
–1
O
1
2
3
x
–1
–2
–3
–4
28 (a)
Write down the value of y when x = 1.5
Answer ......................................................................
28 (b)
(1 mark)
Write down the values of x when y = –1
............................................................................................................................................
Answer ......................................................................
(2 marks)
3
END OF QUESTIONS
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