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AQA GCSE Additional Maths 09 June Paper (Foundaion)
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(JUN099306F01)APW/Jun09/9306/F 9306/F
For Examiner’s UseSurname
Centre Number
Candidate Signature
Candidate Number
Other Names
General Certificate of Secondary EducationJune 2009
ADDITIONAL MATHEMATICS (PILOT) 9306/FFoundation TierCalculator Allowed
Tuesday 23 June 2009 1.30 pm to 3.30 pm
Time allowed: 2 hours
Instructions� Use black ink or black ball-point pen. Draw diagrams in pencil.� Fill in the boxes at the top of this page.� Answer all questions.� You must answer the questions in the spaces provided. Answers
written in margins or on blank pages will not be marked.� Use a calculator where appropriate.� Do all rough work in this book. Cross through any work you do not
want to be marked.� 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� The maximum mark for this paper is 100.� The marks for questions are shown in brackets.� You may ask for more answer paper, graph paper and tracing paper.
This must be tagged securely to this answer book.
Advice� In all calculations, show clearly how you work out your answer.
FFor this paper you must have:
� a calculator� mathematical instruments.
For Examiner’s Use
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Pages Mark
Examiner’s Initials
TOTAL
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Formulae Sheet: Foundation Tier
You may need to use the following formulae:
Area of trapezium = – (a +b)h
Volume of prism = area of cross-section × length
12
a
h
b
length
cross-section
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1 Mary is thinking of a number.
What number is Mary thinking of?
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Answer ....................................................................... (2 marks)
2 Trevor buys five packets of crisps.The change from £3 is 75 pence.
How much does one packet of crisps cost?
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Answer ............................................................. pence (2 marks)
Answer all questions in the spaces provided.
4
The number isless than 10
The numberis even.
The number can bedivided exactly by 3
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3 This shaded bar is 20 centimetres long.
Four of these bars are arranged as shown.
Work out the value of d.
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Answer ................................................................. cm (2 marks)
4 The diagram shows a number machine.All input numbers are positive whole numbers.
4 (a) What is the smallest output number that is a square number?
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Answer ....................................................................... (2 marks)
4 (b) What is the smallest output number that is a prime number?
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Answer ....................................................................... (2 marks)
(04)
20 cm
20 cm20 cm20 cm
20 cm
d13 cm
Not drawnaccurately
OutputInput + 1× 7
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5 Jody has a set of five single-digit number cards.
5 (a) She says the median is greater than the mode.Show that Jody is correct.
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5 (b) Here is another set of five cards.
Jody is asked to write numbers on the remaining two cards so that the median is thesame as the mode.
She says, “If I write down two fives or two sixes or one of each, I cannot fail.”
Show that Jody is correct.
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2 3 1 4 1
5 6 5
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6 Joanne is making shapes using some of these rods.
6 (a) She makes an isosceles triangle using three of the rods.
Draw a sketch to show how she could do this.Show the length on each side.
(1 mark)
6 (b) She makes a quadrilateral using two 3 cm rods and two 5 cm rods.
Write down the names of two possible quadrilaterals that she could make.
Answer .............................. and .............................. (2 marks)
6 (c) She tries to make a triangle using one rod of each length.Explain why she cannot do this.
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(06)
3 cm
5 cm
9 cm 9 cm
5 cm 5 cm
3 cm 3 cm Not drawn accurately
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7 Susan is choosing pairs of numbers from this list.
6 23 34 51 108
7 (a) She multiplies two numbers together.
Which two numbers should she choose to get an answer between 200 and 300?
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Answer .............................. and .............................. (2 marks)
7 (b) She divides one number by another number.
What is the largest possible answer?
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Answer ...................................................................... (2 marks)
8 Billy and Mina are investigating sequences that begin with
1, 2, 4, ……
8 (a) Billy says the fourth term is 8
What rule could Billy be using?
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Answer ...................................................................... (1 mark)
8 (b) Mina says the fourth term is 7
What rule could Mina be using?
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Answer ...................................................................... (1 mark)
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9 A and B are two interlocking shapes as shown.
Complete the following using
greater than or less than or equal to
9 (a) The perimeter of A is ................................................. the perimeter of B.(1 mark)
9 (b) The area of A is ...................................................... the area of B.(1 mark)
10 Fred and Susie each choose a number.Fred’s number is three times bigger than Susie’s number.The difference between the numbers is 70
What numbers did Fred and Susie choose?
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Answer Fred’s number .......................... Susie’s number ............................. (3 marks)
(08)
w wB
l l
A
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11 Here are some circles each containing two numbers.
The numbers are in a pattern.The numbers in the top of each circle are multiples of four.The numbers in the bottom of each circle are multiples of five.
11 (a) Here are two more circles in the pattern.
Write in the missing numbers.
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11 (b) Here is another circle in the pattern.
Write the two numbers in the circle so that their total is closest to 1000
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8
10
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300
300
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12 Write down four different numbers with a mean of 5
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Answer ............. , ............. , ............. , ............... (2 marks)
13 Use each of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 once only.
Put the numbers in a line so that any two numbers that are next to each other always add upto either 10 or 11
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Answer ……, ……, ……, ……, ……, ……, ……, ……, ……, …… (2 marks)
(10)
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15 Three whole numbers add up to 50The two smallest numbers are the same.Two of the numbers have a difference of 8
Find the three numbers.
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Answer ................... , .................... , .................... (4 marks)
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14 The diagram shows two overlapping squares that are the same size.Three regions are formed.
What is largest number of regions that can be formed by two overlapping squares that are thesame size?Draw a diagram to show your answer.
Answer ................................ (4 marks)
1
2
3
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16 On the grid, the horizontal line is x units long and the sloping line is y units long.
Shapes are drawn on the grid that have dots as their vertices.
The perimeter of this shape is 6x + 4y
Work out the perimeter of the following shapes in terms of x and y
16 (a)
Answer ....................................................................... (2 marks)
16 (b)
Answer ....................................................................... (2 marks)
(12)
yx
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17 Shapes tessellate when they fit together with no gaps.Here is a tessellating pattern made from equilateral triangles and regular hexagons.
17 (a) Write down the size of each interior angle in the equilateral triangle.
Answer ......................................................... degrees (1 mark)
17 (b) Write down the size of each interior angle in the regular hexagon.
Answer ......................................................... degrees (1 mark)
17 (c) Use your answers to parts (a) and (b) to explain why the two shapes form atessellating pattern.
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18 Show that there are no square numbers between 9100 and 9200
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Not drawn accurately
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19 This L-shape has measurements as shown on the diagram.
The perimeter of the shape is 72 cm.
Find the length marked h on the diagram.
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Answer ................................................................. cm (3 marks)
(14)
3 cm
3 cm
h
20 cm
Not drawn accurately
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20 In a game you can choose to throw one dice or two dice.If you throw one dice your score is the number you throw.
If you throw two dice your score is the sum of the numbers you throw.
It is your turn.You need to score exactly 4 to win.
Should you choose to throw one dice or two dice?Tick the correct box.
1 dice 2 dice
Explain your answer fully.
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Score = 4
+ Score = 4
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21 Three faces of this cube have shaded triangles on them.The other three faces are blank.
Here is a net of the cube.
Draw the shaded triangles on the net.(3 marks)
(16)
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22 In the following calculations each letter represents a different digit.
A × A = BC
BC × BC = DEC
Which digit does each letter represent?
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Answer A = ......................
B = .....................
C = .....................
D = .....................
E = ..................... (3 marks)
Turn over for the next question
(17)
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(18)
23 (a) Travelling 10 000 kilometres costs £800 for petrol.
How much does it cost to travel 12 500 kilometres?
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Answer £ .................................................................. (1 mark)
23 (b) Last year Mr Taylor travelled 15 000 km in his car and spent £1200 on petrol.This year he expects to travel 20 000 km.He estimates that the price of petrol has increased by 10% on what it was last year.
How much should Mr Taylor expect to pay for petrol this year?
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Answer £ .................................................................. (4 marks)
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24 A rectangular carpet is 7 metres wide and 8 metres long.A square piece of side length x metres is cut from one of the corners.
24 (a) Dean works out the area of the remaining carpet in terms of x.His answer is 56 – x2
Explain how Dean might have obtained his expression.
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24 (b) Lucy also works out the area of the remaining carpet in terms of x.Her answer is x(8 – x) + 8(7 – x)
Use the diagram below to show how Lucy might have obtained her expression.
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(3 marks)
(19)
9
8 m
7 m
x m
x m Not drawn accurately
8 m
7 m
x m
x m
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(20)
25 (a) A sequence starts
2, 7, 17, ……
The rule for finding the next term in this sequence is to multiply the previous term by2 and then add on 3
Work out the next term.
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Answer ...................................................................... (1 mark)
25 (b) The rule for finding the next term in a different sequence is to multiply the previousterm by 2 and then add on a, where a is an integer.
The first term is 8 and the fourth term is 127
8 …… …… 127
Work out the value of a.
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Answer a = ............................................................... (4 marks)
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26 The triangle has lengths (4x – 2) cm, (2x + 5) cm and (6x – 9) cm.
Find the value of x that makes this triangle equilateral.
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Answer ...................................................................... (4 marks)
(21)
Not drawn accurately
(2x + 5) cm(4x – 2) cm
(6x – 9) cm
9
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(22)
27 Here are two rectangles, A and B.
Is rectangle B an enlargement of rectangle A?
Tick the correct box.
Yes No
Explain your answer.
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Not drawn accurately7 cm
5 cm
A
16.5 cm
12.5 cm
B
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28 ABCD is a square.PQRS is a square with vertices on the sides of ABCD.AS = DR = CQ = BP = 9 cmPA = SD = RC = QB = 1 cm
What is the area of the shaded square PQRS?
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Answer ................................................................ cm2 (3 marks)
9 cm
1 cm
9 cm 1 cm
A BP
Q
CDR
S
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29 You may use the grid opposite to help you solve this problem.
At 9 am a man leaves point P and walks along a road at a steady speed of 6 kilometres perhour.
At 12 noon a cyclist leaves P, on the same road in the same direction, at a steady speed of20 kilometres per hour.
After travelling for an hour the cyclist gets a puncture which delays her for 30 minutes.
She then continues at 20 kilometres per hour until she overtakes the walker.
29 (a) At what time did the cyclist overtake the walker?
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Answer ...................................................................... (3 marks)
29 (b) A motorist leaves P, travelling at a steady speed of 50 kilometres per hour.The motorist overtakes the walker at the same time as the cyclist.
At what time did the motorist leave P?
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Answer ...................................................................... (2 marks)
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5
9 am0P
10
20
30
40
50
10 am 11am 12 noon
Time
Distancetravelledfrom P(km)
1 pm 2 pm 3 pm
END OF QUESTIONS
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