Download Q1. (a) The nth term of a sequence is 4n + 1 (i) Write down the first

Q1.
(a)
(i)
The nth term of a sequence is 4n + 1
Write down the first three terms of the sequence.
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Answer ...................., ..................., ....................
(2)
(ii)
Is 122 a term in this sequence?
Explain your answer.
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(1)
(b)
Tom builds fencing from pieces of wood as shown below.
How many of pieces of wood will be in Diagram n?
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Answer .......................................................
(2)
(Total 5 marks)
Q2.
A stacking chair is 100 cm high and 40 cm wide.
Not drawn accurately
Page 1 of 12
When a chair is added to a stack it increases the height by 10 cm and the width by 5 cm.
Not drawn accurately
(a)
Find an expression for the height of a stack of n chairs.
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Answer .................................................
(2)
(b)
A rule for the maximum number of chairs that can be stacked before they fall over is
4n + 35 < 70
What is the maximum number of chairs that can be stacked?
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Answer .................................................
(3)
(Total 5 marks)
Page 2 of 12
Q3.
(a) The first term of a sequence is –2.
The rule for continuing the sequence is
Add 7
then
Multiply by
4
What is the second term of the sequence?
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Answer .................................................
(1)
(b)
This rule is used to continue a different sequence.
Multiply by
2
then
Add 5
The second term of this sequence is 3.
What is the first term?
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Answer .................................................
(3)
(Total 4 marks)
Page 3 of 12
Q4.
Here are the nth terms of 3 sequences.
Sequence 1
Sequence 2
Sequence 3
nth term
nth term
nth term
4n + 1
3n + 3
3n – 1
For each sequence state whether the numbers in the sequence are
A Always multiples of 3
S Sometimes multiples of 3
N Never multiples of 3
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Answer
Sequence 1 ..........................
Sequence 2 ..........................
Sequence 3 ..........................
(Total 3 marks)
Q5.
The nth term of a sequence is given by the expression n2– 3
Write down the first three terms of the sequence.
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Answer ................... , .................... , ....................
(Total 2 marks)
Page 4 of 12
M1.
(a)
(i)
5, 9, 13
–1 each error or omission
B1 for 1, 5, 9 or 9, 13, 17
B2
Page 5 of 12
(ii)
no and valid reason
eg 121 is in the sequence
(all) terms are odd
122 is even
121 ÷ 4 not integer
note: “no” can be implied
B1
Page 6 of 12
(b)
3n + 1 oe
B1 for 3n + c or kn + 1
B1 for n3 + 1 unless notation already penalised
ignore fw
B2
[5]
Page 7 of 12
M2.
(a)
Evidence of searching for a pattern or 10n
eg,
100
110
120
130
140
10
10
10
10
M1
10n + 90
oe
A1
Page 8 of 12
(b)
4n = 35 leading to n = 8.75 is M0 unless n given as 8
M1
or
4n = 35 leading to n < 8.75 is M1, A1
A1
A1
[5]
Page 9 of 12
M3.
(a)
20
B1
(b)
3 – 5
or – 2
M1
(their – 2) ÷ 2
M1
–1
SC2
– 1 × 2 + 5 (=3)
A1
[4]
Page 10 of 12
M4.
S, A, N
–1eeoo
B3
[3]
Page 11 of 12
M5.
–2, 1, 6
–1 each error or emission.
Ignore extra terms
12 – 3, 22 – 3, 32 – 3 is B1
B2
[2]
Page 12 of 12