By : Terrence De Costa B.Sc(Hons) - 0768580111
Sequences
Paper 22
1
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 1
Find the n th term of the sequence below.
1, 5, 25, 125, 625, . . .
[2 marks]
Question 2
These are the first five terms of a sequence.
1
2
Find the next term.
3
4
7
6
13
8
21
10
[1 mark]
Question 3
Find the n th term of the sequence below.
3,
6,
12,
24,
...
[2 marks]
2
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 4a
The n th term of a sequence is given by an 2 + bn where a and b are integers.
The 2nd term of the sequence is —2
The 4th term of the sequence is 12
Find the 6th term of the sequence.
[4 marks]
Question 4b
Here are the first five terms of a different quadratic sequence.
0 2 6 12 20
Find an expression, in terms of n , for the n th term of this sequence.
[2 marks]
Question 5a
Find the n th term of each sequence.
4, 8, 12, 16, 20, .........
[1 mark]
3
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 5b
11, 20, 35, 56, 83, ..........
[2 marks]
4
By : Terrence De Costa B.Sc(Hons) - 0768580111
Sequences
Paper 42
5
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 1a
Find the n th term of each sequence.
4
2
0
-2
-4
...
[2 marks]
Question 1b
1
7
17
31
49
...
[2 marks]
Question 2
Complete the table for the 5th term and the nth term of each sequence.
1st term
2nd term
3rd term
4th term
5th term
9
5
1
-3
4
9
16
25
1
8
27
64
8
16
32
64
n th term
[11 marks]
6
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 3
0, 1, 1, 2, 3, 5, 8, 13, 21 , ...
This sequence is a Fibonacci sequence.
After the first two terms, the rule to find the next term is “add the two previous terms”.
For example, 5 + 8 = 13.
Use this rule to complete each of the following Fibonacci sequences.
2
4
........
........
........
1
........
........
........
11
........
−1
........
........
1
[3 marks]
7
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 4
1
,
3
i)
3
,
4
4
,
7
7
,
11
11
,
18
One term of this sequence is
...
p
.
q
Find, in terms of p and q , the next term in this sequence.
ii)
[1]
Find the 6th term of this sequence.
[1]
[2 marks]
Question 5
Find the n th term of each sequence.
i)
−1,
− 3,
− 5,
− 7,
ii)
2,
9,
28,
65,
126,
− 9,
...
[2]
...
[2]
[4 marks]
8
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 6
Find the next term and the n th term of this sequence.
3
,
5
4
,
7
5
,
9
6
,
11
7
,
13
...
Next term = .................................................
n th term = .................................................
[3 marks]
9
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 7a
These are the first four diagrams of a sequence.
The diagrams are made from white dots and black dots.
Complete the table for Diagram 5 and Diagram 6.
Diagram
1
2
3
4
Number of white dots
1
4
9
16
Number of black dots
0
1
3
6
Total number of dots
1
5
12
22
5
6
[2 marks]
Question 7b
Write an expression, in terms of n , for the number of white dots in Diagram n .
10
[1 mark]
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 7c
The expression for the total number of dots in Diagram n is
i)
ii)
1
(3n 2 − n ) .
2
Find the total number of dots in Diagram 8.
Find an expression for the number of black dots in Diagram n .
Give your answer in its simplest form.
[1]
[2]
[3 marks]
Question 7d
T is the total number of dots used to make all of the first n diagrams.
T = an 3 + bn 2
Find the value of a and the value of b .
You must show all your working.
a = ................................................
b = ................................................
[5 marks]
11
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 8a
Sequence
1st term
2nd term
3rd term
4th term
A
13
9
5
1
B
0
7
26
63
9
32
10
64
7
8
8
16
Complete the table for the three sequences.
C
5th term
nth term
[10 marks]
12
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 8b
One term in Sequence C is
p
.
q
Write down the next term in Sequence C in terms of p and q .
[2 marks]
Question 9
The table shows the first four terms in sequences A, B, and C.
Sequence
1st term
2nd term
3rd term
4th term
A
4
9
14
19
B
3
10
29
66
C
1
4
16
64
Complete the table.
5th term
n th term
[9 marks]
13
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 10a
The sequence of diagrams above is made up of small lines and dots.
Complete the table.
Diagram 1
Diagram 2
Diagram 3
Diagram 4
Number of
small lines
4
10
18
28
Number of
dots
4
8
13
19
Diagram 5
Diagram 6
[4 marks]
Question 10b
For Diagram n find an expression, in terms of n , for the number of small lines.
14
[2 marks]
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 10c
Diagram r has 10 300 small lines.
Find the value of r .
r = ..............................................
[2 marks]
Question 10d
The number of dots in Diagram n is an 2 + bn + 1 .
Find the value of a and the value of b .
a = ..............................................
b = ..............................................
[2 marks]
Question 11a
The table shows the first five terms of sequence A and sequence B.
Term
1
2
Sequence A
7
13
Sequence B
1
3
Complete the table for the 6th term of each sequence.
3
23
9
4
37
27
5
55
81
6
[2 marks]
15
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 11b
i)
ii)
Find the n th term of sequence A.
[2]
Find the n th term of sequence B.
[2]
[4 marks]
Question 12a
The table shows the first five terms of sequences A, B and C.
Sequence
A
B
C
Complete the table.
1st term
0
4
-4
2nd term
1
5
-4
3rd term
4
6
-2
4th term
9
7
2
5th term
16
8
8
6th term
[3 marks]
16
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 12b
Find an expression for the n th term of
i)
sequence A,
ii)
[2]
sequence B.
[1]
[3 marks]
Question 12c
Find the value of n when the n th term of sequence A is 576.
n = ...............................................
[2 marks]
17
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 12d
i)
ii)
Find an expression for the n th term of sequence C.
Give your answer in its simplest form.
[3]
Find the value of the 30th term of sequence C.
[2]
[5 marks]
18
By : Terrence De Costa B.Sc(Hons) - 0768580111
Percentages Toolkit
19
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 1
Increase 42 by 16%.
[2 marks]
Question 2
Increase $22 by 15%.
$ .................................................
[2 marks]
20
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 3
A company sells boxes to factories.
Fred buys boxes.
The boxes are sold in packs of 1000
Each pack costs £193.86
Fred orders 3 packs of boxes.
He gets a discount on his total order.
The table shows the discount he will get.
Total Order
£100 - £300
£301 - £400
£401 and above
Discount
5%
10%
15%
Work out the total cost of the order after the discount.
You must show your working.
[5 marks]
21
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 4
Greg sells car insurance and home insurance.
The table shows the cost of these insurances.
Insurance
Cost
car insurance
£200
home insurance
£350
Each month Greg earns
£530 basic pay
5% of the cost of all the car insurance he sells
and 10% of the cost of all the home insurance he sells
In May Greg sold
6 car insurances
and 4 home insurances
Work out the total amount of money Greg earned in May.
[5 marks]
22
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 5
Mr Watkins needs to buy some oil for his central heating.
Mr Watkins can put up to 1500 litres of oil in his oil tank.
There are already 850 litres of oil in the tank.
Mr Watkins is going to fill the tank with oil.
The price of oil is 67.2p per litre.
Mr Watkins gets 5% off the price of the oil.
How much does Mr Watkins pay for the oil he needs to buy?
[5 marks]
23
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 6
The table gives some information about student attendance at a school on Friday.
Number of students
Year
Present
Absent
Total
Year 7
192
16
208
Year 8
219
22
241
Year 9
234
28
262
Year 10
233
28
261
Year 11
214
24
238
The school has a target of 94% of students being present each day.
Did the school meet its target on Friday?
[3 marks]
Question 7
Sean wants to go on holiday.
He is going to get a loan of £720 to help pay for the holiday.
Sean will have to pay back the £720 plus interest of 15%.
He will pay this back in 12 equal monthly installments.
How much money will Sean pay back each month?
[4 marks]
24
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 8
The table gives information about Ali's spending last month.
Percentage of
total spending
30%
15%
12%
43%
Item
rent
food
transport
other
Ali's total spending last month was £800
Next month Ali's rent, in pounds, is going to rise by 20%.
His total spending will still be the same.
Express the amount of money Ali will spend on rent next month as a percentage of £800.
25
[3 marks]
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 9
Bill buys and sells laptops.
Last month Bill bought 50 laptops.
He paid £400 for each laptop.
He sold
40 of these laptops at a profit of 30% on each laptop
10 of these laptops at a profit of 15% on each laptop
Bill's target last month was to sell all 50 laptops for a total of at least £25 000
Did Bill reach this target?
[5 marks]
Question 10
Renee buys 5 kg of sweets to sell.
She pays £10 for the sweets.
Renee puts all the sweets into bags.
She puts 250 g of sweets into each bag.
She sells each bag of sweets for 65p.
Renee sells all the bags of sweets.
Work out her percentage profit.
[4 marks]
26
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 11
The normal price of a television is reduced by 30% in a sale.
The sale price of the television is £350
Work out the normal price of the television.
[3 marks]
Question 12
Claire is making a loaf of bread.
A loaf of bread loses 12% of its weight when it is baked.
Claire wants the baked loaf of bread to weigh 1.1 kg.
Work out the weight of the loaf of bread before it is baked.
[3 marks]
Question 13
Jules buys a washing machine.
20% VAT is added to the price of the washing machine.
Jules then has to pay a total of £600
What is the price of the washing machine with no VAT added?
27
[2 marks]
By : Terrence De Costa B.Sc(Hons) - 0768580111
Question 14
A force of 70 newtons acts on an area of 20 cm2
pressure =
force
area
The force is increased by 10 newtons.
The area is increased by 10 cm2
Helen says,
"The pressure decreases by less than 20%"
Is Helen correct?
You must show how you get your answer.
[3 marks]
28