Year 8 Christmas Revision Sheet
Number and Arithmetic
Sequences
Set 1 and 2
1) Write the following in ascending
order:
1) Write down the first 5 terms given by
the following nth terms.
0.801, 0.807, 0.825, 0.8, 0.8045
a) 4n+3
2) Work out the value of:
2) The nth term of a sequence is 5n-2.
3) Paul grows apples in his garden. He
picks 25 apples. The table below shows
information about their weight. Draw a
frequency polygon showing the
information in the table.
a) 21×10
a) Find the 6th term
c) 8.78×1000
e) 945÷100
b) 6.3×100
d) 235÷10
f) 13.9÷1000
3) Work out the value of the following.
Show working out:
a) 541×37
b) 6.56×16
4) Work out the value of the following.
Show working out:
a) 560÷16
b) 40.5÷9
b) 7n-5
b) Find the 20th term
3) Find the nth term of the following
sequences:
Weight (w) in g
30≤w<40
40≤w<50
50≤w<60
60≤w<70
70≤w<80
Frequency
1
6
8
7
3
a) 1, 5, 9, 13, 17
Algebra
b) 8, 5, 2, -1, -4
1) Solve the following equations. Show
each line of working out.
Sets 1 and 2
4) Find the next 2 numbers in the
following sequences:
a) 4x=28
c) 3x+2=20
𝑥
b) = 8
4
d) 5x-3=27
5) Evaluate the following:
a) 1, 3, 6, 10, 15
a) (-6)+(-4)
b) 14-(-5)
b) 256, 128, 64, 32, 16
2) Solve the following equations. Show
each line of working out.
c) 8×(-12)
d) (-6)×(-7)
c) 1, 3, 27, 81, 243
a) 3(5x-10)=45
e) 90÷(-9)
f) (-84)÷(-7)
Statistics
6) Evaluate the following:
a) 4+7×8-3
b) 9×(12-7)÷3
Set 1 and 2
a) 13×10
b) 13×0.1
c) 13×0.01
d) 13×0.001
e) 13÷0.1
1) The table show the favourite drink
for 20 pupils in a primary school. Draw
a bar chart showing the information in
the table.
Food
Milk
Fruit Juice
Vimto
Tea
Other
Frequency
4
6
5
3
2
f) 13÷0.01
8) Evaluate the following:
a) 5×33-7×5
3) Simplify the following:
a) 9x+8-7x+5
b) 9x+12y+8x-3y
2
2
c) 8x +2x+4x -6+5x+8
4) Expand the brackets:
a) 4(5x+2)
7) Work out the value of:
b) 50-4×(2+32)
b) 7x+2=3x-30
b) 3x(2x-6)
c) (x+4)(x+6)
5) Factorise the following:
a) 12x-9
b) 8x2-24x
Set 1 and 2
2) The table below show the favourite
football teams for 40 pupils in a school
in London. Draw a pie chart. Label
each sector and show the angles.
Team
Chelsea
Arsenal
Spurs
West Ham
Other
Frequency
12
9
8
5
6
6) Expand the following brackets:
a) 6(3x-4)
c) (x+9)2
b) (x+7) (x-2)
7) Factorise the following:
a) 5x-20
c) x2+8x+15
b) 6x2+18x
d) x2-6x-27
Angles
Ratio
1) Find the size of the lettered angles:
1) Cancel down the ratios.
150°
65°
60°
a
65°
b
a) 25:10
d
c
e
130°
b) 50:45
c) 24:30
2) Write each ratio in its most simple
form.
a) 45 seconds:2 minutes
2) Write down the value of the lettered angles and give a reason for each.
b) 30cm:2m
3) Mike is mixing flour and sugar in the
ratio 4:3. If Mike uses 21 g of sugar
then how much flour does he use.
75°
b
4) Divide £270 in the ratio 5:4
a
5) An IPad normally costs £320. The
IPad is reduced by 30%. What is the
new cost?
c
3) Find the size of the missing angles.
6) Peter bought a house and then sold
it for £234000. He made a 30% profit.
How much did he pay for the house?
c
e
d
85°
65°
75°
a
b
70°
f
4) Think about a regular octagon. Work out the following:
a) The sum of the internal angles.
b) The size of one internal angle.
c) The size of an external angle.
Answers
Approximations
1) Round the following to the number
of decimal places shown in brackets:
a) 5.264 (2dp)
b) 1.289 (1dp)
c) 2.99 (1dp)
d) 4.2699 (3dp)
2) Round the following to the number
of significant figures shown in brackets:
a) 7190 (1sf)
b) 5.08 (2sf)
c) 0.0629 (1sf)
d) 0.004597 (2sf)
3) Estimate the value of the calculation
shown below:
5.12 + 4.89
12.1 − 5.99
c) 40mins:1hour
Number and Arithmetic: 1) 0.8, 0.801, 0.8045,
0.807, 0.825 2) a) 201 b) 6300 c) 8780 d) 23.5
e) 9.45 f) 0.0139 3) a) 20017 b) 104.96
4) a) 35 b) 4.5 5) a) -10 b) 19 c) -96 d) 42
e) -10 f) 12 6) a) 57 b) 15 7) a) 130 b) 1.3
c) 0.13 d) 0.013 e) 130 f) 1300 8) a) 100 b) 6
Sequences: 1) a) 7, 11, 15, 19, 23 b) 2, 9, 16,
23, 30 2) a) 28 b) 98 3) a) 4n-3 b) -3n+11
4) a) 21, 28 b) 8, 4 c) 729, 2187
Algebra: 1) a) x=7 b) x=32 c) x=6 d) x=6
2) a) x=5 b) x=-8 3) a) 2x+13 b) 17x+9y
c) 12x2+7x+2
4) a) 20x+8 b) 6x2-18x
c) x2+10x+24
5) a) 3(4x-3) b) 8x(x-3)
6) a) 18x-24 b) x2+5x-14 c) x2+18x+81
7) a) 5(x-4) b) 6x(x+3) c) (x+5)(x+3) d) (x-9)(x+3)
Angles: 1) a) 55 b) 80 c) 65 d) 115 e) 115
2) a=75 alternate b=105 Interior
c=75 corresponding
7) Sam invested £800 in a bank paying
4% simple interest each year. How
much did Sam have after one year.
Set 1 and 2
8) Paul invested £1500 in a bank paying
3% compound interest each year. How
much did Sam have after 2 years.
9) Sarah bought a table for £150 and
then sold it the next day for £200.
What percentage profit did she make?
10) Paul has a box of red and blue
pens. The fraction of the contents that
are red is
3
10
.
a) What fraction are Blue.
b) What is the ratio of red to blue pens.
Answers continued
Angles: 3) a) 30 b) 75 c) 30 d) 110 e) 70
f) 110 4) a) 1080 b) 135 c) 45
Ratio: 1) a) 5:2 b) 10:9 c) 4:5 2) a) 3:8
b) 3:20 c) 2:3 3) 28g 4) 150:20 5) 224
6) 180000 7) £832 8) £1591.35 9) 33%
10) a) 7/10 b) 3:7
Approximations: 1) a) 5.26 b) 1.3 c) 3.0
d) 4.270 2) a) 7000 b) 5.1 c) 0.06
d) 0.0046 3) 5