Key Stage 4 Higher Tier – How much do you know?
1.
(a)
Write 28 as the product of its prime factors. Give your answer in index form.
(3)
(b)
Find the least common multiple (LCM) of 28 and 42.
(2)
2.
(a)
Here is a list of numbers.
3
18
22
49
51
56
58
68
(i)
Which two numbers from the list add up to 100?
(1)
(ii)
Which two numbers from the list are multiples of 7?
(2)
(b)
Explain how you know that 62 is not divisible by 7.
(1)
3.
Which of these fractions is closest to 1 ?
4
You must show your working.
2
5
3
10
7
20
13
40
(Total 3 marks)
4.
David has 72 balloons. He shares them between his 3 friends in the ratio 4 : 3 : 2
How many balloons are in the largest share?
(Total 2 marks)
5.
You are given that 2x3 = 250 Find the value of x.
(Total 2 marks)
6.
Work out
(a)
2 1
×
5 4
(1)
(b)
0.4 × 0.2
(1)
(c)
3
2
2 ×5
(2)
(d)
4
2
3
+1
3
5
(3)
(Total 7 marks)
West Exe Technology College
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4.
Tom says
Sam says
64 is a square
number
Tom and Sam are both right. Explain why.
...............................................................................................................................................
...............................................................................................................................................
(Total 2 marks)
5.
Work out
(a)
2 1
×
5 4
......................................................................................................................................
......................................................................................................................................
(1)
(b)
0.4 × 0.2
......................................................................................................................................
(1)
(c)
3
2
2 ×5
......................................................................................................................................
(2)
(d)
4
2
3
+1
3
5
......................................................................................................................................
......................................................................................................................................
(3)
(Total 7 marks)
6.
Which of these fractions is closest to 1 ?
4
2
5
3
10
7
20
You must show your working.
13
40
................................................................................................................................................
................................................................................................................................................
(Total 3 marks)
West Exe Technology College
2
7.
Which of these fractions is closest to
1
4
1
?
3
3
8
4
9
7
24
You must show all your working.
..............................................................................................................................................
..............................................................................................................................................
(Total 3 marks)
8.
David has 72 balloons.
He shares them between his 3 friends in the ratio 4 : 3 : 2
How many balloons are in the largest share?
...............................................................................................................................................
...............................................................................................................................................
(Total 2 marks)
9.
(a)
4x – 5x + 7x
Simplify
.....................................................................................................................................
(1)
(b)
Simplify
(i)
x5 × x–2
...........................................................................................................................
(1)
(ii)
y5 ÷ y–2
...........................................................................................................................
(1)
(c)
Expand and simplify (4x – 3) (x + 5)
.....................................................................................................................................
.....................................................................................................................................
(3)
10.
(a)
0
Write down the value of 11
......................................................................................................................................
(1)
(b)
Find the value of 8
2
3
......................................................................................................................................
(2)
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(c)
Simplify 6
–2
× 144
0.5
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(3)
11.
(a)
y=
You are given the formula
5+ x
x
Rearrange the formula to give x in terms of y.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(b)
24
Simplify (3xy ) .
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
12.
(a)
(i)
x
Find the value of x in 4 =
1
16
...........................................................................................................................
...........................................................................................................................
(1)
(ii)
y
Find the value of y in 8 = 2
...........................................................................................................................
...........................................................................................................................
(1)
2
(b)
Write down the value of 27 3
.....................................................................................................................................
.....................................................................................................................................
(2)
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