Make x the subject of the formula
y = 2x + 9
Show answer
See the working
| y | = | 2x + 9 | ||
| -9 | y - 9 | = | 2x | -9 |
| ÷2 | y - 92 | = | x | ÷2 |
x = y - 92
20 mixed questions from 7 Year 7 topics, 50 marks. It covers fractions, decimals and percentages to ratio and proportion, the second third of the year in the order schools usually teach it.
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Make x the subject of the formula
y = 2x + 9
| y | = | 2x + 9 | ||
| -9 | y - 9 | = | 2x | -9 |
| ÷2 | y - 92 | = | x | ÷2 |
x = y - 92
Ben's rent is £240 each week.
His rent is increased by 35%.
Work out Ben's new weekly rent.
| 10% of £240 | = | £24 |
| 30% of £240 | = | 3 × 24 |
| 30% of £240 | = | £72 |
| 5% of £240 | = | £12 |
| 35% of £240 | = | 72 + 12 |
| 35% of £240 | = | £84 |
| New rent | = | 240 + 84 |
| New rent | = | £324 |
£324
Write down the ratio 45 cm : 1.5 m in its simplest form.
Same units first
| 1.5 m | = | 150 cm |
45 : 150
| HCF of 45 and 150 | = | 15 |
Divide both parts by 15
3 : 10
3 : 10
The nth term of a sequence is 20 − 4n
a)
n = 1: 20 - 4 × 1 = 16
n = 2: 20 - 4 × 2 = 12
n = 3: 20 - 4 × 3 = 8
n = 4: 20 - 4 × 4 = 4
16, 12, 8, 4
b)
20 - 4 × 10 = 20 - 40 = -20
-20
Oliver expands 4(3m − 2) and writes
4(3m − 2) = 12m − 2
Explain the mistake Oliver has made and write the correct answer.
The 4 multiplies BOTH terms
4 × 3m = 12m
4 × 2 = 8 (Oliver forgot this)
12m - 8
A bottle contains 850 ml of juice.
34% of the juice is orange juice.
Work out how many millilitres of orange juice are in the bottle.
| 34% | = | 0.34 |
| Orange juice | = | 0.34 × 850 |
| Orange juice | = | 289 |
289 ml
Ella and Ravi share some sweets in the ratio 3 : 5
Ravi gets 12 more sweets than Ella.
How many sweets do they share altogether?
difference = 5 - 3 = 2 parts
2 parts = 12, so 1 part = 6
total = 3 + 5 = 8 parts
8 × 6 = 48
Check: 18 and 30, 30 - 18 = 12
48 sweets
The grid is made of 100 equal squares. Some of the squares are shaded.
a) count the shaded squares
| 3 × 10 + 7 | = | 37 |
per cent means out of 100
37%
b)
| 100 - 37 | = | 63 |
63%
c)
| 37% | = | 37100 |
| = | 0.37 |
0.37
The nth term of a sequence is 5n − 3
a)
| 12th term | = | 5 × 12 - 3 |
| 12th term | = | 60 - 3 |
| 12th term | = | 57 |
57
b)
| 5n - 3 | = | 122 | ||
| +3 | 5n | = | 125 | +3 |
| ÷5 | n | = | 25 | ÷5 |
25 is a whole number
Yes, it is the 25th term
Write these numbers in order of size, starting with the smallest.
25 0.44 39% 14
Change all to decimals
| 25 | = | 0.4 |
| 0.44 | = | 0.44 |
| 39% | = | 0.39 |
| 14 | = | 0.25 |
0.25 < 0.39 < 0.4 < 0.44
14, 39%, 25, 0.44
Write these numbers in order of size, starting with the smallest.
0.3 725 31% 38 0.295
change them all to decimals
| 725 | = | 28100 |
| = | 0.28 | |
| 31% | = | 0.31 |
| 38 | = | 3 × 0.125 |
| = | 0.375 |
compare with 3 decimal places
0.300 0.280 0.310 0.375 0.295
725, 0.295, 0.3, 31%, 38
Make x the subject of each equation.
a)
| x + 5 | = | y | ||
| -5 | x | = | y - 5 | -5 |
x = y - 5
b)
| x - 3 | = | p | ||
| +3 | x | = | p + 3 | +3 |
x = p + 3
c)
| 4x | = | t | ||
| ÷4 | x | = | t4 | ÷4 |
x = t4
The nth term of a sequence is 6n − 1
Write down the first three terms of the sequence.
Substitute n = 1, 2, 3
| 6 × 1 - 1 | = | 5 |
| 6 × 2 - 1 | = | 11 |
| 6 × 3 - 1 | = | 17 |
5, 11, 17
Expand and simplify 2(x + 5) + 3(x + 1)
| 2(x + 5) + 3(x + 1) | = | 2x + 10 + 3x + 3 |
| = | 5x + 13 |
5x + 13
Amy is x years old.
Ben is 5 years older than Amy.
Chloe is twice as old as Amy.
a)
5 years older: add 5
| Ben | = | x + 5 |
x + 5
b)
Twice as old: × 2
| Chloe | = | 2 × x |
| Chloe | = | 2x |
2x
a)
Collect x terms
| 8x - 3x | = | 5x |
| Collect the numbers | ||
| 5 + 2 | = | 7 |
5x + 7
b)
Multiply the numbers
| 2 × 5 | = | 10 |
| Multiply the letters | ||
| g × g | = | g2 |
10g2
A plumber charges a fixed call-out fee of £40 plus £28 for each hour of work.
The plumber works for h hours on a job.
The total charge for the job is £C.
Write a formula for C in terms of h.
£28 for each of h hours
| Hourly part | = | 28 × h |
| Hourly part | = | 28h |
Add the £40 call-out fee
C = 40 + 28h
5 packets of football stickers cost £3.50
Work out the cost of 8 packets of the same stickers.
1 packet = 3.50 ÷ 5 = £0.70
8 packets = 8 × 0.70 = £5.60
£5.60
Three friends compare their scores in a science test.
Put the friends in order, starting with the highest score.
You must show your working.
change them all to percentages
| 1720 | = | 85100 |
| = | 85% | |
| 0.84 | = | 84% |
Leah 85%, Grace 84%, Omar 82%
Leah, Grace, Omar
Asha thinks of a number, n.
She multiplies her number by 4 and then subtracts 7. Her answer is 25.
a) × 4, then - 7, equals 25
4n - 7 = 25
b)
| 4n - 7 | = | 25 | ||
| +7 | 4n | = | 32 | +7 |
| ÷4 | n | = | 8 | ÷4 |
n = 8
Answer the questions above and your score appears here.
Every question here is original and written by Robinson Tuition, drawn from the Year 7 topic worksheets. It follows the Key Stage 3 programme of study.