**48cm**

Area of rectangle is 128cm²

So use algebra to solve (remember area of rectangle = LxW)

2x * x = 128 (where 2x = length and x = width. Use 2x given length is twice width)

3x=128

2x²=128

x²=64

**x=8**

So perimeter = (8*4 for the length + 8*2 for the width) = **48cm**

**84**

120 pupils

2/5ths boys = 48 boys (120/5 * 2)

3/4s of boys write in pencil = 48 * 3/4 = **36**

Girls = (120-48)-72

1/3 in pen so 24.

2/3 in pencil so **48**

Total in Pencil = 36 + 48 = **84**

**£450**

£12,000 full price

Discount = 12,000 * 35/100 = £4,200

So reduced price = £12,000 – £4,200 = £7,800

£7,800 less savings of £7,350 = £450

**B**

£120 * 85/100 = £102

**B**

A+C+D = 70%. Therefore, 30% chose B.

If 25% = 320, what does 30% = ?

The approach is to use HCF of 25 and 30 which is 5%. Work out 5% first of 320

This equals 64

Then 64 * 6 (given that 30/5% = 6 times)

Total is 384

**C**

6+7 = 13 minutes marking.

13+2 = 15 minutes marking + checking

15 * 28 = 420minutes

**420/60 = 7 hours**

**C**

9 * 120 = 1080g

**D**

Work backwards. So 95+8 = 103

103-3 = 100

100/5 = 20

**a) £4**

200 x 2p = 400p

**b) £9.50**

150 x 1p + 160 x 5p

**c) See below:**

**d) No part d in question**

**e) £40.60**

£156.50 – (150x1p) – (200x2p)-(160x5p)-(120x20p)-(90x50p)-(55x£1)

£156.50 – £1.50 – £4 – £8 – £2.40 – £45 – £55 = £40.60

**a) £5.41**

**b) 0.732**

**c) 3.3125**

**a) 399**

**b) 3,990**

**c) 4,389**

**24**

Do inverse which is 624/26 = 24

**a) 55%**

100% – 25% – 15% – 5%

**b) 5**

25% of 20 = 1/4 * 20

**12**

Many options here

**a) 15**

99-84

**b) 9**

63 – 54

**a) 20p**

£2.00 – £1.20 = 80p

80p/4 = 20p

**b) 6**

£1.00 = 100pence

100/15=6.67

So 6 whole kiwi fruits

**a) 26**

**b) (32+9+6)=47 * (9-6) = 141 – (9-6) = 138**

**a) 5**

**b) 3**

(2×3)/2

**c) 22**

(3×6)+(2*2)

Substitution

**c**

5 hour walk at 3km/h = 15km

5 hour walk at 4 km/h = 20km

So distance could only be 19km

**a) Twenty-thousand four hundred**

**b) -21**

A + * by a – is always a –

**c) 27**

BIDMAS. Brackets first

**d) 8**

y=16/2 = 8

**e)i) x = 7**

**e)ii) x = 5**

You firstly have -x = -5 which is the same as x = 5

**f) 6**

**g) 1:3**

**a) i) 1/3**

3/9 = 1/3

**a) ii) 30% shaded. Unshaded therefore = 70%**

**c) 50**

10% of 500 = 50.

10/100 * 500

**d) £127.50**

85/100 * 150

Above formula to calculate 15% reduction

**For the above, work backwards. So for example, 250-75 = 175. Etc**

**a) x = 6**

- 3x + 7 =25
- 3x=25-7
- 3x=18
**x = 6**

**b) 8**

- 3f – 2g
- (3*6) – (2*5)
- 18-10

**a) 4**

BIDMAS. Do multiplication first. So 16-12 = 4

**b) 70%**

When converting decimals to percentages, just move the decimal place 2 places to the right. So 0.7 becomes 70.

**c) 0.6**

3/5ths as a decimal. To convert denominator to 100, multiply both numerator and denom by 20. So 60/100 = 0.6

**d) 18**

15/100 * 120/1

e) 20 **–** 10 **/**5 = 18

Do division first according to BIDMAS. Then subtraction. So 20-2 = 18

f) **16+(32/8/2)-1 = 16 + 2 – 1 = 17**

**4,8 & 20**

**He has enough oranges**

- Each orange in the pictogram is 4 oranges
- So 5 oranges above x 4 per picture = 20 oranges
- Plus half of an orange in the pictogram = 2 oranges
- So total number of oranges = 22 oranges
- 1 1/2 litres = 3 x 500ml. So 3 * 7 oranges per 500ml = 21 oranges
- He has enough in oranges

**25**

1 + 2 x 3 x 4 = 25

**78000**

Number of words = 256 * 33 * 9

Estimate = 260 * 30 * 10

= 78000

**B**

Number of grey tiles = 2*n where n=shape number

So for Shape 3, it would be 2*3 = 6 grey tiles

28 grey tiles = 2 * n so n = 14. Shape 14

For Shape 14, white tiles = (n+1) = 15

**A**

Work backwards. 23 – 3 = 20. Divide by 4 and you get 5

**A**

100 is not a multiple of 3

**A**

1680 = 1680

Quick way is you are doubling the 24 to get to 48 on the other side. Then halving the 70 and getting 35 on the other side. So no calculations required in this question

**C**

(22-10+8) / 4

**C**

- 5((6*9)+(7*3)-(8*6))
- This gives 5(54+21-48)
- This gives 5(27)
- Answer 135

**12**

- The first even multiple of 7 is 14. The first prime number is 2
- Therefore, answer is 12

**0.006**

- If not sure, remove the zeros. So make it 20 * 3 = 60 (ie multiply both numbers by the same amount until the zeros are removed. This would be x100)
- Then , because you removed 3 0s, you need to add these back in.
- So the 60 because 0.006

**a) 27**

8 * 9 = 72. Clotted = 27

**b) 6**

To give 42, reverse would be 24. So 4 * 6 = 24

**c) 5 & 7**

Reverse would be 35. So 2 whole numbers would be 5 & 7

**Area = 200cm²**

- If 2x long as wide, then need to calculate each side
- Double length v width means length is 20cm and width is 10
- Area = 200cm²

**a) 160cm**

**b) 168cm²**

**600g**

- 2:1 Flour:Fat
- 900g of pastry required. Given we have 3 parts, therefore each part is 300g
- Flour is 2 parts so 2 * 300 = 600g

**200miles**

- Calais to Paris is 320km. So 320 * 5/8 = number of miles
- 200miles. Can be done in 1 of 2 ways. Per the above or work out 1/8th which would be 40km. Then 5 * 40km = 200m

**a) £102**

10metres would be £10.20 * 10 = £102

**b) 2.5metres**

£10.20 * 2 = £20.40. This leaves £5.10 (£25.50 – £20.40)

£5.10 is exactly half of £10.20. So therefore total is 2.5 metres

**a) 1/15**

- Convert to the same denominator
- So this would mean Tom 3/5 = 9/15 and Jerry 1/3 = 5/15
- In total, 14/15ths has been eaten leaving 1/15

**b) 250g**

- If Tom had 3/5 = 150g, then 1/5 = 50g
- Therefore 5/5 = 250g

**630**

- Calculate by doing 3/4 x 840
- “of” in maths means multiply
^{3}/_{4}*^{840}/_{1}^{Simplified……..3}/_{1}*^{210}/_{1}- 630

**a) 83**

(14*2)+55 = 28+55 = 83

**b) 13**

(9*2) = 18

31-18 = 13

**c) 22**

**d) 0**

So for d), try c = 4 and 4 = 4. This will mean that 4*2 + 4 = 12 and this is equal to 4*2 + 4 as c & d are the same. So c-d or d-c = 0

**£29.90**

- First divide exactly by 2 as if they have 50/50. So this would be £23
- Then take 15% off Miguel and give this to Jon. So the revised share becomes 35% Miguel and 65% Jon
- So £46 * 65/100 =

**462cm**

Large Triangle = 16cm * 3 (all sides same as its equilateral). So 48cm

Middle Triangle = 7cm * 3 triangles * 3 sides (7 small triangles of 1cm each on the horizontal base tells us its a 7x7x7 triangle). So 63cm

Next size Triangle of which there are 3 = 3cm * 3 triangles * 3 sides = 27cm. There are 3 of them so 27cm

Smallest triangle = 36 small triangles all of 1cm per side. So 3cm *36 triangles * 3 sides = 324cm

Total of all of these is 48 + 63 + 27 + 324

**16**

5 numbers with mean 28 = 140 in total (5 * 28)

12 numbers with mean of 11 = 132 in total (12 * 11)

Total = 272

Mean = 272/17

**a) 120**

(17+13)(17-13) = 30 * 4 = 120

**b) 776,000**

(888+112)(888-112) = 1000 * 776 = 776000

**c) 50**

(7.5+2.5)(7.5-2.5) = 10 * 5 = 50

**a) 12.5%**

3 films = 45 degrees

45/360 = 0.125 = 12.5%

**b) 7/24**

Focus on left hand side (so 0,1, & 4 together = 180 degrees)

0 children = 180 degrees – 45 – 30 = 105 degrees

105/360 = 21/72 = 7/24

**120**

- Use BIDMAS
- 20 + (1 x 7) = 27
- (20 + 1) x 7 = 147
- 147-27

**90ml**

- This is indirectly a question on ratios.
- So if you assume for every 10ml consumed by Jane, Alex consumes 15, the ratio is Alex 15:10 Jane
- So 150ml/25 parts = 6
- Alex = 6 *15 = 90ml
- Check would be Jane which is 10 * 6 = 60
- So confirms Alex consumes 50% more than Jane

**15/26**

When doing this type of question, you can’t answer 7.5/13 obviously. So the solution is to double each fraction and “force” a gap

So this becomes 14/26 and 16/26

Answer is 15/26

**74**

- (4+2) x 13 = 104
- 4 + (2×13) = 30
- Difference = 104 – 30

**a) 4**

- Mean of 7 numbers = 12. Total = 84
- If 8th number added and mean is 11, total must now be 88 (8*11)
- So , the number included = 88-84 = 4

**70**

- Use BIDMAS. (7+3) x 11 = 10 x 11 = 110
- 7+ (3×11) = 40
- 110-40 = 70

**a) 8**

- 30 socks – 10 white; 20 non-whites. Of the 20, 2/5th are blue
- So 20 * 2/5 = 8

**b) 6 pairs**

- Of the non-whites, 8 are blue so this leaves 12
- With 12 left, it could make 6 pairs

**18 days**

- 12 cut knees per day for 30 days = 360 cut knees over this timeframe
- To treat 20 boys, (assuming its only 1 knee that is cut per child), then this would be 360/20 = 18 days

**a) £3.10**

- 8 x 35p = £2.80
- If she had 30p left, her total that she had in the first place would be £2.80 + 30p = £3.10

**b) 45p**

- 5 lollipops @ 35p each = £1.75
- £3.10 less £1.75 = £1.35
- £1.35/3 = 45p

a) 30°

Swimming & Golf together are 90°

Therefore, Golf is 90 – 60 =30

**b) 1/8**

Rugby = 45/360 = 9/72 = 1/8

**c) 90**

- Football = 180° – 45° = 135°
- 135/360 * 240/1

**d) 220**

- 1320 * 60/360

**a) to d) below**

**e) See below**

**a) 30°**

180 – Australia – Africa = 180-90-60

**b) 1/8**

45/360 = 9/72 = 1/8

**c) 30**

180/1 * 60/360 = 180*1/6 = 30

**d) 1000**

Degrees for Europe = 180 – USA = 180-45 = 135

1600 * 225/360. Simplified this is 1600 * 45/72 = 15/24

1600/1 * 15/24

**£1.35**

- 15 * 35p = £5.25
- Multipack = £3.90
- Difference = £1.35

**a) 1200mm²**

Area of rectangle = LxW = 60mm x 20mm

**b) 40 triangles**

2 Triangles will joined together have dimensions of LxW = 12mmx5mm. So they form a rectangle

Therefore, in 60mm across, you get 5 “blocks” of 2 triangles. And you can go to a height of 4 blocks

So in total 5 * 4 blocks = 20 blocks. 2 triangles per block so 40 triangles

**c) 1200mm**

Perimeter of 1 triangle = 12+5+13=30mm

Total number of triangles = 40

Total Perimeter =1200mm

**d) 1.2m**

10mm = 1cm

100cm = 1m

1000mm = 1m

**85p**

- 12 * 65p = £7.80
- £7.80 – £6.95 = 85p

**a) 1/8**

45/360. Start off with 5 as the highest common denominator. Although there is a higher one

So 45/360 would become 9/72

Then 9/72 becomes 1/8

**b) 40**

Its the usual formula approach for this:

60/360 * 240/1

Then simplify each fraction (so 60/360 becomes 1/6)

Revised calculation is 1/6 * 240/1. Cross cancel and then multiply from there. See online videos on Youtube for 123tutors for further guidance

**c) 450**

Football is 135°. So 135/360 * 1200

**a) 12**

1/4 * 48/1

**b) 2**

48 * 1/2 = 24.

24 * 1/3 = 8

8 * 1/4 = 2

Remember of in maths means multiply

**267,120**

**742**

**53424**

**26748**

- Add a zero on. So 267,120
- Its rearranging the formula so it becomes 742 = 26712/36
- Double the base answer of 26712 so it becomes 53424
- Add on 36 to the original answer. So its 26712 + 36 = 26748. (ie an extra 1 x 36 since number changes from 742 to 743)

**Area of 1 rectangle = 15 x 5 = 75cm²**

**4 children**

- 56 legs with 3:1 ratio dogs:children
- 12 dogs = 48 legs. 4 children = 8 legs. So thats 56 legs altogether
- For every 3 dogs there are 12 legs. For every 1 child, 2 legs. So leg ratio is 12:2 = 14 legs
- Then work up in 14s to get to 56 which takes you to 48:8
- So 8 legs = 4 children

**20cm²**

Its 10cm length x 2cm height. So 20cm²

**18**

- A=5/8; P=3/8
- Pears therefore = 3/8 * 48/1
- Pears = 18

**18**

- B=2 ; A=5
- If A = 45 turns, it has done 9 times as many as the “base case”
- Therefore, B will also do 9 times as many so its 18 times

**£1.11**

- 3mins * 7p = 21p
- 18mins * 5p = 90p
- Total cost = 111p

**a) 1 hour 25mins**

7.10pm – 5.35pm = 1 hour 25mins

**b) 16 hours 30 mins**

2 hours 45 mins converted to minutes = 165minutes

165minutes * 2 = 330mins

330mins * 3 = 990mins

990mins/ 60mins

**£208**

- £156/6 = £26 per night
- £26 * 8 = £208

**48**

- Do your 3 x 4 times table to find a number in between 41 and 51
- So 12,24,36,48
- Answer is 48

**15**

- 24/1 * 5/8
- Simplified = 3/1 * 5/1 = 15

**6 weeks**

- Per week she gets (79p-44p) profit. So this is 35p per download
- 150 downloads per day = 150x35p = £52.50 per day
- £2000/£52.50 = 38.1 days
- So this is 6 weeks as this is 42 days as she gets paid at the end of each week so you can’t use part a week

**96 tiles**

3metres long and 4m wide = 12m² area

You will get 12 tiles in the width from 25cm tiles (3metres = 300cm. 300cm/25 = 12 tiles)

Across you will get 8 tiles in the length from 50cm tiles ( 4metres = 400cm/50cm – 8 tiles)

12 x 8 = 96 tiles

Use BIDMAS

**a) £27**

Cost = ((8×3) + (3×1)) = 24+3 = 27

**b) 2 adults. 3 children**

Use £25 and work backwards taking off children until you get to a multiple of 8

So £16 would be the number

£25-£16 = £9. So thats 3 children

Leaving £16 so its 2 adults

**£20.90**

- £25.50 x 3 = £76.50
- £1.30 x 2 = £2.60
- Total = £79.10
- Change = £100 – £79.10

**a) 24**

Half of the 48 students so 24

**b) 1/4**

**c) 4**

Pizza is about 1/3 of 1/4.

1/4 = 12 children given 1/2 = 24

So 1/3 of 12 = 4

**25,100 millimetres**

- 25.1metres = 25.1 x 100 = 2,510 centimetres
- 2,510 x 10 = 25,100 millimetres

**858**

- 22 x 39
- 858

**36**

^{15}/_{100}*^{240}/_{1}- Simplify…
^{3}/_{20}*^{240}/_{1} ^{3}/_{1}*^{12}/_{1}- 36

**£15.96**

Buy 2 get 3rd free so only pay for 2

**£5.32**

£15.96/3 to get equivalent price per bottle

**a) £120**

Car Hire £45

Over 200km is 150km extra driven

Cost is £0.5 per km so total cost is 150 x £0.50 = £75 extra

Total cost is £45 + £75

**b) 390km**

Cost for Daryl £140. Less 200km covered for £45.

This leaves £95

Total mileage from this would be 95/0.5 = 190km

Add base 200km so total distance travelled is 390km

**38**

- Triple 16 = 48 points. Double 20 = 40 points
- Total so far is 88 points
- He therefore needs 38 with this final dart

**175**

- To paint houses, 14 days per house x 14 houses = 168 days
- Add 4 days holiday = 172
- Add 3 days sick leave = 175

**20 students**

- Work on basis 6 students = 30°
- Therefore, 2 students = 10°
- So, 100° = 20 students

**9,600cm³**

Volume = length x width x height

Volume = 3.2 x 1.5 x 2

Volume = 6.4 x 1.5

Volume = 9.6 (this is in metres. Convert to centimetres)

**9.6litres**

1 litre = 1000cm³

**321**

**279**

**20**

- It is one extra “21” So 321
- It is one less “21”. So 279
- It is 20

**£6.42**

- If 9 pairs cost £19.26, work out the cost of 1 pair first via division
- This would be £2.14
- Cost of 3 pairs would be £6.42
- Or you look at 9 pairs and 3 pairs. HCF is 3. Just divide the £19.26 by 3

a) 5

b) 26

c) 112

Apply the rules of BIDMAS. Brackets, Indices, Division, Multiplication, Addition, Subtraction

**a) 3.5 hours**

Time = Distance/Speed = 420/120

**b) 180 miles**

Distance = 180miles

120mph so after 1.5 hours, train will travel 180 miles

**72 stickers**

- 80/10 = 8
- 45/5 = 9
- 8 * 9 = 72

**a) 672**

**b) 264**

**c) 1,081**

**d) 843**