**27,427**

41,096

Use Bus stop method. Keep numbers in a neat column format

**2.38m**

- Usually easier to convert to centimetres first and then back into metres.
- So 2.7m = 270cm. Take away 32cm = 238cm
- 100cm = 1m. So move dp 2 places to the right in 238 which gives 2.38

^{2}/_{3}

- Yet another question which requires the possible use of HCF. You are looking at 60 seconds and 40 seconds.
- The highest common factor of 60 and 40 is 20.
- 6o seconds is split into 3 lots of 20. So denominator is 3
- 40 represents 2 lots. So fraction is
^{2}/_{3}

^{3}/_{5} ^{29}/_{45} ^{2}/_{3}

- Convert to the same denominator to make it easier to compare
- Lowest common Multiple of 3, 5 & 45 is 45.
- 2/3 becomes 30/45
- 3/5 becomes 27/45

**0.092**

- If not sure, put the numbers in a column format like below

**63**

Just go through 9x table. 63

**144**

You can take the factor tree route per this article:

https://123tutors.co.uk/finding-the-lowest-common-denominator/

**9,012,213**

Putting numbers in a column format helps with these types of questions

**1,265**

- Madrid to Paris = [(Madrid minus Lisbon ) + (Munich minus Paris)]
- 2,730 – 638 – 827 = 1,265

**a) 5 coins** £2, 20p, 5p, 2p, 1p

**b) £5.44**

2 magazines cost £2.28 * 2 = £4.56.

£10.00 – £4.56

**b) x by 7 and then +3**

**a) 168cm**

^{140}/_{1} * ^{6}/_{5}

**b) 90cm**

^{105}/_{1} * ^{6}/_{7}

**£563**

- There are 3 free adult tickets because you get 1 free adult ticket with every 10 student tickets
- So its 32 student tickets + 1 adult ticket to buy
- (32 * 14) + (15 * 1) = 448 + 15 = 563

**a) 23C**

- Assess what each marker represents. This is 2C
- Therefore, answer is 23C

**b) -12C (Minus 12C)**

**c) 35C**

**d) i) 68F**

20/5 = 4 * 9 = 36 + 32 = 68

**d) ii) 15C**

- Work backwards
- 59F – 32 = 27 / 9 =3 * 5 = 15

**a) 14:05**

08:20 + 3 hours 45mins = 12:05.

Add on 2 hours for time difference so 14:05

**b) 21:00**

19:15 + 3 hours 45mins = 23:00

Take away 2 hours for time difference so 21:00

**a) 66C**

Use a ruler if needed and remember that each marker is worth 2C on the y axis

**b) 4.5minutes**

Draw a horizontal line from 45C and you will see it intersecting the line chart at 4.5mins

**c) 5 mins 48 seconds**

Tea starts at 80C and to get to 40C takes 5mins 48sec (each marker on the x axis is 12seconds)

**d) 46C**

Use a ruler if required to draw a vertical line from the time in the question

**19**

- There is 1 large triangle that is the outer one
- Then the black triangle below
- Then 5 other triangles like the one beneath that (which occupy the equivalent of 4 small triangles)
- Finally 12 small triangles like the ones on the right

**16units²**

- Break it down into 2 parts
- Shape A = 1/2 x Width x Height. So this is 1/2 x 4 x 4 = 8
- Shape B = 2 x 4 = 8

**59**

- When you have 2 pages next to each other in a 64 page paper, the 2 pages will add up to 65.
- Eg 1 & 64 or pages 2 and 63 and so on
- It will be a page towards the back of the paper. So 6 + x = 65
- Therefore, rearranging, 59

**See below**

**a) 15mins**

- 30 mins / 2 = 15 mins if you have 2 hoses

**b) 15mins**

- To fill 10cm, it takes 1 hose 15mins. So to fill 30cm, I need 45mins for 1 hose.
- With 3 hoses therefore, the time is 15mins (45/3)

**a) 18**

- Comedy represents 1/4 of the total pie. This is 25%.
- The pie is worth 72 students in total
- So 1/4 x 72 = 18

**b) 50º**

- 360 – 90 – 160 – 60 = 50

**3/16**

Total number of small triangles is 16. Of this, 3 are shaded

**See below**

16 triangles. Therefore 6 shaded. 6/16 = 3/8

**a) NE**

**b) 135º**

90 degrees to face North from West . Then a further 45 degrees to get to NE

**c) 225º**

- Reflex angle is 360 degrees less the angle from West to NE.
- 360 less 135 = 225

**d) SE**

- 360 degrees in a circle so of the 495, 360 would bring her back to North
- This leaves 135 degrees. Given 8 markers , each marker is worth 45 degrees
- 135/45 = 3 so she
**moves by 3 markers** - This takes her to SE

**a) x = 2cm, y = 6cm**

x = 2cm (8cm – A – B)

y = 6cm (14cm – E)/2

**b) 52cm**

Perimeter starting at point A = 2+6+2+2+2+6+4+14+4+6+2+2

**c) 72cm²**

Area = (14×4) + (2×2) + (6×2) = 56 + 4 + 12

**a) See below**

**b) A Trapezium**

**a) The middle one is correct. This is because the horizontal dots increase in Pattern 1 from 3 to 5 to 7. So next number of horizontal dots is 9. The vertical dots increase from 2 to 4 to 6. So next number of vertical dots is 8**

**a) 10cm**

- This is a classic question and worth remembering the process to tackle these.
- Perimeter is based on 16 sides.
- Given perimeter is 160cm, each side is 160/16 = 10cm in length

**b) 100cm²**

10×10

**c) 1600cm²**

If each Square is 100cm², area of whole figure is 16 x 100

**15p per apple**

2P + 1M = £1.35 (Formula 1)

1P + 2M = £1.20 (Formula 2)

1P + 1M + 1A = £1.00 (Formula 3)

Take:

4P + 2M = £2.70 (Formula 1 * 2)

1P + 2M = £1.20

Therefore, difference is £1.50 and 3P so **each pear costs 50p**

If each pear costs 50p, then substituting into formula 1 gives:

£1.00 (2P) + 1M = £1.35

IM = £1.35 – £1.00

**1 Mango = 35p**

Therefore, given this:

1P + 1M + 1A = £1.00

50p + 35p + 1A = £1.00

1 Apple = **15p**

**a) 5/18**

Given there are 18 parts altogether, ladies who lost their gloves = 5/18

**b) 11 ladies**

If 52 ladies did not lose gloves, 20 did so the total of gloves this represents is 40. If 40 gloves were found then take 29 off this to leave 11 ladies who lost one glove

**24**

- 36 sweets between them. This is a question on ratios:
- D = 1, H = 2 (Because hannah has twice as many has Dominic)
- A = 6 because Abdul has 3 times as many as Hannah
- So 1:2:6. Total parts = 9. Each part is therefore 36/9 = 4 sweets per part
- Total for Abdul = 6 parts * 4 sweets per part

**a) 5**

Applying the rules, = 3 x 3 – 4

**b) 6**

Working backwards, 32+4 =

So 36 = 6 x 6

**c) 9**

Slightly trickier. But you need a multiple of 72 with one option being 9

x² – x – 72 = 0

**A = 8; B = 1; C = 6; D = 4; E = 9; F = 3; G = 5**

Detailed solution to follow

**a) 144**

The last number in Row 12 will be 144. Spot the pattern which is that its the row number squared to equal the last number

**b) 39**

Again the patttern. (Row Number x 2) -1 . So for Row 20, it will be 20 x 2 -1

**c) 10**

Work backwards. Take away 1 and then divide by 2

**d) 91**

**e) 855**