**2+4+7**

Picking up 8 is a good move as it means he can win on the next hand with different numbers rather than just relying on one number

Robin will win the game because on the next move. This is because he can win with more permutations of the remaining cards than Susan. Eg Robin could pick up a 1 or 3 and win the game as an example. Susans options are limited

**D**

Add up all of the heights which comes to 221,642. Then divide by the number of instances which is 8

Nearest is D 27,700

**A**

Go in 3 stages per below

21:20 to 22:00 = 00:40

22:00 to 06:00 = 08:00

06:00 to 06:15 = 00:15

Add them up to get 08:55

**C**

6+7 = 13 minutes marking.

13+2 = 15 minutes marking + checking

15 * 28 = 420minutes

**420/60 = 7 hours**

**D**

Numbers going up in 9s. So next will be 72 and 81

**A**

Add up all of the numbers and divide it by the number of instances:

So answer is 69

**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) Louise**

**b) 6kg**

41-35

**c) Gillian & Fatima**

**d) 3**

Jeannie, Sarah & Fatima

**e) 11 months**

**f) 224kg**

37+41+35+38+34+39

**g) See below..**

**a) 15**

99-84

**b) 9**

63 – 54

**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

**a) 14**

**b) Bus**

**c) 41**

Bicycle 9; Bus 2; Car 14; Lorry 6; Motorbike 3; Van 7

**3/10 or 0.3**

3 green/ total number of crayons

**a) 5**

Mode is the most common/frequent number in the sequence

**b) 5**

Mean is the average of all of the numbers once added together. Total/Number of numbers

So 50/10

**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**

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

**72cm**

(15 * 4) + (3*4) = 60 + 12

**a) 2**

Mode is the most common number

**b) 15**

Range is highest – lowest

**c) 4**

Mean = Average. Add up all of the numbers and divide by the number of instances

40/10

**13/40**

- You have 1/4 shaded of the first square. 2/5ths shaded of the second square
- This is a question of being able to convert both fractions to the same denominator
- So this would be 20. 1/4 becomes 5/20 and 2/5ths is 8/20
- Then add both these together to get 13/40. Note its not 13/20 as you have to add the squares together which is unlike a normal fraction addition

**a) 39**

1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39

**b) 23**

23 & 25

**c) NO. 42 is not in the sequence**

Going up in 3s. So next is 20,23,26,29,32,35,38,41,44

**d) To be updated**

**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**

**25**

1 + 2 x 3 x 4 = 25

**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

**a) 4mins**

Sally less Anna

**b) 80mins**

15 + 17+ 14+ 18+ 16

**c) 16mins**

80/5

**d) 1km**

Peter took 15mins. If its 4km/h he walks, then after 15mins, he walks 1km

**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) 8.52am**

8.15am + 37mins = 8.52am

**b) 5.46pm**

6.23pm – 37mins.

Slightly harder to calculate so take off 23mins first to get to 6pm. This leaves 14mins (37-23). So then take 14mins off 6pm

So 5.46pm

**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

**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

**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

**64cm**

Perimeter = 14+3+4+6+7+2+17+11

**11/35**

- Convert to the lowest common denominator which is 35
- So 2/5s becomes 14/35 and 2/7s becomes 10/35
- Add together so 24/35
- This leaves 11/35

a) See below. **1.52**

Convert to the same metric. So in this case, its better to convert to decimals

**b) 0.3**

For this, you should use reverse bus stop. So 70 goes outside the bus stop with 21 inside.

Then add zeros on so that you can work out the answer to 2 decimal places

Then change the answer by the number of decimal places you added. So if you added 2 zeros, then your answer of eg. 70 would become 0.7

**120**

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

**a) 1.32**

0.75+0.4+0.17 = 1.32

Convert 2/5 & 17/100 to decimals

**b) 16**

Use the approach below which is “reverse bus stop”

**74**

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

**a) 0.24**

6/25 = 24/100 = 0.24

**b) 1.20**

Convert all to decimals

So 0.35 + 0.6 + 0.25

**70**

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

**a) 8 minutes**

Mode is most common number.

**b) 6 minutes**

Range is highest less lowest. 10 – 4

**c) 7 minutes**

Mean is Average. So add up all the times and divide by number of times

35/5 = 7 minutes

**d) 1 minute**

If mean is 6 and there are 6 days on record, then the total number of minutes late is 6 * 6. Remember , mean= total/number of instances. So 6=total/number of instances

So 36 – 35 = 1 minute

**e) Bus was not late on the other days as the mean is 4 and number of days is 9. So 36 minutes late in total which is the same as the end of day 6**

**a) 7 hours 45 minutes**

- With time questions, always work on going to the next key mark. So see below for the illustration:
- 22:45 – 23:00 = 15minutes
- 23:00 – 06:00 = 7 hours
- 06:00 – 06:30 = 30 minutes
- Then add together = 7 hours 45 minutes

**b) 17:20**

- London to Hong Kong = 22:45 + 11 hours 35 mins
- Time would be 10:20
- But Hong Kong is 7 hours ahead. So time would be 17:20

**10:40**

- Difference between 9am and 11am is 2 hours.
- Your dealing with ratios here 5:1. So 6 parts
- If you have 2 hours this is 120 minutes and each part is 20 minutes
- So 5 of these are 100 minutes. 1 part is 20 minutes
- So 100 minutes has passed which would mean 9am + 100mins = 10:40am

**a) 7**

Mode is the most common number. This is 7

**b) 8**

8+7+11+6+9+7 = 48

48/6

**c) 5**

Range is highest minus lowest

**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)

**11**

- 24 people. 4 got off so this left 20. X people got on
- Assume zero got on for now at the last stop
- Second stop . 20 with 3 people getting on leaving 23
- If there were then 34 people, it means 11 people got on at the first stop

**2 cucumbers**

- 5 tomatoes = 2 pounds weight = £3.00 cost
- So green peppers they bought 3 = 40p x 3 = £1.20 cost
- If they got 20p change and spent £4.20, then 60p was spent on cucumbers
- 60p/ 30p = 2 cucumbers

**1.25**

- 0.012 + 1.238 = 1.250

**a) 45**

- May is 14 and her father is 53
- Mays mother is therefore 45

**b) 16**

- If 5 marbles cost £7.50, then 10 would cost £15. 15 would cost £22.50
- Each marble costs £1.50
- So remaining £1.50 to take you to £24 would get you 1 marble
- Total number being 16 marbles

**-8C°**

- -12C + 4C as it increases for Tues-Fri

**£5.50**

- A+B+C = £19.70
- 2nd £7.50, 1st £5.50, 3rd £6.70

**Cubes 14**

**Triangular Blocks 6**

**42**

- Work through the multiples and add on the remainder where necessary
- 4 – So multiples with 2 added on would be 6,10,14,18,22,26,30,34,38,42
- 5 – So multiples with 2 added on would be 7,12,17,22,27,32,37,42
- 6 – 6,12,18,24,30,36,42,48

**a) 9.30am – 11.30am**

9 hours back from 6.30pm is 9.30am. From 8.30pm its 11.30am

**b) 6pm**

USA 4am means 9am UK time.

UK is 9 hours behind Australia so the time then in Australia will be 6pm

**£1.11**

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

**Cheese £5.30**

**Bananas £0.90**

**Chocolate £1.12**

Total Cost £7.32

**Change = £2.68**

**6**

By second hand, the question is referring to the seconds handle that moves around the clock

Therefore, if its pointing to 2, after one minute it will still point to 2 as it will go around 360 degrees

Add on 20 seconds which represents 4 numbers on the clock (12 numbers = 60 seconds so 1 number move = 5 seeconds)

Therefore add 4 onto 2 to get 6

**a) x=-65**

x+80=15

x=15-80

**b) y=11**

6y=46+20

6y=66

y=11

**c) g=9.8**

10g+15g = 645-400

25g = 245

g=9 20/25

g = 9.8

Use BIDMAS

**£20.90**

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

**3**

- Work backwards
- 38 + 7 =45
- 45 /15 = 3

^{13}/_{24}

- Convert to Lowest Common Denominator
^{ 9}/_{24}+^{4}/_{24}^{13}/_{24}

**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

**5.75kg**

- Total weight is best done by converting into common metric. So lets say kg

**5.25kg**

a) 5

b) 26

c) 112

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

**a) 10**

Mean is average. So its 17+12+8+16+2+5+10 = 70 / number of instances = 70/7

**b) 15**

Range is Highest – Lowest

**c) 14**

If mean is 10, then work backwards. Mean = Total/number of instances

This means 40 = Total/4

So total has to come to 40 and therefore, missing number is 40-5-7-12

**a) 1/3**

**b) 7/8**

**c) 1/3**

**d) 6 4/7**

**a) 672**

**b) 264**

**c) 1,081**

**d) 843**

**A**

- 10:28 to 11:00 is 32 minutes
- 11:00 to 16:00 is 5 hours
- 16:00 to 16:06 is 6 minutes
- Add them together gives 5 hours 38 minutes

**B**

- 180 – 25 – 107 = 48

**B**

- Go 09:34 to 10:00 = 26 minutes
- Go 10:00 to 13:00 = 3 hours
- Go 13:00 to 13:21 = 21 minutes
- Total is therefore 3 hours 47 minutes

i) The warmest day at midday was **Friday**

ii) The coldest day at midday was **Thursday**

iii) Sunday temperature was **+4C** (-1 + 5)

**10kg**

- Add up all of the numbers
- 3+6+9+22+28+1+6+5 = 80
- 8 sharks so average weight is 10kg

**a. £22.50**

- 2 Adults = £6.25 * 2 = £12.50
- 4 Children = £2.50 * 4 = £10.00
- Total = £22.50

**b. 8 children**

- 4 adults = £5 * 4 = £20.00
- Remaining is £24
- £24/£3 = 8 children

**7,11 & 39**

- The multiples of 13 are 13,26,39,42,55
- The different factors of 77 are 1,11 and 7
- Answer is 7,11 & 39 = 57

**-16 & +4**

- Six less than -10 is working backwards on the number line. So -16
- Twelve more than -8 = -8+12 = +4

**116cm**

- Number of days = 5
- Height sunflower grows is (68 – 48) = 20cm
- Per Day growth therefore = 4cm
- Taking 21st August through to 2nd September = 12 days
- Therefore, growth during this period is 48cm
- Adding on the height as of 21st August of 68cm = 116cm

**28th July**

- Work Backwards. 4cm per day = 12 days
- Therefore, 12 days from 16th August 4th August
- Then take a week off this and you get 28th July

**11,908,368**

- Just add on 123
- 11,908,245 + 123

**25**

- 17J + 8C = 25 sweets
- If even chance of a toffee, then there must be 25 toffees

**36**

8, 12, 16

Use the inverse operation of 17 * 11 = 187

**E**

Use substitution of values:

Orange costs 10p, Apple costs 5p

A – 35p (2 x 10p) + (3 x 5p)

B – 35p

C – 35p (1 x 10p) + (5 x 5p)

D – 35p (3 x 10p) + (1 x 5p)

E – 40p

Put numbers in a neat column format