**20p**

£10 = 1000p

1000/70 = 980p so 14 full cookies. Leaving 20p change

**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

**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

**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) 0.09

b) 0.05

c) 0.375

If not sure, you can use “reverse bus stop”. So for example, calculate per below:

**a) £5.41**

**b) 0.732**

**c) 3.3125**

**24**

Do inverse which is 624/26 = 24

**16**

48/3 = 16

**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) 5**

**b) 3**

(2×3)/2

**c) 22**

(3×6)+(2*2)

Substitution

**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**

**a) 20mins**

Use HCF & LCM. Work on the normal basis that 3 is 1/3 of 9. So if 9km = 1 hour, 3km = 1/3rd of 1 hour

**b) 2km**

1/4 of the 8km/h = 15mins. So this is 2km

**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

**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**

**17**

130/8 = 16.25

Cannot buy 0.25 of a packet so need to buy 17 packets

**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

**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

**6.9**

Make 62.1 to 621 to remove the decimal

Then work through and you 69. Then add the decimal back in to get 6.9

**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) 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

**1.08**

- Sometimes, these questions can be done in 2 parts. First 6/6 and then 0.48/6
- 6/6 = 1
- 0.48/6. Treat this is 48/6 = 8.
- Then move 8 2 decimal places to the right. So 0.08
- So answer is 1.08

**8.6**

One way to tackle this is to initially remove the decimal so to do 602/7

Then use bus stop. Then remember to divide your answer by 10 as you added in one zero

**a) 7hours 27mins**

10.17pm – 11.00pm = 43minutes

11.00pm – 05:00am = 6 hours

05:00am – 05:44am = 44minutes

43mins + 6hours + 44mins

**b) 800kmph**

5600km/7 hours = 800km ph

**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

**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)

**8**

- Work backwards. So 192/3 = 64
- 64 square root = 8

**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

**80cm**

- 9 identical squares with area of 144 means square has an area of 16cm
- Each square must be 4×4
- Number of sides showing on the shape above if you count all the way around as a perimeter is 20
- So perimeter is 80cm

**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

**28%**

- 7/25. To convert to a % you can do reverse bus stop
- So this would be per below:

**£208**

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

**8**

- Convert £ to pence
- 300/36 = 8.33
- So 8 full bars

**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

**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

**3**

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

**2**

- 170/24 = 7 remainder 2
- Teacher eats 2

**£15.96**

Buy 2 get 3rd free so only pay for 2

**£5.32**

£15.96/3 to get equivalent price per bottle

**100°**

- At 4:40, hour hand will be 2/3rds of the way between 4 and 5
- Minute handle at 40
- So each hour or number on the clock is 30°
- From 4:40 to 5:00 the degree angle is 10°
- From 5:00 to 8 (Which is for 40 mins), the angle is 3 x 30 – 90°
- Add 10 degrees per note 4 and you get 100

**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

**20 students**

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

**65°**

- Triangle = 180°
- 180 – 50 – 130
- 130/2 = 65

**8m**

- Area is LxW
- So working backwards, 72=9xW
- Rearrange. W=8

**a) 52**

5 x 10 + 2

**b) 127**

5 x 25 + 2

**c) 67**

Work backwards. 337 – 2 = 335

335/5 = 67

**d) Van = 2.5 metres; Car = 1.8 metres**

Additional 5 metres = 2 vans

Van = 2.5m

If a van is 2.5metres, then using the first jump of 14 metres, we take 2 vans off this which is 5 metres leaving 9 metres.

Per car, this will be 9 metres/ 5 cars = 1.8m

**33**

- Use division so you get 6240/192 = 32.5
- So we need 33 trips

**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) 3.7**

(3.5+3.9)/2 = 7.4/2

**b) 1.55**

(1.3+1.8)/2 = 3.1/2

**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) 127cm**

Convert to cm. 214-87

**b) 25 bags**

290/12 = 24.2

Round up as you need to cover the “0.2” requirement. So 25 bags

**a) 672**

**b) 264**

**c) 1,081**

**d) 843**

**44 stickers**

- Use division as a starting point
- So 60/15 = 4
- 55/5 = 11
- Multiply the 2 to get 44 stickers

**a) 49cm**

Length of cane that snapped off is 2.05m = 205cm minus 156cm

Converting all to cm makes the question much easier

**b) 14**

Would need 14 = 168m²

13 would give 156m² so not quite enough

**D**

- If the pen costs 50p more, then the way to start with this question is to assume they cost the same
- This would be 55p each
- Then take the difference of 50p and split it into 25p and 25p
- Add 25p to the pen and take 25p from the pencil
- So the pen would be 55p + 25p = 80p

**25**

- 5 litres = 5000ml (1 litre = 1000ml)
- 5000/200 = 25

a) **4 & 58** which would give an answer of 232

b) **30** ( 120/4)

**10kg**

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

**275g**

- Always convert to the same metric. That will make this style of question easier
- So if the total is 1.25kg, its 1250g
- 1250g less the large can of beans of 425g = 825g
- Therefore, 3 small cans = 825g
- This would be 275g per can

**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

- Division question with a small twist
- See notes above….Need bus for the remainder of people as well so answer is 20 not 19

**6**

- Can use bus stop and x each number by 10. So 5s into 30 instead
- This is 6

**QUESTION 3….After 10 days**

**3 metres per minute**

- Use Distance/Speed. So this would be 400m/800m per minute = 0.5 seconds
- If the tortoise needs to travel 1.5meters, then it will need to run at 1.5/0.5 seconds = 3

- Use bus stop method.
- 1590/122 = 13 remainder 4

**£23.95**

- £167.65/7
- Remove the decimals to make it 16775 divided by 7
- Then work bus stop
- Then move your answer by 2 decimal places as you multiplied the number inside the bus stop by 100 from 167.75 to 16775

**30**

- You can do this a few ways. 0.2 x 5 gives 1
- Then you multiply 5 by 6 = 30. So 30 times
- Or you x both numbers by 10 so you remove the decimal.
- Then its how many 2s go into 60
- Bus stop method
- The second approach is better because when you get numbers such as 0.3, the maths becomes more awkward with option 1

Use the inverse operation of 17 * 11 = 187

**3 Hours**

If it takes 4 people 6 hours, (24 man hours) then 8 people will take half this time.

**10 Hours**

twice the length = 48 hours.

48/5 = 9.6 which is near enough to 10 hours

**19**

75/4 = 18.75

Answer is 19 not 18. Because you need 19 boxes to ensure all 75 cakes are stored

**£4.20**

- Work on HCF route. 12 eggs and 18 eggs
- HCF = 6. Therefore, first calculate what 6 eggs costs
- If 12 costs £2.80, 6 costs £1.40
- Therefore, 18 would be 3x what 6 costs. So £4.20

See below

**45km**

1817 – 1747 = 30 minutes. If train travels 90km/h, it will travel half this distance in 30 minutes

**1917**

Detailed workings to follow

**23**

Very easy to use the bus stop method for this question

**£1.64**

- Use the HCF Principle. This always works if there is a HCF
- So the HCF of 9 & 12 is 3. Find the cost of 3 bananas first
- This is £1.23 / 3 = £0.41 for 3 (divide by 3 because there are 3 lots of 3 in 9)
- For 12 bananas, the cost is £0.41 * 4 = £1.64

**a) 45,670**

**b) 8,101**

- 4567 x 5 x 2
- (40,505 / 25) x 5

**23**

- Its just a division question…….in words
- Use bus stop

**38**

Use Bus Stop method if needed

**a) 8g**

- If each tea leaves weighs 0.008g, then multiply this by 1000 to get weight of 1000 tea leaves
- Move the decimal place 3 places (number of zeros after the 1) to the right. 1000x.008g
- This would give 8

**b) 125,000**

- The number of leaves = 125 x 1000

**c) 100**

- A tea bag = (250 x 0.008) + 0.5g = 2.5g
- 250/2.5g = 100

**a) 300ml**

8 * 150ml = 1,200ml

- Always worth converting everything to the denomination in which the answer is required.
- So 1,5 litres = 1,500ml.
- 1,500ml – 1,200ml = 300ml

**b) 6 full jugs**

- 2 Litres * 5 bottles = 10,000ml.
- 10,000 / 1,500 = 6 full jugs = 9,000ml.
- There will be 1,000ml remaining/ left over
- Read the question carefully as it asks for FULL jugs

**a) 6**

500/78 = 6 (remainder 32p). £4.68 spent therefore

**b) 4**

32/8 = 4

**a i) 80**

**ii) 23**

Work backwards. 120/4 = 30. 30 minus 7 = 23

**b) x2 -6 OR -3 x2**

**1.5**

1/10 * 5 = 0.5 (Move decimal one place to the left when dividing

1/5 of 10 = 2

So difference is 1.5

**a) 2040**

Move the decimal 2 places to the right when multiplying

**b) 1050**

- You can do the inverse operation here and multiply 1000 x 1.05 to get to the answer
- If not sure, then do the calculation in 2 parts:
- 1000 x 1 = 1000
- 1000 x 0.05 = 50 (Remember 0.1 = 10% = 100. So 0.05 = 5% = 50)
- Then add both numbers together

**a) 9**

Work backwards. 47 – 2 = 45. 45/5 = 9

**b) 48**

Work backwards. 5 + 3 = 8. x 6 = 48

**c) 12**

(50-x)/2 = 19

50-x = 38

x=12

**d) 8**

100 – (x + x) = 36

x² = 100 – 36

x² = 64

x = 8

See below

**Ensure BIDMAS rules are applied**

**a) 24**

- Give that Cats = 48 = 120º
- Hamsters = 60º. Therefore, they are half of cats = 24

The true way to look at this question is to say if 120º = 48, then what is the HCF of 60 & 120. This is 60. Therefore, take the 120 and say how many 60s go into 120. This is 2. Therefore, 60 = 24

**b) 60**

- Cats 120º + Hamsters 60º + Other 30º = 210º
- Remainder is 360 – 210 = 150º
- Again, HCF principle. Given you know 60º = 24, what is 150º?
- HCF = 30. So 30 is half of 60 so it equals 12
- Then how many 30s into 150 = 5
- Therefore 5 * 12 =
**60**

**£10.50**

- Ratios. Josie:Holly = 3:1
- Given its 4 shares and £42 in total, each part is worth £10.50
- Therefore Holly has £10.50

- The easiest way to complete these questions is to think about the HCF multiple.
- Look at how many cupcakes you have ingredients for. Its 8. You need to complete for 12.
- HCF of 8 & 12 is 4. Therefore, if you work out the ingredients for 4 cupcakes, then you can multiply up by 3x to get to 12
- So for 4, its half of what is required for 8
- So butter would be 75g.
- x3 would give you butter for 12 cakes etc

**0,0,1,1**

**a) 11 balloons**

- Always best to convert to the same denomination.
- If she has a 4metres, then this is 400cm. Each string 35cm, then the total is 400/35 = 11.4
- Total number of balloons = 11

**b) 15cm**

- 11 balloons would take 11 x 35cm of string
- This is 385cm
- Therefore, 15cm is left over

**30**

A classic question on the concept of fractions. If Ravi is left with 12 sweets and this equals 2/5, then you have to calculate what 1/5 equals. This is 12/2 so it equals 6 sweets

Therefore, each 1/5 = 6 sweets. There were therefore 30 sweets to start with in the box

**536**

Use bus stop method if needed

**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) 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

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

**a) 50**

- Substitute into the “rules” per the example. So this would give (10 x 10) / (1 + 1) = 100/ 2 =
**50**

**b) 5**

- First solve (3☺4) = (4×4) / (3+1) = 16/4 = 4
- Then (4☺5) = (5×5)/ (4+1) = 25/5 =
**5**

**c) 7**

- Have to solve with algebra. 6 ☺ y = (y x y ) / (6 + 1) = y² / 7
- So y² / 7 = 7. Therefore, rearranging,
- y² = 7 x 7 . So y² = 49
- Therefore ,
**y =7**

Change from £5 = £5-£1.39 = **£3.61**

55p + 84p = £1.39

500g of Sugar. £1.10 per kg. Therefore 500/1000 = 1/2 so 1/2 * £1.10 = 55p

750g of flour. £1.12 per kg. Therefore 750/1000 * 112/1. Think of HCF though. The HCF of 750 *& 1000 is 250. Therefore, given you know what 1000g (1kg) costs, you can work out 250g.

This would be £1.12/4 = 28p per 250g

So 750g of flour = 28p * 3 = 84p

**36 coins**

For every 2p there is a 5p. Therefore, a 1:1 ratio. Together, its 7p. So its 126/7 = 18 “sets of” 2p and 5p pieces

In total therefore, 18 * 2 = 36 coins

**318**

Use bus stop method

**a) 555**

Given 6*37 answer and 9*37, 15 * 37 will be these 2 answers added together

**b) 888**

(9*37 + 3*37) * 2

**c) 499.5**

(9*37)*3 = 999.

999/2

**d) 962**

(6*37) * 4 = 888. So this is 24 lots of 37. To get another 2 lots of 37, you take 1/3 of the answer for 6 * 37.

So 222/3 = 74. Then 888 + 74

**a) 20**

W 10 – 5 =X + 5 = Y * 2= 10 + 10 = Zoe

**b) 2**

Work backwards: Zoe calls out 4. Take away 10 as she added 10 to the number. This gives minus 6. Therefore, Yana must have had minus 3. Xanthe must have had 2.

**c) 6.5**

If Yana whispers 3, she was originally given 1.5. Xanthe must have had 6.5 from Wendy

**d) 0**

**e) 9**

**f) 16**

**8cm**

If Square area is 36cm², then each side is 6cm. Perimeter is therefore 24cm. Given the perimeter of the triangle is the same, each side of the triangle must be 24/3 = 8cm

**a) 1224**

Will be half of 2448 . So 1224

**b) 2496**

Will be 48 greater than 2448. So 2496

**c) 2.448**

The numbers moved by a combined 3 decimal places. So move the decimal place in the original answer by 3 places

**d) 51**

Do 2448 ÷ 48 = 51. Then move decimal place 1 place to the left. This is because you multiplied 24.48 x 100 and 4.8 x 10. Therefore, the difference is 1 decimal place to adjust the number by

494

Use bus stop method

**a) 5**

10T = 18 papers per teacher over the 3 hour timeframe. Which equals 6 papers per teacher per hour

To mark 90, requires total of 15 hours. Therefore 5 teachers

10/180 * T/90 = (10*90)/180 = T. T=5

**b) 5**

3 x 10 = T x 5 = 30/5

**c) 120**

6 papers per hour * 20 Teachers = 120 papers

**a) 56**

Work backwards. 20 MINUS 6 = 14 MULTIPLY BY 4 = 56

Sense check and work through from 56. 56/4 + 6 = 20

**b) 7.5**

6/4 = 1.5 + 6

c) even and multiples of 4

**d) 48**

18 minus 6 = 12. Multiply by 4 = 48

**e) 216**

Work backwads twice. 9 MINUS 6 = 15 X 4 = 60. Then again. 60 minus 6 = 54 x 4 = 216

**a) 11**

Work out RHS first = 26. Then rearrange formula if needed. ? = 26 – 15. Therefore ? =11

**b) 5**

2+20 = 27 – ?

BIDMAS

**c) 0.5**

18/3 = 6. ? x 12 = 6. This would bee 0.5

**a) 800**

Move decimal 3 places to the right. So it becomes 800

**b) 3.49**

Move decimal 2 places to the left

**987**

Simple division question

**a) 18**

3=40p. Therefore, number of 40p’s in £2.40. 6 times.

**b) £4.40**

If 3 stickers cost 40p, then 3’s into 33 = 11x . Therefore 40p x 11

**917**

Bus stop method. A great tip is to ensure the answer you get is a whole number. In MOST 11+ questions, the answer will be a whole integer. So if you get for example 916.5 as your answer, go back and check as there could be a small error

**a) 15 laps**

Convert the 6km to m which gives 6000m. 400 into 6000

Remove like for like zeros to make it easier to work through. So it becomes 4 into 60. This gives 15 laps

**b) 13.8km**

Always step by step on what you know:

- Marathon 13.4km
- Running Track 3 laps @ 400m = 1.2km
- Total of the above is 14.6km
- This leaves 42.2-14.6 as the town run. Which is 27.6km
- Half of this town run (as its 2 laps) would give 13.8km per town run lap

a) 9,180

The approach is to take 17 x 2. Given that you already have 17 x 538, its just another 17 x 2 that needs to be added onto the answer. So add 34 to 9146

b) 14,526

The change is from 17 to 27. So just take the difference of 10 and multiply by 538. This is 5380. Add this to the original answer

c) 269

Re-arrange the formula. 9146/17 = 538. So 9146/34 is half of the prior answer

a) See below…

(6×4)-3 = **21**

(33+3) / 4 = **9** (need to work backwards so therefore, reverse the signage)

(-1+3) / 4 = **0.5**

b) **x2 + 2**

Try with the bottom line first as these are positive numbers so slightly easier to work with

**a) 2**

Solve what you can. So 23 x ? = 46. Then re-arrange the formula. ? = 46/23 = 2

**b) 4**

Remember BIDMAS. Solve 5-2 first = 3. So 3 to power of 2 is 3×3 = 9.

13 = ? + 9. Re-arrange to give 4

**c) 9**

2 + 6 = 8

72 ÷ ? = 8. Re-arrange to give 9

**28**

Look at the pattern in the first 2 numbers and the relationship. So 112 to 56. So 56 is half of 112. This tells you that its *possible *that the number is 28. This is confirmed because when you halve this, you end up at 14 as the final number

**787**

Simple Operations Question

704

Similar to a prior question. Try a simpler example to see what happens. 25X4=100. So , substituting this into the question means 100/2=50

The divide by 2 is halving the prior number of 4 because in the question, 100 is halved to 50. Applying this approach, gave us 704 because we take 352 x 2

a) 3/7

The way to look at this is how you would approach a simpler question: Lets say….10+6 = 16. So 16-6=10

Therefore, the same approach says that 3/7ths is the answer. Proven, you can do the following:

25/42 – 1/6 = 25/42 – 7/42 = 18/42 = 3/7

b) 11/12

Same test using Example numbers. 3X7=21. Therefore, 21/3 = 7 .

The examples given above are simply that. Its easier to think of the same principles using examples and then substitute in the real question numbers rather than think of the question as a tricky fractions question and try and work it out.

12

The best way to solve this question is with the use of Algebra. In fact many maths questions where they have someone or something being “X” times more or less than the other, Algebra comes in handy. So lets solve….

2Harsha=1Ravi

2Ravi=1Harpreet

If 42 sweets altogether, then lets work out the total number of “shares” of sweets:

4Harsha+2Ravi+1Harpreet

In the above, you start with Harpreet as being 1 share (or x if you like) and then work through to Harsha

The objective is to get to the number of “shares” to see how many portion you divide the sweets between. Its 7 times

So 42/7 means each share of sweets is worth 6.

Ravi gets 2 shares so he gets 12

i) 10cm

ii) 2 inches

iii) 295cm

i) Calculate number of cm per inch. So 30cm/12.5inches = 2.5cm per inch.

4 x 2.5 = 10cm

ii) Work backwards now that you know its 2.5cm per inch

5cm/2.5cm per inch = 2 inches

iii) cm in 9ft 10 inches

9ft = 30cm (per foot) * 9 = 270cm

10 inches = 2.5 x 10 = 25cm

Total 295cm

47.6

0.392

Standard Operations questions but just moving the decimals. Number of zeros in first qtn is 1, move 1 place to right. Number of zeros in second question being 2, move 2 places to left.

Multiply, move decimal to right. Divide, move decimal to left

£1.20

Can be done a few ways. Easiest way is to think of HCF of 750g and 1kg. This is 250g. Then to work out 250g cost and from there, x by 4

£11

Standard Division question. Use Bus stop method

36

Use Bus Stop method as the easiest approach