**9,134**

Simple Addition Question

**8,778**

Simple Subtraction carry. Remember the rules to “borrow” from the next column if needed. So you can’t do 5 minus 7 in the units. You have to borrow 1 (meaning 10) from the tens column in 9,135 revising the equation to 15 minus 7

**2,303**

**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) 1920**

If not sure, write down the initial number, 2020. Then take away 100 from this. Its simply subtraction in words

**b) 220**

2.2 as the starting point. Move decimal 2 places to the right. So this gives 220

**63**

Think about the multiples of 7 & 9 between 60 & 70

**1.006**

If not sure, put all the numbers in a column format. This is exactly the same requirement if you are ranking numbers

0.993

1.006

1.100 (add zeros on so that all the numbers have the same number of digits)

0.940

0.990

**30**

Use the approach of 5/8 * 48/1

Then cross cancellation etc and simplify this to 5/1 * 6/1

Cross cancellation is essential as it makes the calculation far easier overall and reduces error rates

**19.8**

With sequences, the approach is always to look at the sequence of the numbers that are already there. And then work from there. The clue lies in looking at the sequence change and not the underlying numbers. So if you see 0.2,0.2 difference between 20 & 20.2 and then 20.2 and 20.4, it tells you alot about what the answer should be

**a) 31**

Reverse Maths. 87 – 56

**b) 2**

54/6 = 9. Therefore, X + 7 has to be 2

**c) 10,000**

Question on how many places you have to move the decimal. Its 4 places

**52.4, 52.402, 52.42**

Put in Column format if not sure and pay note to whether your starting with smallest or largest first

52.400

52.420

52.402

**11 & 6**

Start with 66 and think of multiples of 66. So 11 & 6

**a) -6C**

Remember its negative so important to read numbers carefully. Also one key point should be to interpret what each dash equates to

**b) -11C**

**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

**2 years 9 months**

Step 1: The way to work these questions is to count up from 5years 8 months to 8 years. So this is 2 years 4 months

Step 2: Add on the remaining 5 months

**a) 11**

2 x 3 + 5 = 11

**b) 13**

2 x 5 + 3

**c) 6**

Work backwards. Output = 23 minus 5 = 18. Divide by 3

**d) 1**

**a) 75g**

150g required to make 8. Therefore, to make 4, it is half of this

**b) See below**

With these questions, its vital to think of HCF. What is the HCF of 8 (in the start of the question) and 20 portions? The answer is 4. Therefore, if you can determine the amount required for 4 Cheesy Pasta’s , you can then calculate the amount required for 20 as it will be x5 what you have for 4 Cheesy Pasta’s

**£2, 50p, 2p & 2p**

£10 – £7.46 = £2.54

**32**

If 24 = 3/4 then he has made 3 of his full amount. So each “portion” is worth 8. Total therefore Denominator x 8

**a)** 24/36 = **2/3**

Remember question is asking for how much he eats. So he used 12 letters. Leaving 24. Always simplify your answer if it doesn’t specify to leave it as the long hand version

**b) 25%**

ALSATIAN letters in common to TERRIER & HOUND are T,I & N. So 12 letters on Marks Plate. Of these, 3 letters can be found in ALSATIAN. So its 3/12 which as a % is 25%

**4.5m**

Freda Frog = 25 x 30 = 750

Teddy Toad = 40 x 30 = 1200

Remember to convert to metres.

**a) 87**

She always tells the truth and the answer has to fulfill each statement. Given that its a multiple of 29 and is <100, its logical to start with going through multiples of 29. So 29,58,87

**b) 60**

She never tells the truth. So:

The number is less than 100. It is a multiple of 10. It does divide by 3 exactly and it has NO remainder when divided by 4.

Think of multiples of 10 and those multiples that divide exactly by 3 and are less than 100. These are 30,60 & 90. Of these the only number that is a multiple of 4 leaving no remainder is 60

**See below**

**a) 7.5 or 7.6cm**

Count up to the nearest whole cm and note this. Then from cm to cm up to 9cm. Finally add on the small amount at the end

**b) 22:12**

It is 24 hour so remember this.

**c) 10:25pm**

If clock is 5 minutes slow, real time is 22.17.

If Sarahs watch is 8 minutes fast, then the time on her watch will be 8 minutes ahead of the real time. So 22:25

Convert t0 12 hour clock as question requests

**a) 12cm²**

Count whole squares first = 11

Partial half squares = 2 halves = 1

**b) See below**

**a) Parallelogram**

*…A rectangle pushed over sideways*

**b) 0**

A parallelogram has zero lines of symmetry

…A square however pushed over sideways, has 2 lines of symmetry (A rhombus)

**c) (2,0)**

Always read X Axis first

**d) See below**

One example of many are below with co-ordinates below of (8,4). Provided you do not use co-ordinates of (5,5) for point E, then any replacement of the X Axis will suffice. So eg (1,4), (2,4) etc all work as does (9,4), (10,4) etc

**a) See below**

**b) 2**

**c) 21**

Go from left to right remembering to include number of children with 2 pairs of shoes

3+5+10+2+1

**d) 56**

Formula as per follows:

(3×1 pair) + (5*2 pairs) + (10 * 3 pairs) + (2 * 4 pairs) + (1*5 pairs)

3+10+30+8+5

**a) 80cm**

Quite a tricky question so key to label like for like sides

X = 13cm. There are 4 of these so thats 13 x 4 = 52cm

Y = 12-5cm (Take away 5 because the height is the central part that is not part of the perimeter. So thats 7 * 4 = 28cm

**b) 30cm²**

Just divide the total by 4

**3.6kg**

Try doing the question in the same metric. So in this case, probably grams is easier to work with

Basket = 500g

Kitten = (600*4) = 2400g

Cat therefore = 6,500g (6.5kg) – 2400 – 500

Total = 3,600g.

Then convert back to KG

**a) B**

Probability (of A) = 2 Black/ 9 Total

Probability (of B) = 1 Black/ 4 Total

If not sure which fraction is larger (and therefore has the greater probability), convert to the Lowest Common Denominator which would give fractions of 8/36 & 9/36 respectively. So B has the greater chance

**b) See below**

**Side = E**

**Plan = F**

**Front = C**

**a) 14 minutes 30 seconds**

Add up minutes first = 4+5+4 = 13minutes

Add up seconds and convert to minutes and seconds = 90 seconds = 1minute 30 seconds

Total = 14 mins 30 seconds

**b) 4 minutes 50 seconds**

Mean = Total /3

So 14 mins 30 seconds / 3

One approach is to convert to seconds and then back to minutes. So (14*60)+30 = 840+30 = 870

870/3 = 290 seconds = 4 minutes 50 seconds

**a) See below**

**b) See below**

**c) 9**

Always one more than the pattern number

**d) 15**

Spot the pattern? Divide lines by 2 to get to the pattern number

**e) 60**

Formula would be : (Dots x 2) – 2 = number of lines. 31 * 2 = 2 = 60

Just read one statement at a time and use it to complete the table where possible

- 35 Boys. Therefore , 45 girls
- 2/3 of girls play stringed instrument. So 45 x 2/3 = 30. Which means 15 do not
- 38 do not play stringed instrument. Therefore, for boys, its 38 – 15 = 23

**a) £2.60**

Questions which mention something is “twice as much as something else” or a multiple of something else, requires a few possible approaches. One is to use ratios. So Cake:Drink is 2:1

There are 3 parts altogether. So £3.90/3 = £1.30 per part

Cake is 2 parts so cost is £2.60

**b) £1.45**

Tea + Fizzy drink = £2.60

Fizzy drink 30p more. So £2.60/2 = £1.30 if it was an equal price. To get a 30p difference, you add 15p to one and take 15p to the other. So Fizzy drink will cost £1.45 and revised cost for Tea will be £1.15

**c) 91p**

A+B = 57p

B+P = 56p

A+P = 69p

Therefore, there are 2 apples, 2 bananas and 2 pairs. If you add all of the above together and x2, you get £1.82

Divide by 2 gives 91p

**M,C,J,D,R**

**D,R,J,C,M**

Another solution or approach is that the middle 2 squares touching a lot of squares have to be 1 and 8 since they have only 1 adjacent number which allows you to put more numbers around them… once you start there, the puzzle virtually solves itself

**35**

Lets count the number of triangles where side of the pentagon is one of the side of the triangle, for each one such side there are 6 triangles. but two of triangle has other side of the pentagon, those will be counted twice so we will count only one triangle for each side, so for five sides, total 5*5 = 25 such triangles.

Now, lets count the triangles where side of the pentagon is not the side of the triangle: there are 5+5 = 10 such triangles

**a) 19**

(5 x 4) -1

**b) 8**

Remember that normally, it would be takeaway 6 on the left hand side. If you take this to the other side, it will become addition. So lets do this:

m ? = 26 + 6

m ? = 32. So given its ? x 4, ? must be 8

**c) 7**

5 ? (4 * 4 – 3)

5 ? – (13) = 5 * 4 – (13) = 20 – 13 = 7

**d) 9**

[(6 X 4) – p ] x 4 = 56

[24 – p] x 4 – 4= 56

96 -4p-4 = 56

-4p=56-96+4

-4p = -36

p=9

**29**

He has **20** bars which means he gets 6 free bars. So 20/3 = 18 Remainder 2

He then has **6** free bar wrappers + 2 reminder = 8 bars

He then uses these 8 wrappers to get 2 free bars and this also leaves a remainder of **2**

Then he uses the 2 remainder + 2 new wrappers he gets from the 2 free bars to get **1** more bar

So total is 20 + 6+ 2 + 1