5,632

## Difficulty Rating

1/10

#### Question 2

4,556

Simple subtraction question

## Difficulty Rating

1/10

#### Question 3

4,781

Simple multiplication question

## Difficulty Rating

1/10

#### Question 4

494

Use bus stop method

## Difficulty Rating

1/10

#### Question 5

a)0.569

Move decimal 2 places to the left when going smaller.

b) 2.007

1997 + 10

Write it out as a maths operations question per above

## Difficulty Rating

3/10

#### Question 6

36 & 64

Think of all the square numbers over 64….

81,100,121,144,169

36 + 64 = 100

## Difficulty Rating

3/10

#### Question 7

27

3/8 * 72/1 = 3/1 * 9/1 = 27

## Difficulty Rating

3/10

#### Question 8

0.603

Ranked smallest to largest below ## Difficulty Rating

3/10

#### Question 9

87

The trick always with sequences is to look number change v number. So from 100 to 93, its minus 7.

From 82-78 its minus 5. So the 1st sequence was minus 7. The 4th sequence was minus 4. This means that its possible the second sequence is minus 6 because there are 2 sequences between 1st and 4th. It looks like the sequence is going down in 1s. This would take us to 87

## Difficulty Rating

4/10

#### Question 10

12 & 5

Think first of multiples of 60.  6 * 10, 12 * 5, 30 * 2, 60 * 1. And so on. The answer being 12 * 5 since 12 -5 gives 7

## Difficulty Rating

4/10

#### Question 11

a) 38

BIDMAS. Do the multiplication first. 7×9 = 63. So, 63 – ? =25. Rearrange. -?=25-63. -?=-38.

b) 9

64/4 = 16. 16= ?+7

c) 10

36 = 16 + (2 x?). Rearrange. 36-16 = 2x?.  20/2 = ?

You can always substitute the numbers back into the equations to ensure your answer is correct

## Difficulty Rating

5/10

#### Question 12

3/4

Count the number of triangles = 20

Shaded = 15/20 = 3/4. Always simplify unless otherwise stated

## Difficulty Rating

4/10

#### Question 13

£1.79

£10 – £3.85 = £6.15. So if she received £4.36 change, the muffin was £6.15 – £4.36 = £1.79

## Difficulty Rating

4/10

#### Question 14

a) -10C

-4-6 = -10

b) +9C

-4 to + 5 is a change of +9

## Difficulty Rating

5/10

#### Question 15

a) 876,512

b) 876,215

c) 2,568

The Rule for 6: The prime factors of 6 are 2 and 3. So for a number to be divisible by 6, it must also be divisible by 2 and 3. Therefore, we need to check if a number is even and then check if the sum of the digits is divisible by 3.

d) 6,198

Largest 4 Digit Number is 8765. Smallest 4 Digit Number is 2567. Difference is

## Difficulty Rating

7/10

#### Question 16

a) 27

540 ÷ 20

b) 50ml

20ml is added to 4 litres of water. Therefore, think in HCF of 4 & 10. This is 2. So first calculate 2 litres which would be 10ml. Therefore, 10 litres would be 5 * 10ml = 50ml

c) 3 weeks

6 litres of water would be 30ml of Kleeno per day. Therefore if a bottle contains 540ml, this would be equivalent to:

540 ÷ 30 = 18 daily cleans.

Given that the floor is cleaned every day apart from 1 day, then 1 week is 6 days of cleaning. Therefore this represents 3 weeks of cleaning

## Difficulty Rating

6/10

#### Question 17

31

The number would have to start and end with an odd number because every even number apart from 2 is not a prime number. So the first one would be 31

## Difficulty Rating

4/10

#### Question 18

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

## Difficulty Rating

7/10

#### Question 19

a) 8

Hattie = 12. Therefore, Imogen = 12. This is 24 in total. If 24 represents 3/4, then each quarter is 24/3 = 8. Total sweets would have been 32. Georgia therefore took 8

b) 3/8

12/32 = 6/16 = 3/8

## Difficulty Rating

5/10

#### Question 20

£2.65

250g bags cost £3.90 each. So 1kg = £15.60

100g costs £1.85. Buy 6 bags and he gets 3 free. This equals 9. Therefore, he has to buy 7 bags in total

7 * £1.85 = £12.95

Saving is £15.60 – £12.95

## Difficulty Rating

6/10

#### Question 21 ## Difficulty Rating

7/10

#### Question 22

8.3cm

3.8cm to 12.1cm = 8.3cm

## Difficulty Rating

3/10

#### Question 23 ## Difficulty Rating

4/10

#### Question 24

a) E b) D

Perimeter – A = 16; B = 18; C = 18; D = 20; E = 12

c) See below d) See below ## Difficulty Rating

6/10

#### Question 25

a) 9 hours

The key to note here is that the shape is split into 12. So its a Dodecagon. Each line represents 2 hours of the day. Sleep occupies 4 1/2 lines so in total, that is 4.5 * 2 = 9 hours

b) 1/3

Working = 8 hours. So as a fraction , its 8/24 = 1/3

c) See below ## Difficulty Rating

5/10

#### Question 26

a) D Even

24 = 3G :2B :1R

Therefore, if there are “6” equal shares, then each share = 24/6=4

Green = (3*4) = 12. So 12/24 = 50% chance

b) E

Not Blue = Green or Red. This is (3*4) + (1*4) = 16/24 = 2/3rds

c) A

No yellow counters so zero chance

## Difficulty Rating

5/10

#### Question 27

a) 20 minutes 20 seconds

In total its 19 minutes and 80 seconds = 20 minutes 20 seconds

b) 5 minutes 5 seconds

(20 minutes 20 seconds)/ 4 . If not sure, do the minutes first which is 5 minutes average. Then do the seconds which is 5 seconds average

c) 6 minutes 14 seconds

Range is the difference between the highest and lowest times. (8 minutes 17 seconds) less (2 minutes 3 seconds) = 6 minutes 14 seconds

## Difficulty Rating

4/10

#### Question 28

a) & b) See below c) Square

## Difficulty Rating

6/10

#### Question 29

a) See the diagram below

b) (5,4) c) 17.5cm²

Area: Point A (1,5); B (4,9); C (8,8); D (5,4)

2 Triangles in effect with ABD & BCD.

ABD Area – A to midpoint BD is 3.5. Base is 5 for B to D (co-ordinate for Y axis for B of 9 less co-ordinate for D of 4)

So area of ABD = (1/2 * 3.5 * 5) =  15.75 * 2 = 8.75. * 2 as there are 2 triangles = 17.5

## Difficulty Rating

8/10

#### Question 30

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

## Difficulty Rating

5/10

#### Question 31 For these styles of questions, its vital to SENSE CHECK your answer. Its relatively easy to go back to your workings and ensure what you have done is correct

## Difficulty Rating

6/10

#### Question 32

7

jj = jupiterian jellyfish

Summarise the question in algebra format. It will make it easier to solve. Total Tentacles:

(jj x 25 ) + (20 – jj) * 8 = 279

25jj + 160-8jj = 279

17jj + 160 = 279

17jj = 119

jj = 7

## Difficulty Rating

8/10

#### Question 33

a) 21cm

6 x 3.5cm = 21cm

b) 63cm

Pattern 2 has 3 sides per hexagon on the outside. So its 18 sides altogether. 18 X 3.5

c) 19 hexagons

Pattern 3 will require 12 additional hexagons. 1 hexagon will cover 2 of the outsides and the next one 1 outside of pattern 2. And so on. So it will be 1+6+12 (Pattern 1 + Pattern 2 + Pattern 3)

d) 105cm

30  sides will be showing for Pattern 3 on the outside. So 30 * 3.5

## Difficulty Rating

6/10

#### Question 34

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

## Difficulty Rating

9/10

#### Question 35

a) 555

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

## Difficulty Rating

7/10

#### Question 36

a) See below b) The pattern that is there at present (1,4,9,7,7,9,4,1,9) continues to repeat. The way to test this is to apply the same digital root test for 10², 11², 12² and you will see the pattern continue

c) 1

d) 4

e) 9

1. A number that is a perfect square never ends in 2, 3, 7 or 8. If your number ends in any of those numbers, you can stop here because your number is not a perfect square.
2. Obtain the digital root of the number. The digital root essentially is the sum of all of the digits. If you’re lost, don’t worry, we’ll go over each step in more detail below.
3. All possible numbers that are a perfect square have a digital root of 1, 4, 7, 9.

## Difficulty Rating

9/10

#### Question 37

a) 14

A diagonal is a line that connects two non-adjacent corners. All polygons, except for the triangle, have a number of diagonals. The formula to find the number of diagonals is n(n – 3)/2, where n is the number of sides the polygon has

b) 54

So using the above formula, 12(12-3)/2 = (144-36)/2 = 108/2

## Difficulty Rating

10/10

#### Question 38

a) 14

(4 * 5)- (2 * 3). Just substitute the numbers in the formula remembering to add brackets

b) 7

Rearrange the formula. k – (2*3) = 29

29 – – 6 = k

35 = k. Therefore, given you have to multiply by 5 to get to k, k must be 7

c) -3

Calculate as per part a by substituting values into the formula remembering to rearrange

d) 13

10/10