**5,632**

Simple addition question

4,556

Simple subtraction question

4,781

Simple multiplication question

494

Use bus stop method

**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

**36 & 64**

Think of all the square numbers over 64….

81,100,121,144,169

36 + 64 = 100

**27**

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

**0.603**

Ranked smallest to largest below

**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

**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

**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

**3/4**

Count the number of triangles = 20

Shaded = 15

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

**£1.79**

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

**a) -10C**

-4-6 = -10

**b) +9C**

-4 to + 5 is a change of +9

**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

**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

**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

**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

**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

**£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

**8.3cm**

3.8cm to 12.1cm = 8.3cm

a) E

**b) D**

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

**c) See below**

**d) See below**

**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**

**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

**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

**a) & b) See below**

**c) Square**

**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

**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

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

**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**

**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

**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**

**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) 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**

- 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.
- 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.
- All possible numbers that are a perfect square have a digital root of 1, 4, 7, 9.

**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

**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**