14,002
10,034 + 3,968. Write in Column format to ensure you align digits correctly
6,646
Remember to borrow as you cannot do 4 minus 8 in the units column so you have to borrow from the tens and so on.
578
Simple multiplication question
318
Use bus stop method
12 & 3
Think of factors of 36 in order to solve
90
^{Work out as 2}/_{7} * ^{315}/_{1}
Simplify this to ^{2}/_{1} * ^{45}/_{1}
Far easier to then calculate
3.025 3 1/4 3.34 3 3/4
Try and convert all numbers to the same metric if possible. So in this case, lets convert all the numbers to decimals.
3.25 3.34 3.75 3.025
It becomes far easier to rank smallest to largest then
290cm
Remember the question is asking for the difference in cm. So :
3.2m = 320cm. Less 30cm = 290cm
Usually easier to convert everything to cm as the question is asking for this denomination
20
Calculate the Right hand side first which gives 12. Then re arrange. Take “8” over to the right hand side from left so it becomes a positive. So 12 + 8 = 20.
11, 12.5
With sequences, its vital to look at the change number on number. So 5 up to 6.5 is +1.5. Then 6.5 to 8 is +1.5 etc
The pattern becomes clear. So 9.5 +1.5 = 11. 11+1.5 = 12.5
a) 7538
b) 13785
a) 750g
With these types of questions, ALWAYS think of HCF. So for 12 cookies, you need ingredients per above. For 30 you need…..
Well you take the HCF of 12 & 30 which is 6.
Step 1: Calculate what you need for 6 cookies first. 12 cookies requires 300g so 6 requires 150g plain chocolate.
Step 2: 30 is a multiple of 6. So take what you had for 6 cookies and * by 5. To give you chocolate for 30 cookies. So 150g * 5 = 750g
b) £2.70
26p x 30 = £7.80. Less £5.10 cost = £2.70 profit
£18
50 calls @ 17p per call = £8.50. Plus £9.50 for the fixed charge
E 11yrs 4months
M is younger so she will be 7 years 6months
If unsure, count forward in years and months from your answer to be sure
5,575
Work backwards and reverse the signage to get to the starting point
5745 +67 – 237
a) 45minutes
Ensure you look at the depart Ludlow row. This means the train departs at 0845 and arrives at Shrewsbury at 0930. This is 45minutes
b) See below
12
If ^{3}/_{5} were eaten and this represents 18, then each ^{1}/_{5} is equal to 6. (18/3). Therefore, there were 30 sweets to start with and 12 remain uneaten
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
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
a) ^{4}/_{11}
5G, 2Y, 4P
b) ^{5}/_{9}
If 2Y is removed, it leaves 5G+4P.
E & A have one line of symmetry
20
If we draw a grid of 3×4, you would have 12 small squares (each grid space) of size 1×1.
Then we could produce 6 medium squares of size 2×2 (we could produce 4, 2×2 squares from each corner and then 2, 2×2 squares using the centre two squares and the 2 centre squares on the 4 length edge).
Finally, we could produce 2 large squares of 3×3 by starting at each corner.
a) 15/23
 Consider total area of shape = 23 squares
 Shaded area is equal on all 3 sides. Each side has 5 shaded squares
 Total shaded area = 15/23
b) See below
 16 triangles in total
 3/4 shaded = 12/16 shaded
c) i) Shape A DOES NOT have a greater fraction shaded than Shape B
 Shape A – 10 squares altogether. 2/10 shaded = 1/5th shaded
 Shape B – 16 squares altogether. 4/16 shaded = 1/4 shaded
c) ii) Shape B DOES have a greater fraction shaded than Shape A. (Inverse of the statement for i). So this is the right statement
c) iii) This is NOT CORRECT
a) 30º
 Yellow + Purple is a right angle so is 90º
 Therefore, Yellow is 30º
b) 25%
 100% for the pie chart. Therefore, Red occupies 1/4 of this.
 100/1 * 1/4
c) 90

 ^{180}/_{360} * ^{180}/_{1}
 This is 180 degrees/360 degrees * 180. The equation above can be simplified and you should always do this
 ^{1}/_{1} * ^{90}/_{1}
 Area of the shape is 18 full squares + 7 other squares from partially filled squares
 Total area = 25 squares
20cm
 Very Standard style question where you are given the area and have to work out the perimeter.
 x * 4 = 24cm² would give the area. So rearrange this. Where x = Length. 4 is Width
 24/4 = x
 x = 6
 So if x = 6, the solution is [(2 * 6) + (2 * 4) ]
a) 2
b) 1
c) 13
1+3+4+2+1+2
C
 Non Verbal Reasoning question so follow just one part of the pattern at a time
 The dots are moving clockwise. So 1 opposite 2 becomes 3 in the next segment. Then it becomes 2 opposite 1. So the next logical pattern is 3 in the first quartile segment. Answer is B or C
 Next look at the ++. These go anticlockwise 90º at a time. Next logical box is 2nd quartile
 So answer is C
B & D
Imagine you have to draw a shape on a piece of paper, which can be cut out and folded into a cube. On the paper you will draw the six squares that will fold up to make the six sides of the cube. Can you imagine the shape you would draw on the paper to make the cube?
It is not easy to do, as this imaginary exercise requires two important mathematical skills – mental visualisation (being able to ‘see’ with your mind’s eye a twodimensional [2D] or threedimensional [3D] mathematical image) and mental transformation (being able to ‘manipulate’ or change that image in some way)
a) 2.6cm
 Diameter being from one side to the other of the coin. So diameter will be the same all the way round the coin
 On the left hand side, the marker is at 1.7cm. On right hand side it is at 4.3cm. Therefore, difference is 2.6cm
b) 21:24
Remember 24 hour clock is 13:00 when it is 1.00pm on a 12 hour clock
c) 52kg
Each marker is 1kg on the kg scale
5 cubes
 Tall Cube. Number of cubes is W * L * H. This equals 2 * 2 * 8. = 32
 Small Cube. Number of cubes is W * L * H. This equals 3 * 3 * 3 = 27
C
 This is similar to a prior question in this paper where we talked about visualisation and nets.
 The image is on the top left and if you unfold it and open it up, there will be a box on each edge. So its B or C
 There will be a triangle on each page so it has to be C
a) 7 squares
 There are 2 patterns at play here. Firstly, the shapes alternate. So circle, x, square, plus sign etc. So the next shape will be a square
 Second pattern is that the number of each shape increases by 1. So 1 circle, 2 x, 3 squares etc. So the next one will have 7 squares
b) + sign
 This is because after adding the squares above per a), this takes you to 28 shapes. The next shape will be 8 + symbols. So number 30 will be a + sign
a) 12
b) 13
 Meera always tells the truth. Given this, David is 12. Since he said he was 13 and he never tells the truth.
 Meera is 11 since David is older than Meera
 Anne has to therefore be 13
a) See below
b) 21
 Its important to recognise the relationship.
 So with 9 Dark Squares, there would be (2*d) + 3. This is the pattern there for 1 to 5
 So for 9 it will be (2 * 9) + 3 = 21
c) 10
 You have to work backwards given W=(2*d) + 3
 Given w=23, 23 = (2d) + 3. Rearrange to 233 = 2d
 20=2d. So d must equal 10
d) 31
 If a pattern has 45 squares in total so again the trick is to recognise the pattern that derives the total
 First calculate dark. So Dark = (Total/3 – 1 ). = 45/3 1 = 14
 Given this, white must equal (2*d) + 3 = 31
a) 30º
 Acute means an angle < 90º. So this is when the hour handle is at 12 and minute handle at 1.
 12 numbers on a regular clock so each one is 30º. (360/12)
 Therefore, at 1 O’Clock, its 30º
b) 15º
 At 6.30pm, the hour handle is exactly in the middle between 6 & 7. The Minute handle is at exactly 6.
 A move from 6 to 7 would be 30º
 So half of this is 15
6
Xp + Yp = 38. Where X = 4 page letter and Y = 3 page letter
 Some points to remember. The 3 page letter number of penpals should be an even number of penpals. This is because a 4 page letter * any number of penpals will always given an even number. Therefore, the 3 page letter can only be * 2, * 4, * 6 or * 8.
 The answer is * 6 (So 6 * 3 = 18) + (5 * 4 = 20) = 38
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
a) 2
b) 5
c) 11
 With this question, you have to work backwards by each statement
 “He eats one more and gives the last one to Sean”. So before he did this, he had 2
 “He then eats another and then shares the rest out equally between himself and Detti”. So if he shared equally per sentence 2, then he had 4 before he ate one to start with. So this gives 5
 “He eats one and then shares the rest out equally between himself and Emily”. He had 10 before he ate one at the start of sentence 4. So he had 11
a) B E C
b) A E C & C A D
c) 14 different ways