48cm
Area of rectangle is 128cm²
So use algebra to solve (remember area of rectangle = LxW)
2x * x = 128 (where 2x = length and x = width. Use 2x given length is twice width)
3x=128
2x²=128
x²=64
x=8
So perimeter = (8*4 for the length + 8*2 for the width) = 48cm
84
120 pupils
2/5ths boys = 48 boys (120/5 * 2)
3/4s of boys write in pencil = 48 * 3/4 = 36
Girls = (12048)72
1/3 in pen so 24.
2/3 in pencil so 48
Total in Pencil = 36 + 48 = 84
£450
£12,000 full price
Discount = 12,000 * 35/100 = £4,200
So reduced price = £12,000 – £4,200 = £7,800
£7,800 less savings of £7,350 = £450
B
£120 * 85/100 = £102
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
C
6+7 = 13 minutes marking.
13+2 = 15 minutes marking + checking
15 * 28 = 420minutes
420/60 = 7 hours
C
9 * 120 = 1080g
D
Work backwards. So 95+8 = 103
1033 = 100
100/5 = 20
a) £4
200 x 2p = 400p
b) £9.50
150 x 1p + 160 x 5p
c) See below:
d) No part d in question
e) £40.60
£156.50 – (150x1p) – (200x2p)(160x5p)(120x20p)(90x50p)(55x£1)
£156.50 – £1.50 – £4 – £8 – £2.40 – £45 – £55 = £40.60
a) £5.41
b) 0.732
c) 3.3125
a) 399
b) 3,990
c) 4,389
24
Do inverse which is 624/26 = 24
a) 55%
100% – 25% – 15% – 5%
b) 5
25% of 20 = 1/4 * 20
12
Many options here
a) 15
9984
b) 9
63 – 54
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) 26
b) (32+9+6)=47 * (96) = 141 – (96) = 138
a) 5
b) 3
(2×3)/2
c) 22
(3×6)+(2*2)
Substitution
c
5 hour walk at 3km/h = 15km
5 hour walk at 4 km/h = 20km
So distance could only be 19km
a) Twentythousand 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
a) i) 1/3
3/9 = 1/3
a) ii) 30% shaded. Unshaded therefore = 70%
c) 50
10% of 500 = 50.
10/100 * 500
d) £127.50
85/100 * 150
Above formula to calculate 15% reduction
For the above, work backwards. So for example, 25075 = 175. Etc
a) x = 6
 3x + 7 =25
 3x=257
 3x=18
 x = 6
b) 8
 3f – 2g
 (3*6) – (2*5)
 1810
a) 4
BIDMAS. Do multiplication first. So 1612 = 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 202 = 18
f) 16+(32/8/2)1 = 16 + 2 – 1 = 17
4,8 & 20
He has enough oranges
 Each orange in the pictogram is 4 oranges
 So 5 oranges above x 4 per picture = 20 oranges
 Plus half of an orange in the pictogram = 2 oranges
 So total number of oranges = 22 oranges
 1 1/2 litres = 3 x 500ml. So 3 * 7 oranges per 500ml = 21 oranges
 He has enough in oranges
25
1 + 2 x 3 x 4 = 25
78000
Number of words = 256 * 33 * 9
Estimate = 260 * 30 * 10
= 78000
B
Number of grey tiles = 2*n where n=shape number
So for Shape 3, it would be 2*3 = 6 grey tiles
28 grey tiles = 2 * n so n = 14. Shape 14
For Shape 14, white tiles = (n+1) = 15
A
Work backwards. 23 – 3 = 20. Divide by 4 and you get 5
A
100 is not a multiple of 3
A
1680 = 1680
Quick way is you are doubling the 24 to get to 48 on the other side. Then halving the 70 and getting 35 on the other side. So no calculations required in this question
C
(2210+8) / 4
C
 5((6*9)+(7*3)(8*6))
 This gives 5(54+2148)
 This gives 5(27)
 Answer 135
12
 The first even multiple of 7 is 14. The first prime number is 2
 Therefore, answer is 12
0.006
 If not sure, remove the zeros. So make it 20 * 3 = 60 (ie multiply both numbers by the same amount until the zeros are removed. This would be x100)
 Then , because you removed 3 0s, you need to add these back in.
 So the 60 because 0.006
a) 27
8 * 9 = 72. Clotted = 27
b) 6
To give 42, reverse would be 24. So 4 * 6 = 24
c) 5 & 7
Reverse would be 35. So 2 whole numbers would be 5 & 7
Area = 200cm²
 If 2x long as wide, then need to calculate each side
 Double length v width means length is 20cm and width is 10
 Area = 200cm²
a) 160cm
b) 168cm²
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
a) £102
10metres would be £10.20 * 10 = £102
b) 2.5metres
£10.20 * 2 = £20.40. This leaves £5.10 (£25.50 – £20.40)
£5.10 is exactly half of £10.20. So therefore total is 2.5 metres
a) 1/15
 Convert to the same denominator
 So this would mean Tom 3/5 = 9/15 and Jerry 1/3 = 5/15
 In total, 14/15ths has been eaten leaving 1/15
b) 250g
 If Tom had 3/5 = 150g, then 1/5 = 50g
 Therefore 5/5 = 250g
630

 Calculate by doing 3/4 x 840
 “of” in maths means multiply
 ^{3}/_{4} * ^{840}/_{1}
 ^{Simplified……..3}/_{1} * ^{210}/_{1}
 630
1596
a) 83
(14*2)+55 = 28+55 = 83
b) 13
(9*2) = 18
3118 = 13
c) 22
d) 0
So for d), try c = 4 and 4 = 4. This will mean that 4*2 + 4 = 12 and this is equal to 4*2 + 4 as c & d are the same. So cd or dc = 0
£29.90
 First divide exactly by 2 as if they have 50/50. So this would be £23
 Then take 15% off Miguel and give this to Jon. So the revised share becomes 35% Miguel and 65% Jon
 So £46 * 65/100 =
462cm
Large Triangle = 16cm * 3 (all sides same as its equilateral). So 48cm
Middle Triangle = 7cm * 3 triangles * 3 sides (7 small triangles of 1cm each on the horizontal base tells us its a 7x7x7 triangle). So 63cm
Next size Triangle of which there are 3 = 3cm * 3 triangles * 3 sides = 27cm. There are 3 of them so 27cm
Smallest triangle = 36 small triangles all of 1cm per side. So 3cm *36 triangles * 3 sides = 324cm
Total of all of these is 48 + 63 + 27 + 324
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) 120
(17+13)(1713) = 30 * 4 = 120
b) 776,000
(888+112)(888112) = 1000 * 776 = 776000
c) 50
(7.5+2.5)(7.52.5) = 10 * 5 = 50
a) 12.5%
3 films = 45 degrees
45/360 = 0.125 = 12.5%
b) 7/24
Focus on left hand side (so 0,1, & 4 together = 180 degrees)
0 children = 180 degrees – 45 – 30 = 105 degrees
105/360 = 21/72 = 7/24
120
 Use BIDMAS
 20 + (1 x 7) = 27
 (20 + 1) x 7 = 147
 14727
2646
90ml
 This is indirectly a question on ratios.
 So if you assume for every 10ml consumed by Jane, Alex consumes 15, the ratio is Alex 15:10 Jane
 So 150ml/25 parts = 6
 Alex = 6 *15 = 90ml
 Check would be Jane which is 10 * 6 = 60
 So confirms Alex consumes 50% more than Jane
15/26
When doing this type of question, you can’t answer 7.5/13 obviously. So the solution is to double each fraction and “force” a gap
So this becomes 14/26 and 16/26
Answer is 15/26
74
 (4+2) x 13 = 104
 4 + (2×13) = 30
 Difference = 104 – 30
1691
a) 4
 Mean of 7 numbers = 12. Total = 84
 If 8th number added and mean is 11, total must now be 88 (8*11)
 So , the number included = 8884 = 4
70
 Use BIDMAS. (7+3) x 11 = 10 x 11 = 110
 7+ (3×11) = 40
 11040 = 70
2737
a) 8
 30 socks – 10 white; 20 nonwhites. Of the 20, 2/5th are blue
 So 20 * 2/5 = 8
b) 6 pairs
 Of the nonwhites, 8 are blue so this leaves 12
 With 12 left, it could make 6 pairs
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
a) 30°
Swimming & Golf together are 90°
Therefore, Golf is 90 – 60 =30
b) 1/8
Rugby = 45/360 = 9/72 = 1/8
c) 90
 Football = 180° – 45° = 135°
 135/360 * 240/1
d) 220
 1320 * 60/360
3702
a) to d) below
e) See below
a) 30°
180 – Australia – Africa = 1809060
b) 1/8
45/360 = 9/72 = 1/8
c) 30
180/1 * 60/360 = 180*1/6 = 30
d) 1000
Degrees for Europe = 180 – USA = 18045 = 135
1600 * 225/360. Simplified this is 1600 * 45/72 = 15/24
1600/1 * 15/24
£1.35
 15 * 35p = £5.25
 Multipack = £3.90
 Difference = £1.35
3258
a) 1200mm²
Area of rectangle = LxW = 60mm x 20mm
b) 40 triangles
2 Triangles will joined together have dimensions of LxW = 12mmx5mm. So they form a rectangle
Therefore, in 60mm across, you get 5 “blocks” of 2 triangles. And you can go to a height of 4 blocks
So in total 5 * 4 blocks = 20 blocks. 2 triangles per block so 40 triangles
c) 1200mm
Perimeter of 1 triangle = 12+5+13=30mm
Total number of triangles = 40
Total Perimeter =1200mm
d) 1.2m
10mm = 1cm
100cm = 1m
1000mm = 1m
85p
 12 * 65p = £7.80
 £7.80 – £6.95 = 85p
a) 1/8
45/360. Start off with 5 as the highest common denominator. Although there is a higher one
So 45/360 would become 9/72
Then 9/72 becomes 1/8
b) 40
Its the usual formula approach for this:
60/360 * 240/1
Then simplify each fraction (so 60/360 becomes 1/6)
Revised calculation is 1/6 * 240/1. Cross cancel and then multiply from there. See online videos on Youtube for 123tutors for further guidance
c) 450
Football is 135°. So 135/360 * 1200
a) 12
1/4 * 48/1
b) 2
48 * 1/2 = 24.
24 * 1/3 = 8
8 * 1/4 = 2
Remember of in maths means multiply
2184
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)
Area of 1 rectangle = 15 x 5 = 75cm²
4 children
 56 legs with 3:1 ratio dogs:children
 12 dogs = 48 legs. 4 children = 8 legs. So thats 56 legs altogether
 For every 3 dogs there are 12 legs. For every 1 child, 2 legs. So leg ratio is 12:2 = 14 legs
 Then work up in 14s to get to 56 which takes you to 48:8
 So 8 legs = 4 children
20cm²
Its 10cm length x 2cm height. So 20cm²
18
 A=5/8; P=3/8
 Pears therefore = 3/8 * 48/1
 Pears = 18
18
 B=2 ; A=5
 If A = 45 turns, it has done 9 times as many as the “base case”
 Therefore, B will also do 9 times as many so its 18 times
£1.11
 3mins * 7p = 21p
 18mins * 5p = 90p
 Total cost = 111p
a) 1 hour 25mins
7.10pm – 5.35pm = 1 hour 25mins
b) 16 hours 30 mins
2 hours 45 mins converted to minutes = 165minutes
165minutes * 2 = 330mins
330mins * 3 = 990mins
990mins/ 60mins
£208
 £156/6 = £26 per night
 £26 * 8 = £208
48
 Do your 3 x 4 times table to find a number in between 41 and 51
 So 12,24,36,48
 Answer is 48
15
 24/1 * 5/8
 Simplified = 3/1 * 5/1 = 15
6 weeks
 Per week she gets (79p44p) profit. So this is 35p per download
 150 downloads per day = 150x35p = £52.50 per day
 £2000/£52.50 = 38.1 days
 So this is 6 weeks as this is 42 days as she gets paid at the end of each week so you can’t use part a week
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
Use BIDMAS
a) £27
Cost = ((8×3) + (3×1)) = 24+3 = 27
b) 2 adults. 3 children
Use £25 and work backwards taking off children until you get to a multiple of 8
So £16 would be the number
£25£16 = £9. So thats 3 children
Leaving £16 so its 2 adults
£20.90
 £25.50 x 3 = £76.50
 £1.30 x 2 = £2.60
 Total = £79.10
 Change = £100 – £79.10
a) 24
Half of the 48 students so 24
b) 1/4
c) 4
Pizza is about 1/3 of 1/4.
1/4 = 12 children given 1/2 = 24
So 1/3 of 12 = 4
25,100 millimetres
 25.1metres = 25.1 x 100 = 2,510 centimetres
 2,510 x 10 = 25,100 millimetres
858
 22 x 39
 858
36


 ^{15}/_{100} * ^{240}/_{1}
 Simplify…^{3}/_{20} * ^{240}/_{1}
 ^{3}/_{1} * ^{12}/_{1}
 36

£15.96
Buy 2 get 3rd free so only pay for 2
£5.32
£15.96/3 to get equivalent price per bottle
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
38
 Triple 16 = 48 points. Double 20 = 40 points
 Total so far is 88 points
 He therefore needs 38 with this final dart
175
 To paint houses, 14 days per house x 14 houses = 168 days
 Add 4 days holiday = 172
 Add 3 days sick leave = 175
20 students
 Work on basis 6 students = 30°
 Therefore, 2 students = 10°
 So, 100° = 20 students
9,600cm³
Volume = length x width x height
Volume = 3.2 x 1.5 x 2
Volume = 6.4 x 1.5
Volume = 9.6 (this is in metres. Convert to centimetres)
9.6litres
1 litre = 1000cm³
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) 3.5 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) 672
b) 264
c) 1,081
d) 843
E
 £1.99 x 6 = £11.94
 Change would be £20.00 – £11.94
D
 Use BIDMAS. Therefore…
 328
 24
D
 60 seconds per minute. 4 minutes = 60 x 4 – 240
a) 12 seconds
 After 2 seconds, Gary is at 20metres which is when Andy starts running
 So Andy has 20 metres to make up
 It will take him 10 seconds to close this gap as he makes up 2 metres per second
 Add the initial 2 second start that Gary had over Andy
b) 120 metres
 Distance = Speed x Time
 Therefore = 12m/s x 10 seconds = 120 metres
a) 4 & 58 which would give an answer of 232
b) 30 ( 120/4)
Test 1
 60/80 = 75% (60/80 *100/1)
 70/100 = 70% (70/100 * 100/1)
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
a. 10 seconds
If turn is 360 degrees every 40 seconds, 90 degrees as a right angle would take 1/4 of 40 = 10 seconds
b. 84 turns
In 56 minutes, the sails make 56/1 * 60/40 turns
Again, use of fractions to calculate these types of questions
6 & 8
 Think about numbers that multiply to give 48. Thats going to be starting with low numbers, 2 * 24, 3 * 16, 4* 12, 6 * 8 etc
 Answer is 6 * 8 as these numbers when added give 14 and multiplied, give 48
Start with Sneezy as this is given as 24 and work from there
Grumpy gets 1 more so is on 25 etc etc
116cm
 Number of days = 5
 Height sunflower grows is (68 – 48) = 20cm
 Per Day growth therefore = 4cm
 Taking 21st August through to 2nd September = 12 days
 Therefore, growth during this period is 48cm
 Adding on the height as of 21st August of 68cm = 116cm
28th July
 Work Backwards. 4cm per day = 12 days
 Therefore, 12 days from 16th August 4th August
 Then take a week off this and you get 28th July
180
 23 – 13 = 10.
 23 – 5 = 18
 10 x 18 = 180
13, 5
 13 as the first number. So he would end up with zero
 Or for the second number, 5 so he ends up with zero for the second number
5 Pens 4 Pencils
 Whatever you buy in pens, just end in a 5 or 0. So the only number this applies to between 0 and 55 is 35
 So its 5 Pens. This leaves 20p
 20p is for pencils @ 5p each
 So 4 pencils
£14.90
1. £2.98 * 5
2. Multiplication question in words
£32
 Working backwards, 25% discount would mean discount on ticket cost was 25/75 * 30/1 = £10
 Full Price Child = £40
 Senior Citizen therefore pays 80/100 * 40/1 = £32
36
8, 12, 16
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
E
Use substitution of values:
Orange costs 10p, Apple costs 5p
A – 35p (2 x 10p) + (3 x 5p)
B – 35p
C – 35p (1 x 10p) + (5 x 5p)
D – 35p (3 x 10p) + (1 x 5p)
E – 40p
95p
 85p x 3 = £2.55
 30p x 5 = £1.50
 Total Cost = £4.05
 Change = £5.00 – £4.05 = 95p
£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
£660
^{120}/_{100} * ^{550}/_{1}
Simplify the calculation per normal rules of simplification and cross cancellation and then calculate
£1000
^{100}/_{120} * ^{1200}/_{1}
70 hours
Process:
 If Lazy Living = 2/7ths, Celeb Gossip is 5/7
 ^{5}/_{7} * ^{98}/_{1}
 Simplified this is = ^{5}/_{1} * ^{14}/_{1}
 This is 70
0.4
Process:
 One option is to change 0.08 to 8. So x 100
 Then multiply 8 by 5
 This gives 40
 Then to divide the answer by 100 as you originally multipied the question x 100
 This gives 0.4
52,272
product means multiplication
150ml
 Ratios question. 1R:2O:3A = 6 parts
 Each party is 50ml
 So 3 parts is 150ml