Maths-11-plus-LondonIndependent-2009

27,427

41,096

Use Bus stop method. Keep numbers in a neat column format

2.38m

1. Usually easier to convert to centimetres first and then back into metres.
2. So 2.7m = 270cm. Take away 32cm = 238cm
3. 100cm = 1m. So move dp 2 places to the right in 238 which gives 2.38

²/₃

1. Yet another question which requires the possible use of HCF. You are looking at 60 seconds and 40 seconds.
2. The highest common factor of 60 and 40 is 20.
3. 6o seconds is split into 3 lots of 20. So denominator is 3
4. 40 represents 2 lots. So fraction is ²/₃

³/₅ ²⁹/₄₅ ²/₃

1. Convert to the same denominator to make it easier to compare
2. Lowest common Multiple of 3, 5 & 45 is 45.
3. 2/3 becomes 30/45
4. 3/5 becomes 27/45

0.092

1. If not sure, put the numbers in a column format like below

63

Just go through 9x table. 63

144

You can take the factor tree route per this article:

https://123tutors.co.uk/finding-the-lowest-common-denominator/

9,012,213

Putting numbers in a column format helps with these types of questions

1,265

1. Madrid to Paris = [(Madrid minus Lisbon ) + (Munich minus Paris)]
2. 2,730 – 638 – 827 = 1,265

a) 5 coins £2, 20p, 5p, 2p, 1p

b) £5.44

2 magazines cost £2.28 * 2 = £4.56.

£10.00 – £4.56

b) x by 7 and then +3

a) 168cm
¹⁴⁰/₁ * ⁶/₅

b) 90cm
¹⁰⁵/₁ * ⁶/₇

£563

1. There are 3 free adult tickets because you get 1 free adult ticket with every 10 student tickets
2. So its 32 student tickets + 1 adult ticket to buy
3. (32 * 14) + (15 * 1) = 448 + 15 = 563

a) 23C

1. Assess what each marker represents. This is 2C
2. Therefore, answer is 23C

b) -12C (Minus 12C)

c) 35C

d) i) 68F

20/5 = 4 * 9 = 36 + 32 = 68

d) ii) 15C

1. Work backwards
2. 59F – 32 = 27 / 9 =3 * 5 = 15

a) 14:05

08:20 + 3 hours 45mins = 12:05.

Add on 2 hours for time difference so 14:05

b) 21:00

19:15 + 3 hours 45mins = 23:00

Take away 2 hours for time difference so 21:00

a) 66C

Use a ruler if needed and remember that each marker is worth 2C on the y axis

b) 4.5minutes

Draw a horizontal line from 45C and you will see it intersecting the line chart at 4.5mins

c) 5 mins 48 seconds

Tea starts at 80C and to get to 40C takes 5mins 48sec (each marker on the x axis is 12seconds)

d) 46C

Use a ruler if required to draw a vertical line from the time in the question

19

1. There is 1 large triangle that is the outer one
2. Then the black triangle below
3. Then 5 other triangles like the one beneath that (which occupy the equivalent of 4 small triangles)
4. Finally 12 small triangles like the ones on the right

16units²

1. Break it down into 2 parts
2. Shape A = 1/2 x Width x Height. So this is 1/2 x 4 x 4 = 8
3. Shape B = 2 x 4 = 8

59

1. When you have 2 pages next to each other in a 64 page paper, the 2 pages will add up to 65.
2. Eg 1 & 64 or pages 2 and 63 and so on
3. It will be a page towards the back of the paper. So 6 + x = 65
4. Therefore, rearranging, 59

See below

a) 15mins

1. 30 mins / 2 = 15 mins if you have 2 hoses

b) 15mins

1. To fill 10cm, it takes 1 hose 15mins. So to fill 30cm, I need 45mins for 1 hose.
2. With 3 hoses therefore, the time is 15mins (45/3)

a) 18

1. Comedy represents 1/4 of the total pie. This is 25%.
2. The pie is worth 72 students in total
3. So 1/4 x 72 = 18

b) 50º

1. 360 – 90 – 160 – 60 = 50

3/16

Total number of small triangles is 16. Of this, 3 are shaded

See below

16 triangles. Therefore 6 shaded. 6/16 = 3/8

a) NE

b) 135º

90 degrees to face North from West . Then a further 45 degrees to get to NE

c) 225º

1. Reflex angle is 360 degrees less the angle from West to NE.
2. 360 less 135 = 225

d) SE

1. 360 degrees in a circle so of the 495, 360 would bring her back to North
2. This leaves 135 degrees. Given 8 markers , each marker is worth 45 degrees
3. 135/45 = 3 so she moves by 3 markers
4. This takes her to SE

a) x = 2cm, y = 6cm

x = 2cm (8cm – A – B)

y = 6cm (14cm – E)/2

b) 52cm

Perimeter starting at point A = 2+6+2+2+2+6+4+14+4+6+2+2

c) 72cm²

Area = (14×4) + (2×2) + (6×2) = 56 + 4 + 12

a) See below

b) A Trapezium

a) The middle one is correct. This is because the horizontal dots increase in Pattern 1 from 3 to 5 to 7. So next number of horizontal dots is 9. The vertical dots increase from 2 to 4 to 6. So next number of vertical dots is 8

a) 10cm

1. This is a classic question and worth remembering the process to tackle these.
2. Perimeter is based on 16 sides.
3. Given perimeter is 160cm, each side is 160/16 = 10cm in length

b) 100cm²

10×10

c) 1600cm²

If each Square is 100cm², area of whole figure is 16 x 100

15p per apple

2P + 1M = £1.35 (Formula 1)

1P + 2M = £1.20 (Formula 2)

1P + 1M + 1A = £1.00 (Formula 3)

Take:

4P + 2M = £2.70 (Formula 1 * 2)

1P + 2M = £1.20

Therefore, difference is £1.50 and 3P so each pear costs 50p

If each pear costs 50p, then substituting into formula 1 gives:

£1.00 (2P) + 1M = £1.35

IM = £1.35 – £1.00

1 Mango = 35p

Therefore, given this:

1P + 1M + 1A = £1.00

50p + 35p + 1A = £1.00

1 Apple = 15p

a) 5/18

Given there are 18 parts altogether, ladies who lost their gloves = 5/18

b) 11 ladies

If 52 ladies did not lose gloves, 20 did so the total of gloves this represents is 40. If 40 gloves were found then take 29 off this to leave 11 ladies who lost one glove

24

1. 36 sweets between them. This is a question on ratios:
2. D = 1, H = 2 (Because hannah has twice as many has Dominic)
3. A = 6 because Abdul has 3 times as many as Hannah
4. So 1:2:6. Total parts = 9. Each part is therefore 36/9 = 4 sweets per part
5. Total for Abdul = 6 parts * 4 sweets per part

a) 5

Applying the rules, = 3 x 3 – 4

b) 6

Working backwards, 32+4 =

So 36 = 6 x 6

c) 9

Slightly trickier. But you need a multiple of 72 with one option being 9

x² – x – 72 = 0

A = 8; B = 1; C = 6; D = 4; E = 9; F = 3; G = 5

Detailed solution to follow

a) 144

The last number in Row 12 will be 144. Spot the pattern which is that its the row number squared to equal the last number

b) 39

Again the patttern. (Row Number x 2) -1  . So for Row 20, it will be 20 x 2 -1

c) 10

Work backwards. Take away 1 and then divide by 2

d) 91

e) 855