Maths-11-plus-Alleyns-Sample1

C

1. In 1 hour = 60 minutes
2. Therefore 3 hours = 180 minutes. 1/2 hour = 30 minutes
3. Total is therefore 210 minutes

B

1. For 0.8, convert fractions to either 10ths or 100ths.
2. Convert 4/5ths to 10ths = 8/10 = 0.8

B

Way to rank numbers is to put them in Column Format like below:

Go Column by Column

C

1. Logical Thinking. 17cm

E

1. Apply the rules of BIDMAS
2. 12-8+3
3. 12-11
4. 1

E

1. Isosceles triangles have 2 angles the same
2. So, if 30 degrees is one of the angles, then this leaves 150 degrees
3. Therefore, 75 degrees is a possible other triangle

C

1. Always use dummy numbers if not sure. So if we assume 40 children in class and 1/4 are girls, then thats 10 girls
2. There are therefore 30 boys. So ratio girls to boys is 1:3

B

1. Go 09:34 to 10:00 = 26 minutes
2. Go 10:00 to 13:00 = 3 hours
3. Go 13:00 to 13:21 = 21 minutes
4. Total is therefore 3 hours 47 minutes

D

1. 9 is in the hundredths column
2. So answer is 9 hundredths

D

1. If the pen costs 50p more, then the way to start with this question is to assume they cost the same
2. This would be 55p each
3. Then take the difference of 50p and split it into 25p and 25p
4. Add 25p to the pen and take 25p from the pencil
5. So the pen would be 55p + 25p = 80p

3.55, 5.35, 5.53, 35.5, 53.5, 55.3

a) 3

Mean = 3+4+2+0+1+8 = 18/(number of instances) = 18/6

b) 8

Range = Difference lowest v highest = 8-0

c) 10

If Mean increases to 4 after 7 games, then total of 28 goals scored.

Next game would be 10

a) 7:10

Ratio of Men:Women = 140:200. This is the same as 14:20 = 7:10

b) 240cm

Real tower is 120m tall. Therefore, on a scale of 1:50, smaller version will be 50x smaller

So convert firstly m to cm. So thats adding 2 zeros. 12,000

Then divide by 50 to give 240cm

c) 3:160

Firstly again, conversion. 80m = 8000cm

8000/150 = 160/3

a) 49cm

Length of cane that snapped off is 2.05m = 205cm minus 156cm

Converting all to cm makes the question much easier

b) 14

Would need 14 = 168m²

13 would give 156m² so not quite enough

44 stickers

1. Use division as a starting point
2. So 60/15 = 4
3. 55/5 = 11
4. Multiply the 2 to get 44 stickers

a) 12 seconds

1. After 2 seconds, Gary is at 20metres which is when Andy starts running
2. So Andy has 20 metres to make up
3. It will take him 10 seconds to close this gap as he makes up 2 metres per second
4. Add the initial 2 second start that Gary had over Andy

b) 120 metres

1. Distance = Speed x Time
2. Therefore = 12m/s x 10 seconds = 120 metres

a-b) See below for plotted data

c) Coordinates of D are (1,-3)

d) Its a 4 by 4 square so 16 square units

a) 120km

b) Car B

c) Car B

d) 40km

100km – 60km

e) Car B overtook Car A

f) Car B between 3.15pm and 3.45pm. Speed of 70/0.5 = 140km/h

g)  Car B as it got to its destination in a quicker time

A=1, B= 4, C=8

There is a bit of trial and error involved here.

When you work through some permutations, you know C can’t be 0-3. This is because you do need a number that drives some form of carry. This impacts the tens and hundreds columns

So its 4-9

b) 1089
For 4-digit numbers, let a, b, c, and d be the digits, so

     9*(1000*a+100*b+10*c+d) = 1000*d + 100*c + 10*b + a

              8999*a + 890*b = 10*c + 991*d

This implies that d = 10 - a, by looking at last digits, which we 
substitute, and get

              9990*a + 890*b = 10*c + 9910

When we divide by 10, we get

                999*a + 89*b = c + 991

This implies that a = 1, so

                        89*b = c - 8

This implies that b = 0 and c = 8, and there is only one solution 
9*1089 = 9801.