11 PLUS MATHS PRACTICE PAPERS

Problem 11 :

A village has a population of 13295 people. It increases by an average number of 400 people every year. In a recent survey, it was realized that the population of the village would increase by one less than the average number. What will be the population of village in the successive year assuming that nobody dies in the village in the considered years?

a) 13695      b) 13694    c) 13690     d)  13200

Solution :

Population of the village = 13295

Increasing rate = 400 per year.

Population in the next year = 13295 + 400 - 1

= 12694

Problem 12 :

Volume of a box is found by multiplying its length, width and height. If the measure of volume of the box is 455 cubic cm. What could be its dimension?

a) 5 x 7 x 13       b) 3 x 5 x 11       c) 13 x 5 x 5     d)  It is prime

Solution :

Volume of the box = 455 cubic cm

455 = 5 x 13 x 7

= 5 x 7 x 13

So, option A is correct.

Problem 13 :

If a bus travels 160 km in 4 hours and a train travels 320 km in 5 hours at steady speed then what is the ratio of the distance travelled by bus and train in 1 hour?

a) 1 :  2      b) 4 : 5      c) 5 : 8     d)  8 : 5

Solution :

Time = distance / speed

Distance travelled by bus = 160 km

distance travelled in 1 hour = 160/4 = 40 km

Distance travelled by train = 320 km

distance travelled in 5 hours = 320/5 = 64 km

Ratio between bus to train = 40 : 64

= 5 : 8

Problem 14 :

A farmer planted 1890 tomato plants in a field, each row having 63 plants. A certain type of worm destroyed 18 plants in each row. How many plants did the worm destroy in the whole field?

a) 342      b) 540    c) 450     d)  756

Solution :

Number of plants planted = 1890

number of plants in each row = 63

Number of rows = 1890/63

= 30

Number of plants destroyed in each row = 18

total number of plants destroyed = 18 x 30

= 540

Problem 15 :

What is the sum of first 4 multiples of 8?

a) 180      b) 100   c) 80     d)  32

Solution :

First 4 multiples of 8 are

8, 16, 24 and 32

Sum of them = 8 + 16 + 24 + 32

= 80

Problem 16 :

A train departs from Berlin at 08:20. Usually it takes 8 hours and 35 minutes to reach Dresden. If the train delayed by 25 minutes then what time will be the train arrive Dresden?

a) 5:15 PM      b) 4:55 PM   c) 5:20 PM     d)  4:40 PM

Solution :

Since the train delayed 25 minutes,

4 : 55 + 25

= 5 : 20 PM

Problem 17 :

Following tally chart shows the number of students and their favorite game

How many more students like cricket than basketball?

a) 14      b) 17      c) 8     d)  9

Solution :

Number of students who like cricket = 22

Number of students who like basketball = 8

Difference = 22 - 8

= 14

 So, 14 more students like cricket than basketball.

Problem 18 :

There are four unknown positive whole numbers.

The mean of the two smallest numbers is 3.

The mean of the three smallest numbers is 5.

The mean of all four numbers is 7.

All the numbers are different and odd.

What are the four numbers?

a) 3, 5, 7, 9      b) 6, 15, 28, 35      c) 2, 5, 3, 7     d)  1, 5, 9, 13

Solution :

Option a :

3, 5, 7, 9

mean of smallest of two numbers = (3 + 5)/2

= 8/2

= 4(not true)

Option d :

1, 5, 9, 13

mean of smallest of two numbers = (1 + 5)/2

= 6/2

= 3

Mean of smallest three numbers = (1+5+9)/3

= 5

Mean of four numbers = (1+5+9+13)/4

= 7

So, option d is correct.

Problem 19 :

The scale in a diagram is 1cm represents 5000 cm. Find the actual length if the scale length is 4 cm

a) 5000 m      b) 504 m     c) 200 m     d)  2000 m

Solution :

1 cm : 5000 cm

If scale = 1 cm, actual length = 5000 cm

If scale = 4 cm, actual length = ?

1 : 5000 = 4 : x

1/5000 = 4/x

x = 4(5000)

= 20000 cm

100 cm = 1 m

= 200 m

So, option c is correct.

Problem 20 :

Xuen has £7500 in her bank account. She must pay each of her 7 employees a wage of £327 per week for 3 weeks. How much money will be remaining in her account?

a) £2289      b) £327     c) £6867     d)  £633

Solution :

Number of employees = 7

number of weeks = 3

  number of payments = 21

Total payment = 21(327)

= 6687

Remaining = 7500 - 6687

= 633