Welcome to this, the second of our Medium level Eleven Plus maths quizzes on Solving Problems. Solving Problems is something you will have to do, not only in your lessons and exams, but also in real life situations. The more you practice your skills, then the easier you will find the answers.

Imagine that you are planning to walk from Land's End to John o' Groats, a distance of 874 miles. If you want to know how long it will like you, you will need to divide 874 (the distance in miles) by the number of miles you can walk in one day (let’s say 30 miles).

874 ÷ 30 = 29.133 days.

Unusually, you would have to round this answer up, rather than down. That’s because even a small part of a day is still an extra day. So, your journey from Land's End to John o' Groats will take you a total of 30 days.

1.

The circumference of a wheel is 150 cm. How far will it travel if it makes 2,000 complete revolutions (turns)?

30 km

3 km

300 metres

30 metres

2.

If the area of a square room is 81 square feet, what is the length and width of the room?

9 feet

40.5 feet

18 feet

20.125 feet

First of all, do not be put off by the measurements being in feet. It doesn’t matter which units are involved – the calculations will be the same.

The length and width of the room are the same because the sides of a square are the same. You need to find a number which when multiplied with itself gives 81 because area = length × width:

9 x 9 = 81

The length and width of the room are the same because the sides of a square are the same. You need to find a number which when multiplied with itself gives 81 because area = length × width:

9 x 9 = 81

3.

The French writer Jules Verne wrote the adventure novel 'Around the World in Eighty Days'. If the distance around the world is 24,000 miles, how many miles would one have to travel per day (on average) to complete the journey in 80 days?

3 miles per day

30 miles per day

300 miles per day

3,000 miles per day

To find out how many miles one would have to travel per day, we must divide 24,000 (the total distance) by 80 (the total number of days):

24,000 ÷ 80 = 300 miles per day!

24,000 ÷ 80 = 300 miles per day!

4.

A builder ordered a tonne of bricks. If she received 400 bricks, how heavy is one brick?

250 g

1.25 kg

2.5 kg

12.5 kg

If 400 bricks weigh one tonne, then one brick weighs 1,000 (the number of kg in one tonne) ÷ 400 (the number of bricks).

1,000 ÷ 400 = 2.5

1,000 ÷ 400 = 2.5

5.

A sweetshop owner is filling up jars with bonbons. If each jar can hold 352 bonbons, how many jars will the sweetshop owner need for 3,000 bonbons?

6 jars

7 jars

8 jars

9 jars

The number of jars required = 3,000 (the number of bonbons) divided by 352 (the number of bonbons which will fit inside one jar):

3,000 ÷ 352 = 8.523

Be careful here – jars cannot be cut into pieces! The sweetshop owner will need 9 jars in total – 8 jars won’t be enough

3,000 ÷ 352 = 8.523

Be careful here – jars cannot be cut into pieces! The sweetshop owner will need 9 jars in total – 8 jars won’t be enough

6.

The number of bacteria in a Petri dish doubles every 20 minutes. If there is are 2 bacteria to begin with, how many will be in the Petri dish after 2 hours?

32 bacteria

64 bacteria

128 bacteria

256 bacteria

First we need to know how many lots of 20 minutes there are in 2 hours. There are 60 minutes in one hour so there are three lots of 20 minutes in one hour (60 ÷ 20 = 3).

If there are 3 lots of 20 minutes in one hour, then there are 6 of them in 2 hours (3 x 2 = 6).

Now we need to double 2 (the original number of bacteria) 6 times:

First doubling: 2 x 2 = 4

Second doubling: 4 x 2 = 8

Third doubling: 8 x 2 = 16

Fourth doubling: 16 x 2 = 32

Fifth doubling: 32 x 2 = 64

Sixth doubling: 64 x 2 = 128

If there are 3 lots of 20 minutes in one hour, then there are 6 of them in 2 hours (3 x 2 = 6).

Now we need to double 2 (the original number of bacteria) 6 times:

First doubling: 2 x 2 = 4

Second doubling: 4 x 2 = 8

Third doubling: 8 x 2 = 16

Fourth doubling: 16 x 2 = 32

Fifth doubling: 32 x 2 = 64

Sixth doubling: 64 x 2 = 128

7.

Blackpool Tower is 158.1 metres tall. The tallest building in the world (the Burj Khalifa in Dubai) is 5.237 times taller. How high is the Burj Khalifa to the nearest metre?

528 metres

628 metres

728 metres

828 metres

The Burj Khalifa is 5.237 times taller than Blackpool Tower, so to find its height we multiply 158.1 (the height of Blackpool Tower) by 5.237:

158.1 x 5.237 = 827.9697

This is 3.03 cm short of 828 metres, so we round it up

158.1 x 5.237 = 827.9697

This is 3.03 cm short of 828 metres, so we round it up

8.

There are 7 days in a week. How many weeks are there in 3,640 days?

520

530

540

550

To work this one out, we have to divide 3,640 by 7:

3,640 ÷ 7 = 520. That’s very nearly 10 years

3,640 ÷ 7 = 520. That’s very nearly 10 years

9.

A machine in a factory makes 40 circuit boards every 2 minutes. How many circuit boards can the machine make in an 8-hour shift?

4,800

9,600

14,400

19,200

First we need to know how many minutes there are in 8 hours. We find this out by multiplying 8 by 60 (the number of minutes in one hour):

8 x 60 = 480

Next we need to find out how many circuit boards the machine can make in 480 minutes. First we find out how many lots of 2 minutes are in 480 minutes by dividing by 2:

480 ÷ 2 = 240

If the machine can make 40 circuit boards in each 2-minute period then we multiply 240 by 40 to get the answer:

240 x 40 = 9,600

8 x 60 = 480

Next we need to find out how many circuit boards the machine can make in 480 minutes. First we find out how many lots of 2 minutes are in 480 minutes by dividing by 2:

480 ÷ 2 = 240

If the machine can make 40 circuit boards in each 2-minute period then we multiply 240 by 40 to get the answer:

240 x 40 = 9,600

10.

6 cars raced at average speeds of 74 mph for 3 hours. What is the total distance travelled by all 6 cars?

222 miles

444 miles

888 miles

1,332 miles

To work this one out, first find the distance travelled by one car:

74 (average number of miles per hour) x 3 (number of hours):

74 x 3 = 222

There were 6 cars in all so to find the answer we need to multiply 222 (the distance travelled by one car) by 6 (the number of cars):

222 x 6 = 1,332

74 (average number of miles per hour) x 3 (number of hours):

74 x 3 = 222

There were 6 cars in all so to find the answer we need to multiply 222 (the distance travelled by one car) by 6 (the number of cars):

222 x 6 = 1,332

150 x 2,000 = 300,000 cm

Next, we want to convert 300,000 cm to km. We do this by dividing 300,000 (the number of cm travelled) by 100,000 (the number of cm in one km):

300,000 ÷ 100,000 = 3