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In this worksheet, students test their maths knowledge by answering these mixed questions as quickly and accurately as possible. Most can be answered without writing anything down.

Key stage:  KS 3

Curriculum topic:   Number

Curriculum subtopic:   Use Four Operations for All Numbers

Difficulty level:

QUESTION 1 of 10

In this worksheet, you must answer short mental arithmetic questions which get progressively harder.

Remember some quick short cuts, such as:

1.  To multiply by 4, just double and double again.

2.  To find a quarter of something, just halve and halve again.

3.  To find 10% of something, just divide by 10.

What is the product of 8 and 9?

How many centimetres are there in 4½ metres?

Work out three-fifths of 20.

Write 6.745 correct to 1 decimal place.

Write 8.45 pm in 24-hour clock time.

(just write numbers)

What is the order of rotational symmetry of a rectangle?

Ed beats Ben in 16 matches out of 20.

What percentage is this?

Choose two prime factors of 70.

1

2

7

10

14

Sam and Henry share £30 in the ratio 3:2.

1

2

7

10

14

Anna has a 20 gigabyte hard drive on her MP3 player.  Three quarters of it is used.  How many gigabytes are not used?

1

2

7

10

14

How many equal angles are there in an isosceles triangle?

1

2

7

10

14

Sophie cycles a distance of 6850 metres.  Write this distance in kilometres.

(Just write the number)

1

2

7

10

14

What is the value of 3n + 2 when n equals 25?

1

2

7

10

14

Charlotte buys a sandwich costing £1.45 and a drink costing 90 p.  How much change does she get from a £5 note?

1

2

7

10

14

Lily and Patrick have 20 marbles each.  Lily gives Patrick four marbles.

What in its lowest terms is the ratio of the number of marbles that Lily now has to the number of marbles that Patrick has?

1

2

7

10

14

What is the area of a parallelogram in cm2 with base 14 cm and height 3 cm?

1

2

7

10

14

Issy pays £3.84 for a book of 12 stamps.  What is the cost of each stamp in p?

A recipe for Aunty Alice’s Artichoke Soup requires 300 ml of cream for 4 people.  How many ml of cream will be needed in a similar recipe for 10 people?

A train travels 400 km in three hours and twenty minutes.  What is its average speed in kilometres per hour?

The radius of the Earth is approximately 6 400 kilometres.  Estimate the circumference of the Earth to the nearest 10 000 km?

• Question 1

What is the product of 8 and 9?

72
EDDIE SAYS
8 x 9 = 72 When you hear the word product, think about multiplications.
• Question 2

How many centimetres are there in 4½ metres?

EDDIE SAYS
Did you work out what to do here? When you move from metres to cm you need to multiply the number 4.5 by 100 to get the number of cms as there are 100 cm in a metre.
• Question 3

Work out three-fifths of 20.

12
EDDIE SAYS
First, you need to work out what one fifth would be, so to do this we divide 20 by 5, and we get 4. The second part is that we then multiply/times 4 by three (4 x 3) to find the answer 12. How did you do?
• Question 4

Write 6.745 correct to 1 decimal place.

6.7
EDDIE SAYS
This was a bit of a tricky one. One decimal place means one digit after the decimal place. SO in order to know what to do to that digit, we look at the second number after the decimal place. If this is 5 or greater we round the number directly after the decimal up. In our case, this number is 4, so we leave the answer as 6.7.
• Question 5

Write 8.45 pm in 24-hour clock time.

(just write numbers)

EDDIE SAYS
How did you do? It's good to know what numbers are in the 12-hour clock (that's the easy part!) and the 24-hour clock. 8 is 20 hours in the 24-hour clock as 12 (morning hours) + 8 (hours after midday) = 20. The minutes stay the same in the 12-hour and the 24-hour clock.
• Question 6

What is the order of rotational symmetry of a rectangle?

EDDIE SAYS
Remember rotational symmetry is the number of times a shape can be rotated around its centre and appear to look exactly the same.
• Question 7

Ed beats Ben in 16 matches out of 20.

What percentage is this?

EDDIE SAYS
16/20 is the same as 8/10. Think back to the start we know that to find a percent we need to have a number out of 10, which we do! We then just need to times that number by 10, and there we have it!
• Question 8

Choose two prime factors of 70.

2
7
EDDIE SAYS
Did you spot the clue in the question? it asked for the PRIME factors, not just factors. In this list, the only two numbers are prime, 2 and 7. Don't be fooled by the number 1, this is not a prime number!
• Question 9

Sam and Henry share £30 in the ratio 3:2.

EDDIE SAYS
Can you remember what to do here? Firstly work out the total number of pieces here, which is done by adding 3 to 2 = 5. We know that £30 divided equally by 5 is £6. Now, all we have to do is work out what a ration of 3 would be = 3 x £6 = £18 We could then do £30 - £18 to work out what Henry gets = £12. We can double-check this by doing 2 (the ratio) x £6 = £12. So, it seems clear that Henry gets £12.
• Question 10

Anna has a 20 gigabyte hard drive on her MP3 player.  Three quarters of it is used.  How many gigabytes are not used?

EDDIE SAYS
How did you get on with this one? Firstly we need to know what a quarter of 20 is. To do this we divide the number by 4. 20 / 4 = 5. We know that 3/4 are used so 15 gigabytes are accounted for, which we can then subtract from 20, i.e. 20 - 15 = 5 OR we already know what a quarter is, as we calculated this initially. Always good to double-check our working!
• Question 11

How many equal angles are there in an isosceles triangle?

EDDIE SAYS
This is something that you just need to know! If you didn't why not make a note of it?
• Question 12

Sophie cycles a distance of 6850 metres.  Write this distance in kilometres.

(Just write the number)

EDDIE SAYS
Top tip - kilo means 1000. So in this question, we need to divide the answer by 1000, and then we get 6.85.
• Question 13

What is the value of 3n + 2 when n equals 25?

EDDIE SAYS
When you see 3n what we are really seeing is 3 x n. In this case, we can substitute in numbers and complete a simple calculation. (3 x 25) + 2 = Remember the rules of BODMAS/BIDMAS = 75 + 2 = 77. Take it slowly and you can do it!
• Question 14

Charlotte buys a sandwich costing £1.45 and a drink costing 90 p.  How much change does she get from a £5 note?

EDDIE SAYS
In this scenario, first of all, we need to know how much Charlotte spent. £1.45 + 90 p = £2.35. That's the start. Now, we need to work out how much change is left from £5 or 500 p. 500 - 235 = 265 p. We need to now put this into pounds and we can do this by dividing this number by 100 (there are 100 pennies in £1) and we have £2.65.
• Question 15

Lily and Patrick have 20 marbles each.  Lily gives Patrick four marbles.

What in its lowest terms is the ratio of the number of marbles that Lily now has to the number of marbles that Patrick has?

EDDIE SAYS
This was a bit tricky. If we break it down we can solve this without too much panic. First of all, we work out that if Lily gives 4 marbles to Patrick, she has 16 marbles and he now has 24 marbles. Lilly has 16/40 marbles Patrick has 24/40 marbles We can simplify these fractions to 4/10 and 6/10 We can further simplify this to get 2/5 and 3/5. If we know that the ratio of marbles Lily has to Patrick must be 2:3
• Question 16

What is the area of a parallelogram in cm2 with base 14 cm and height 3 cm?

EDDIE SAYS
You need to commit these formulae to memory! It will help you further on too. Area of a parallelogram = base x height 14 x 3 = 42 cm ²
• Question 17

Issy pays £3.84 for a book of 12 stamps.  What is the cost of each stamp in p?

32
32 p
32p
32 pence
EDDIE SAYS
First of all, we make the number into pennies, as we can then divide. £3.84 = 384p. 384 / 12 = 32 p
• Question 18

A recipe for Aunty Alice’s Artichoke Soup requires 300 ml of cream for 4 people.  How many ml of cream will be needed in a similar recipe for 10 people?

EDDIE SAYS
That's quite a lot of cream from Aunty Alice! There are a few ways to do this, but a quick way is: 300 / 4 = 75 ml 75 x 100 = 750 ml
• Question 19

A train travels 400 km in three hours and twenty minutes.  What is its average speed in kilometres per hour?

EDDIE SAYS
Ok for this one there are a few ways to do this. We're going to work it out by first thinking about the amount 3 hours and 20 minutes. There are 10 blocks of 20 minutes in this journey. Which must mean that every 20 minutes the train has travelled 40km. (400km / 10 = 40 km) We need to know what the average speed is per hour, so we multiply 40 by 3 (the number of 20-minute sections in an hour) and we arrive at 120 km/h
• Question 20

The radius of the Earth is approximately 6 400 kilometres.  Estimate the circumference of the Earth to the nearest 10 000 km?

EDDIE SAYS
Ok a bit of a tough one to finish! We know the formula to find the circumference is π d which means π x diametre. So to get the diameter we must multiply the value for the radius by 2: 6400 x 2 = 12800 We will use 3.142 for pi so 12800 x 3.142 = 40,192 km Which to the nearest 10,000 km is 40,000.
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