Expressions are very important in algebra, and in maths generally. This KS3 Maths quiz deals with interpreting expressions; by this we mean applying algebra to real-life situations. It is worth remembering that the purpose of maths is to eventually be able to use it in real life!

An expression is a mathematical sentence. Mathematical sentences are numbers and symbols grouped together in such a way that they show the value of something. So, in algebra, you can think of an expression as one or a number of mathematical symbols that represent a number or quantity. Expressions can contain any number of numbers, letters and symbols. Even a single number on its own is an expression.

Think you've mastered expressions? Then see how well you can express yourself by playing this quiz! As with any test, take your time, read each question carefully and think about your answer. Good luck!

1.

Solution a boils at x degrees centigrade. Solution b has a boiling point five degrees higher than solution a. Solution c has a boiling point 25 degrees higher than solution b. How would you express the boiling point of solution c?

x + 5 + 25

x + b + c

x + y + z

xyz

Don't get baffled! Write it down and work it out

2.

There were x pens in the cupboard. Paula took out three pens, John took out two pens and Pamela put seven pens back into the cupboard. How would you write the number of pens now in the cupboard?

2x + 3x

x - 3 - 2 + 7

x + 3 + 2 - 7

x + 3 + 2 + 7

There are now x + 2 pens in the cupboard

3.

There are y number of students in a class. If seven of the students are away ill, how would you write the number of students still attending class?

2y

7 - y

y - 7

y + 7

In algebra the letters 'a' and 'x' are often used to represent unknown numbers but any letter can be used

4.

Peter has a number of brothers (let's call the number 'x') and John has two brothers more than Peter. How would you write the number of brothers that John has?

2x

-2x

x - 2

x + 2

If John has two brothers more than Peter (x) then he must have x + 2 brothers

5.

There are x number of chess boards at the school chess club. What is the total number of squares on all the boards?

64x

64 - x

64 + x

It is impossible to say

The correct answer means 64 times x. If we were then told that there were four boards at the club we could work out that the total number of squares was 256 (64 x 4)

6.

In the first three football matches of the season James scored x goals. In the fourth match James scored two goals and in the fifth match he scored one goal. How would you write the total number of goals that James scored?

12x

2x + 1

x + 2 + 1

x + x + x

Don't get baffled with complicated questions. Sort out just the information that is required

7.

Joseph has x rabbits and Sam has three more rabbits than Joseph. How many rabbits have they between them?

3x

x + 3

x + x + 3

x + x - 3

If Joseph has x rabbits then Sam has x + 3 so, between them, Joseph and Sam have x + x + 3 or 2x + 3

8.

On a chess board there are eight squares across and eight squares down. Which of these would be the best way of writing the number of squares?

8 + 8 + 8 + 8 + 8 + 8 + 8

8 x 8 x 8 x 8

8^{2}

8x

8 lots of 8 is the same as 8 x 8 or 8^{2}

9.

Five people each start the day with x sweets. During the day, each of them eat two of their sweets. What is the total number of sweets that have not been eaten at the end of the day?

5(x - 2)

5 - x

10 - x

x - 10

If you answered x - 10 then you need to remember that EACH PERSON started with x sweets. x sweets DOES NOT represent the total number of sweets at the start

10.

It takes a person five minutes to pick a sack of potatoes. How long will it take z people to pick 20 sacks of potatoes? You may assume that all the people work together to fill the same sack before moving onto the next sack. Give your answer in minutes.

20 + z minutes

20 x 5 / z minutes

20z minutes

z - 20 minutes

If it takes 5 min for one man, then 2 men will take 1/2 that time, 3 men will take 1/3 that time,... z men will take 1/z of that time - that is 5/z min for each sack. Therefore, 20 sacks will take 20 x 5/z min. Of course, if they each filled their own sack, it would only take 5 min to fill 20 sacks