In your KS3 Maths lessons, you've probably encountered expressions. These are super important in algebra and overall in maths.

Algebra is like a secret code using symbols, often letters, to stand in for unknown numbers, called variables. These variables can change, or vary, depending on the situation. When you write down a situation as a maths sentence, it becomes an expression.

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1 .

Jane is c years old and her sister Katie is three years younger so how old is Katie?

c3

c + 3

c - 3

c - 3 - 3

If she is younger then her age is less than. 3 less than is the same as minus 3

2 .

Which of these is a simplification of 2a x 3a?

5a

6a

23aa

6a^{2}

You must multiply the numbers together AND the letters. Remember a x a = a^{2}

3 .

Simplify 5a + 7a.

12a

12aa

57a

57aa

Let us suppose that a = 3. (5 x 3) + (7 x 3) = 36. This is the same as saying 12 x 3 (12a) = 36

4 .

If I have x rabbits and you have twice as many, how many rabbits have you got?

2x

2 + x

2 - x

x^{2}

You have two times the number that I have got and 2 times x is the same as 2x

5 .

In an algebraic expression letters are often used to represent what?

Other letters

Only numbers greater than 1

Only numbers less than 1

Values

A letter can be used in place of any number - especially if the number has not yet been worked out

6 .

Simplify 4a + 5b + 6b + 11a

26ab

15a^{2} + 11b^{2}

15a + 11b

9a + 17b

Here we are adding numbers together, NOT multiplying them together

7 .

Which of the following is not a mathematical expression?

6

6a x 14

5a - 4b +16c x 8d

Oh my gosh!

The correct answer might well be an English expression but it is NOT a mathematical one!

8 .

What is the simplification of 3a + 4b + 6c + 3a - 6c - a - 3b?

4a + 2b - 3c

5a + b

6a - 3b

9a - 2b - c

Be careful to account for all the a's, then all the b's and then all the c's. In this case + 6c and - 6c cancel each other out and therefore they do not appear in the simplification

9 .

Peter has x brothers, Paul has y brothers and Graham has z brothers. Between the three boys, how many brothers have they got?

xyz

x + y + z

x + y - z

x - y + z

Don't get baffled by complicated wording - often the answer is easier than you think

10 .

Suzie is x years old and she has a sister called Rosie who is four years older. Rosie's mother was 28 when Rosie was born. How old is Rosie's mother now?

7x

x + 28

x - 4

x + 32

If you got the answer wrong then think carefully through each aspect of the question. Rosie's mother was 28 when Rosie was born. 4 years later, Suzie was born. Suzie is now x years old so Rosie's mother's age is now

28 + 4 + x = 32 + x

28 + 4 + x = 32 + x

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