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Maths Quiz - Level 3-4 Algebra - Expressions (Questions)

Learn how algebraic expressions work in KS3 Maths. Combine like terms, use brackets, and substitute values to simplify expressions and model real problems.

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Fascinating Fact:

A rectangle with length (x + 3) and width (x + 1) has an area of x² + 4x + 3, showing algebra in geometry.

In KS3 Maths, expressions use letters and numbers to represent patterns and problems. You’ll simplify by collecting like terms, expand and factorise brackets, and substitute values to test or solve situations.

Key Terms

Variable: A letter that stands for a number which can change, like x or n.
Coefficient: The number multiplying a variable, e.g. in 5x the coefficient is 5.
Like terms: Terms with exactly the same variable part (e.g. 3x and -2x) that can be combined.

Frequently Asked Questions (Click to see answers)

What is an algebraic expression in KS3?

An algebraic expression is a mix of numbers, variables, and operations without an equals sign, such as 4x + 7 or 2a(b + 3).

How do I simplify expressions with like terms?

Group like terms and add or subtract their coefficients. For example, 3x + 5x ? 2x simplifies to 6x.

What’s the difference between expanding and factorising?

Expanding removes brackets, e.g. 2(x + 3) = 2x + 6. Factorising puts a common factor outside brackets, e.g. 6x + 9 = 3(2x + 3).

Try These Related Quizzes

1.

Which of the following is not a mathematical expression?

[ ]	6
[ ]	6a x 14
[ ]	5a - 4b +16c x 8d
[ ]	Oh my gosh!

2.

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

[ ]	Other letters
[ ]	Only numbers greater than 1
[ ]	Only numbers less than 1
[ ]	Values

3.

Simplify 5a + 7a.

[ ]	12a
[ ]	12aa
[ ]	57a
[ ]	57aa

4.

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

[ ]	5a
[ ]	6a
[ ]	23aa
[ ]	6a²

5.

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

[ ]	26ab
[ ]	15a² + 11b²
[ ]	15a + 11b
[ ]	9a + 17b

6.

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

[ ]	4a + 2b - 3c
[ ]	5a + b
[ ]	6a - 3b
[ ]	9a - 2b - c

7.

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

[ ]	2x
[ ]	2 + x
[ ]	2 - x
[ ]	x²

8.

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

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

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

You can find more about this topic by visiting BBC Bitesize - Expressions and formulae

Maths Quiz - Level 3-4 Algebra - Expressions (Answers)

1.

Which of the following is not a mathematical expression?

[ ]	6
[ ]	6a x 14
[ ]	5a - 4b +16c x 8d
[x]	Oh my gosh!

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

2.

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

[ ]	Other letters
[ ]	Only numbers greater than 1
[ ]	Only numbers less than 1
[x]	Values

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

3.

Simplify 5a + 7a.

[x]	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.

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

[ ]	5a
[ ]	6a
[ ]	23aa
[x]	6a²

You must multiply the numbers together AND the letters. Remember a x a = a²

5.

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

[ ]	26ab
[ ]	15a² + 11b²
[x]	15a + 11b
[ ]	9a + 17b

Here we are adding numbers together, NOT multiplying them together

6.

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

[ ]	4a + 2b - 3c
[x]	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

7.

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

[x]	2x
[ ]	2 + x
[ ]	2 - x
[ ]	x²

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

8.

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

[ ]	c3
[ ]	c + 3
[x]	c - 3
[ ]	c - 3 - 3

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

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]	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]	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