Expressions, equations and identities

Foundation and Higher

The idea

An expression has no equals sign ( $3x + 2$ ). An equation is true for particular values ( $3x + 2 = 11$ ). A formula links quantities ( $A = lw$ ). An identity is true for every value ( $2(x + 1) \equiv 2x + 2$ ).

Write $3 \times n$ as $3n$ and $n \times n$ as $n^2$ .
Terms are the parts joined by $+$ or $-$ .
Check the sign in front of a term belongs to it.

Watch out You simplify an expression but solve an equation.

See it worked

Worked exampleNon-calculator4 marks

Simplify or write each expression.

(a) Simplify $a + a + a + a$

(b) Simplify $3 \times m \times n$

(c) Pens cost $45$ p each and rubbers cost $30$ p each. Write an expression for the total cost, in pence, of $x$ pens and $y$ rubbers.

(a) Four lots of $a$ is $4a$ .
(b) Write the number first and leave out the multiplication signs: $3mn$ .
(c) $x$ pens cost $45x$ pence and $y$ rubbers cost $30y$ pence, so the total is $45x + 30y$ .

Answer (a) $4a$ ; (b) $3mn$ ; (c) $45x + 30y$

Your turn

Question 1Non-calculator1 mark

Which expression is equal to 4 $\times$ p $\times$ p?

Question 2Non-calculator4 marks

A rectangle has length $(x+3)$ cm and width $x$ cm.

(a) Write and simplify an expression for its perimeter.

(b) The perimeter is 30 cm. Find x.

Question 3Non-calculator4 marks

A coach charges a fixed £12 plus £4 per passenger. There are n passengers.

(a) Write a formula for the total charge C.

(b) Find the average cost per passenger when n = 7. Give your answer to the nearest penny.

In past papers

77 official questions in 62 papers since 2017. The latest:

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