Expressions, equations, formulae and identities - Edexcel GCSE Maths (Calculator) Exam Questions

Practise 18 exam-style questions on Expressions, equations, formulae and identities for Edexcel GCSE Maths (Calculator). Write your answer as you would in the exam and get it marked in seconds against the mark scheme, point by point, with an AI tutor on hand if you get stuck.

18 questions
1–5 marks each
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18 questions, marked as you go

Sample questions with model answers

Here are 4 of the questions in this topic, each with a model answer, an explanation of why it earns the marks and the mark scheme an examiner would use.

Question 1

2 marks

For each of the following, write down whether it is an expression, an equation, a formula or an identity.

P \(5x - 3 = 2(x + 6)\)
Q \(5x - 3x + 2\)
R \(s = \dfrac{d}{t}\)
S \(5(x - 3) \equiv 5x - 15\)

Model answer

P is an equation (it is true for only one value of x).
Q is an expression (there is no equals sign).
R is a formula (it connects different quantities, distance, speed and time).
S is an identity (it is true for all values of x).

Explanation

An expression is a collection of terms with no equals sign. An equation has an equals sign and is true only for particular values, which you can solve for. A formula is a rule linking different variables, and an identity (often written with ≡) is true for every value of the letter.

Mark scheme

2 marks
B2 for all four correct: P equation, Q expression, R formula, S identity
B1 for two or three correct

Question 2

2 marks

Here are four numbers.

2.4 2.5 2.6 2.7

Which of these numbers satisfy the inequality \(3x - 4.6 \le 2.9\)?
You must show your working.

Model answer

\(3x - 4.6 \le 2.9\)
\(3x \le 7.5\)
\(x \le 2.5\)
The numbers that satisfy the inequality are 2.4 and 2.5.

Explanation

Solve an inequality like an equation: add 4.6 to both sides, then divide by 3. The sign ≤ means "less than or equal to", so 2.5 is included. A common mistake is to leave out 2.5, which would be correct only for the strict inequality <.

Mark scheme

1 mark
M1 for \(3x \le 7.5\) or \(x \le 2.5\), or for substituting all four values (2.6, 2.9, 3.2, 3.5)
oe
1 mark
A1 for 2.4 and 2.5 (and no others)
cao

Question 3

3 marks

A taxi firm charges a fixed fee of £3.20 plus £1.85 for each mile travelled.

Write down a formula for the cost, £C, of a journey of m miles.

Leah's taxi journey cost £24.66
Use your formula to work out how many miles Leah travelled.

Model answer

\(C = 3.20 + 1.85m\)
\(24.66 = 3.20 + 1.85m\)
\(21.46 = 1.85m\)
\(m = 21.46 \div 1.85 = 11.6\)
Leah travelled 11.6 miles.

Explanation

A formula connects two variables, so it must start "C = ...". The fixed fee is added once, and the cost per mile is multiplied by m. To use it backwards, substitute C = 24.66 and solve the equation: subtract the fixed fee first, then divide by 1.85.

Mark scheme

1 mark
B1 for \(C = 3.20 + 1.85m\)
oe, e.g. \(C = 1.85m + 3.2\); must be a formula (C = ...); accept \(C = 320 + 185m\) only if C is defined in pence; correct answer with no working scores full marks
1 mark
M1 for \(24.66 = 3.20 + 1.85m\) or \((24.66 - 3.20) \div 1.85\)
oe
1 mark
A1 for 11.6 miles
cao

Question 4

4 marks

Zara says,
"\((x + 4)(x - 1) - (x + 2)(x - 3) = 3x + 5.4\) is an identity."

Show that Zara is wrong, and find the value of x that makes the statement true.

Model answer

\((x + 4)(x - 1) = x^2 + 3x - 4\)
\((x + 2)(x - 3) = x^2 - x - 6\)
Left-hand side \(= x^2 + 3x - 4 - x^2 + x + 6 = 4x + 2\)
\(4x + 2\) is not identical to \(3x + 5.4\), so the statement is not true for all x: it is an equation, not an identity.
\(4x + 2 = 3x + 5.4\)
x = 3.4

Explanation

Simplify the left-hand side fully. If it were an identity, it would simplify to exactly \(3x + 5.4\); it does not, so it is an equation, true for only one value of x. Take care subtracting the second product: every term changes sign, so −(−x) = +x and −(−6) = +6.

Mark scheme

1 mark
M1 for expanding both products: \(x^2 + 3x - 4\) and \(x^2 - x - 6\)
oe; at least 3 of the 4 terms in each correct
1 mark
A1 for simplifying the left-hand side to \(4x + 2\)
cao
1 mark
C1 for a correct explanation, e.g. \(4x + 2\) is not the same as \(3x + 5.4\), so the statement is only true for one value of x and is an equation, not an identity
oe
1 mark
A1 for x = 3.4
exact answer 3.4 (accept \(\frac{17}{5}\)); ft their linear left-hand side

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