Algebraic notation - Edexcel GCSE Maths (Non-calculator) Exam Questions

Practise 18 exam-style questions on Algebraic notation for Edexcel GCSE Maths (Non-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

Simplify \(3a \times 2b \times a \times b \times b\)

Model answer

\(3 \times 2 = 6\)
\(a \times a = a^2\)
\(b \times b \times b = b^3\)
So \(3a \times 2b \times a \times b \times b = 6a^2b^3\)

Explanation

Multiply the numbers together, then count how many times each letter is multiplied: there are two a's and three b's. Powers show repeated multiplication, so \(a \times a = a^2\) and \(b \times b \times b = b^3\). Do not add the numbers (\(3 + 2 = 5\)) - they are multiplied.

Mark scheme

2 marks
B2 for \(6a^2b^3\)
B1 for a single term with two of the three parts correct, e.g. \(6a^2b^2\), \(6ab^3\), \(5a^2b^3\) or \(a^2b^3\) with a wrong coefficient; or for \(6 \times a^2 \times b^3\) not fully simplified

Question 2

2 marks

Here are six expressions.
A: \(2x \div 5\)
B: \(\dfrac{2}{5x}\)
C: \(0.4x\)
D: \(\dfrac{2}{5}x\)
E: \(\dfrac{5x}{2}\)
F: \(x \div \dfrac{5}{2}\)

Write down the letters of all the expressions that are equivalent to \(\dfrac{2x}{5}\)

Model answer

A: \(2x \div 5 = \dfrac{2x}{5}\) - equivalent
B: \(\dfrac{2}{5x}\) has \(x\) in the denominator - not equivalent
C: \(0.4x = \dfrac{4}{10}x = \dfrac{2}{5}x\) - equivalent
D: \(\dfrac{2}{5}x = \dfrac{2x}{5}\) - equivalent
E: \(\dfrac{5x}{2}\) is the reciprocal fraction - not equivalent
F: \(x \div \dfrac{5}{2} = x \times \dfrac{2}{5} = \dfrac{2x}{5}\) - equivalent
Answer: A, C, D and F

Explanation

The fraction line means divide, so \(\dfrac{2x}{5} = 2x \div 5 = \dfrac{2}{5} \times x\). Dividing by \(\dfrac{5}{2}\) is the same as multiplying by \(\dfrac{2}{5}\). Watch where the \(x\) is: in B it is in the denominator, which gives a different expression.

Mark scheme

2 marks
B2 for A, C, D and F only
B1 for three of A, C, D, F and no incorrect letters, or for all four of A, C, D, F with one incorrect letter

Question 3

3 marks

Adult tickets for a show cost £\(a\) each.
A child ticket costs half the price of an adult ticket.

Write an expression, in terms of \(a\), for the total cost in pounds of 2 adult tickets and 3 child tickets.
Give your answer in its simplest form, writing any coefficient as a fraction.

Model answer

One child ticket: \(\dfrac{a}{2}\)
Total: \(2a + 3 \times \dfrac{a}{2} = \dfrac{4a}{2} + \dfrac{3a}{2} = \dfrac{7a}{2}\)

Explanation

Half the price is \(\dfrac{a}{2}\), so three child tickets cost \(\dfrac{3a}{2}\). Write \(2a\) as \(\dfrac{4a}{2}\) to add the fractions. In algebra, coefficients such as \(\dfrac{7}{2}\) are written as fractions rather than decimals.

Mark scheme

1 mark
M1 for \(\dfrac{a}{2}\) or \(\dfrac{1}{2}a\) as the cost of a child ticket
oe, e.g. \(a \div 2\) or \(0.5a\); correct answer with no working scores full marks
1 mark
M1 for \(2a + 3 \times \dfrac{a}{2}\)
oe, e.g. \(2a + \dfrac{3a}{2}\) or \(2a + 1.5a\)
1 mark
A1 for \(\dfrac{7a}{2}\)
oe, e.g. \(\dfrac{7}{2}a\); do not accept \(3.5a\) for this mark

Question 4

4 marks

A cyclist rides \(x\) km at an average speed of 12 km/h.
She then rides a further \(2x\) km at an average speed of 16 km/h.

Write an expression, in terms of \(x\), for the total time of the ride in minutes.
Give your answer in its simplest form, writing any coefficient as a fraction.

Model answer

Time = distance ÷ speed
First part: \(\dfrac{x}{12}\) hours
Second part: \(\dfrac{2x}{16} = \dfrac{x}{8}\) hours
Total: \(\dfrac{x}{12} + \dfrac{x}{8} = \dfrac{2x}{24} + \dfrac{3x}{24} = \dfrac{5x}{24}\) hours
In minutes: \(\dfrac{5x}{24} \times 60 = \dfrac{300x}{24} = \dfrac{25x}{2}\) minutes

Explanation

Use time = distance ÷ speed for each part separately, then add the times - you cannot average the two speeds. Use a common denominator of 24 to add the fractions, then multiply by 60 to change hours into minutes. Check with a value: if \(x = 12\), the ride takes 1 hour + 1.5 hours = 150 minutes, and \(\dfrac{25 \times 12}{2} = 150\).

Mark scheme

1 mark
P1 for a time for one part of the ride, \(\dfrac{x}{12}\) or \(\dfrac{2x}{16}\) hours
oe, e.g. \(5x\) minutes or \(\dfrac{15x}{2}\) minutes; correct answer with no working scores full marks
1 mark
P1 for adding the two times with a common denominator, e.g. \(\dfrac{2x}{24} + \dfrac{3x}{24}\) or \(\dfrac{5x}{24}\) hours
or \(5x + \dfrac{15x}{2}\) minutes
1 mark
P1 for converting hours to minutes, e.g. \(\dfrac{5x}{24} \times 60\)
may be done earlier for each part
1 mark
A1 for \(\dfrac{25x}{2}\)
oe, e.g. \(\dfrac{25}{2}x\) or \(12\frac{1}{2}x\); do not accept \(12.5x\) for this mark

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