Algebraic notation - Edexcel GCSE Maths (Calculator) Exam Questions

Practise 19 exam-style questions on Algebraic notation 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.

19 questions
1–5 marks each
Instant marking
No sign-up needed

19 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

1 mark

Write \(0.5x + 0.25y\) using fractions instead of decimals for the coefficients.

Model answer

\(0.5 = \dfrac{1}{2}\) and \(0.25 = \dfrac{1}{4}\)
\(0.5x + 0.25y = \dfrac{1}{2}x + \dfrac{1}{4}y = \dfrac{x}{2} + \dfrac{y}{4}\)

Explanation

In algebra, coefficients are usually written as fractions rather than decimals. \(\dfrac{1}{2}x\) means the same as \(\dfrac{x}{2}\): half of x. Fractions are exact, which matters for coefficients such as \(\dfrac{1}{3}\) that have no exact decimal.

Mark scheme

1 mark
B1 for \(\dfrac{x}{2} + \dfrac{y}{4}\)
accept \(\dfrac{1}{2}x + \dfrac{1}{4}y\) or \(\dfrac{2x + y}{4}\)

Question 2

2 marks

Write down an expression, using fraction notation, for the mean of a, 2a and b.

Model answer

Total = \(a + 2a + b = 3a + b\)
There are 3 values.
Mean = \(\dfrac{3a + b}{3}\)

Explanation

The mean is the total divided by the number of values. Write the division as a fraction with the whole total on top: \(\dfrac{3a + b}{3}\). Writing \(3a + \dfrac{b}{3}\) is wrong because it divides only the b by 3.

Mark scheme

1 mark
M1 for \(a + 2a + b\) or \(3a + b\) seen as the total
correct answer with no working scores full marks
1 mark
A1 for \(\dfrac{3a + b}{3}\)
oe, e.g. \(\dfrac{a + 2a + b}{3}\) or \(a + \dfrac{b}{3}\); do not accept \(3a + b \div 3\) or \(3a + \dfrac{b}{3}\)

Question 3

3 marks

Kim has simplified four expressions.

Card A: p × p × p = 3p
Card B: 4 × q ÷ r = \(\dfrac{4q}{r}\)
Card C: 2 × m × n × m = \(2m^2n\)
Card D: t + t + t + t = \(t^4\)

Two of Kim's answers are wrong.
Write down the letters of the two cards that are wrong, and write the correct answer for each.

Model answer

Card A is wrong: \(p \times p \times p = p^3\) (3p means \(p + p + p\)).
Card D is wrong: \(t + t + t + t = 4t\) (\(t^4\) means \(t \times t \times t \times t\)).
Cards B and C are correct.

Explanation

Kim has mixed up repeated addition and repeated multiplication. Adding the same letter several times gives a coefficient (\(4t\)); multiplying it by itself gives a power (\(p^3\)). You can check with a number: if p = 2, then \(2 \times 2 \times 2 = 8\), but \(3 \times 2 = 6\).

Mark scheme

1 mark
B1 for identifying cards A and D as wrong
B0 if any other card is also identified; correct answer with no working scores full marks
1 mark
B1 for the correction for card A: \(p^3\)
cao
1 mark
B1 for the correction for card D: \(4t\)
cao

Question 4

4 marks

The diagram shows a shape made from a rectangle and a triangle.
The rectangle has width 2x cm and height (x + 3) cm.
The triangle has base 2x cm and perpendicular height x cm.

Show that the area, A cm², of the shape is given by \(A = 3x(x + 2)\).

Geometry diagram, marked "Diagram NOT accurately drawn". Pentagon ABCDE. Dashed line segments join the midpoint of EC to D. Dashed line segment EC is drawn. Side AB is labelled 2x cm. Side BC is labelled (x + 3) cm. The line from D to the midpoint of EC is labelled x cm. The angle at the midpoint of EC between the lines to D and C is marked as a right angle (90°).

Model answer

Area of the rectangle = \(2x \times (x + 3) = 2x^2 + 6x\)
Area of the triangle = \(\dfrac{1}{2} \times 2x \times x = x^2\)
\(A = 2x^2 + 6x + x^2 = 3x^2 + 6x\)
\(3x^2 + 6x = 3x(x + 2)\)
So \(A = 3x(x + 2)\)

Explanation

Find each area separately, using a bracket for the side \((x + 3)\), then add and collect the \(x^2\) terms and the x terms. Finally take out the common factor \(3x\) to reach the form asked for. In a "show that" question every step must be written down.

Mark scheme

1 mark
M1 for the area of the rectangle: \(2x(x + 3)\) or \(2x^2 + 6x\)
1 mark
M1 for the area of the triangle: \(\dfrac{1}{2} \times 2x \times x\) or \(x^2\)
1 mark
M1 for adding and collecting like terms: \(3x^2 + 6x\)
1 mark
A1 for a complete correct argument ending with \(3x^2 + 6x = 3x(x + 2)\)
all working must be shown; answer only scores 0

Ready to try the rest? Every answer you write is marked against the mark scheme, so you can see exactly where the marks are.

AI Tutor Hints first, answers after you try

Hi! Stuck? Ask me for a hint and I’ll help you work it out. Once you’ve checked your answer I can explain exactly where the marks are.