Practise 28 exam-style questions on Expanding, factorising and simplifying 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.
28 questions
1–5 marks each
Instant marking
No sign-up needed
20 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.
Multiply every term inside each bracket by the number outside. The −3 multiplies both terms in the second bracket, so \(-3 \times -5 = +15\). The most common mistake is to write −15, which gives \(6x - 23\).
Mark scheme
1 mark
M1 for 3 of the 4 terms correct: \(12x\), −8, \(-6x\), +15
oe; correct answer with no working scores full marks
Multiply each term in the first bracket by each term in the second (four products), then collect the x terms. The constant is \(1.5 \times -2.4 = -3.6\), and the x terms are \(-2.4x + 1.5x = -0.9x\). A common mistake is to add 1.5 and 2.4 to get \(3.9x\).
Mark scheme
1 mark
M1 for 3 of the 4 terms correct: \(x^2\), \(-2.4x\), \(+1.5x\), −3.6
oe; correct answer with no working scores full marks
Expand each part separately, keeping the second product in a bracket so that the minus sign changes every one of its signs. \((3x - 2y)^2\) has a middle term, \(-12xy\). A common mistake is to subtract only the first term of the second product, giving \(8x^2 - 15xy\).
Mark scheme
1 mark
M1 for \((3x - 2y)^2 = 9x^2 - 12xy + 4y^2\)
at least 3 of the 4 terms of \(9x^2 - 6xy - 6xy + 4y^2\) correct; correct answer with no working scores full marks
1 mark
M1 for \((x + y)(x - 4y) = x^2 - 3xy - 4y^2\)
at least 3 of the 4 terms of \(x^2 - 4xy + xy - 4y^2\) correct
1 mark
A1 for \(8x^2 - 9xy + 8y^2\)
cao
Question 4
4 marks
Mia is asked to simplify fully \(\dfrac{x^2 + 4x - 12}{x^2 - 36}\)
Explain the mistake Mia has made. Simplify the expression fully.
Model answer
Mia cancelled \(x^2\) from the top and bottom, but \(x^2\) is a term, not a factor of the whole numerator and denominator. You must factorise first and cancel only common factors. \(\dfrac{x^2 + 4x - 12}{x^2 - 36} = \dfrac{(x + 6)(x - 2)}{(x + 6)(x - 6)} = \dfrac{x - 2}{x - 6}\)
Explanation
In an algebraic fraction you can only cancel something that multiplies the whole of the top and the whole of the bottom. Factorise both: the numerator is a quadratic and the denominator is a difference of two squares. You can test Mia's answer: when x = 1 the original is \(\frac{-7}{-35} = \frac{1}{5}\), but hers gives \(\frac{2}{9}\).
Mark scheme
1 mark
C1 for a correct explanation, e.g. she cancelled the \(x^2\) terms, but you can only cancel common factors, not terms; she should factorise first
oe
1 mark
M1 for \((x + 6)(x - 2)\)
numerator factorised
1 mark
M1 for \((x + 6)(x - 6)\)
denominator factorised
1 mark
A1 for \(\dfrac{x - 2}{x - 6}\)
cao
Ready to try the rest? Every answer you write is marked against the mark scheme, so you can see exactly where the marks are.
Ctrl + Enter to check
AI TutorHints 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.
