Cambridge IGCSE Maths (0580) · Topic 2: Algebra and graphs · 2.1
Algebraic Expressions and Substitution questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).
\(a = 3\) and \(b = -2\). Work out the value of
(a) \(4a + 5b\)
(b) \(a^2 - b^2\)
(c) \(ab^2\)
Answer: (a) \(2\) (b) \(5\) (c) \(12\)
Pens cost \(x\) cents each and rulers cost \(y\) cents each.
Write an expression for the total cost, in cents, of \(4\) pens and \(3\) rulers.
Answer: \(4x + 3y\)
\(v = u + at\). Find \(v\) when \(u = 4.5\), \(a = 9.8\) and \(t = 3\).
Answer: \(33.9\)
\(v = u + at\). Find \(v\) when \(u = 12\), \(a = 9.8\) and \(t = 2.5\).
Answer: \(v = 36.5\)
The cost, \(T\) dollars, of hiring a hall for \(n\) hours is \(T = 5n + 40\).
(a) Find the cost of hiring the hall for \(6\) hours.
(b) The cost was $\(105\). For how many hours was the hall hired?
Answer: (a) $\(70\) (b) \(13\) hours
Find the value of \(2x^3 - x^2 + 5\) when \(x = -3\).
Answer: \(-58\)
Find the value of \(2x^2 - 3x\) when \(x = -2\).
Answer: \(14\)
The area of a trapezium is \(A = \frac{1}{2}(a + b)h\). Find \(A\) when \(a = 6.4\), \(b = 9.2\) and \(h = 3.5\).
Answer: \(27.3\)
\(s = ut + \frac{1}{2}at^2\). Find \(s\) when \(u = 4\), \(a = -1.5\) and \(t = 6\).
Answer: \(s = -3\)
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Algebraic Expressions and Substitution is on both tiers (syllabus 2.1), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
In the 0580 practice for topic 2 (Algebra and graphs), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.
IGCSE Math Revision