Cambridge IGCSE Maths (0580) · Topic 2: Algebra and graphs · 2.10
Graphs of Functions 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).
Here is part of a table of values for \(y = x^2 - 2x - 3\).
(a) Complete the table.
(b) Use your values to write down the solutions of \(x^2 - 2x - 3 = 0\).
| x | −2 | −1 | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|---|
| y | 5 | −3 | −3 | 5 |
Answer: (a) \(0, -4, 0\) (b) \(x = -1\) or \(x = 3\)
Complete the table of values for \(y = \dfrac{12}{x}\).
\[\begin{array}{c|cccccc} x & 1 & 2 & 3 & 4 & 6 & 12 \\ \hline y & & & & & & \end{array}\]
Answer: \(12, 6, 4, 3, 2, 1\)
\(y = \frac{12}{x}\).
(a) Find \(y\) when \(x = 1.5\).
(b) Find \(x\) when \(y = -3\).
Answer: (a) \(8\) (b) \(-4\)
(a) Complete the table of values for \(y = 4 - x^2\).
\[\begin{array}{c|ccccccc} x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline y & & & & & & & \end{array}\]
(b) Use your table to solve \(4 - x^2 = 0\).
Answer: (a) \(-5, 0, 3, 4, 3, 0, -5\) (b) \(x = \pm 2\)
Extended content, for Papers 2 and 4. Core students can skip these.
The graphs of \(y = x^2 - 2\) and \(y = 2x + 1\) cross at two points.
Find the coordinates of the two points.
Answer: \((3, 7)\) and \((-1, -1)\)
\(y = 2^x + 1\).
(a) Find \(y\) when \(x = 3\).
(b) Find \(x\) when \(y = 33\).
Answer: (a) \(9\) (b) \(5\)
The graph of \(y = x^2 - 3x\) has been drawn.
Find the equation of the straight line to draw on the same grid to solve \(x^2 - 5x + 2 = 0\).
Answer: \(y = 2x - 2\)
\(y = x^3 - 4x\).
(a) Find \(y\) when \(x = -1\) and when \(x = 3\).
(b) Find the three values of \(x\) where the graph crosses the \(x\)-axis.
Answer: (a) \(3\) and \(15\) (b) \(x = -2, 0, 2\)
The graph of \(y = x^3 - 2x\) is drawn. By drawing a suitable straight line on the same grid, the equation \(x^3 - 5x + 2 = 0\) can be solved. Find the equation of this straight line.
Answer: \(y = 3x - 2\)
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).
Graphs of Functions is on both tiers (syllabus 2.10), 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