IGCSE Math RevisionQuestion 1
A straight line goes up \(6\) units for every \(2\) units across.
Work out its gradient.
Show the worked answer
- Gradient \(= \frac{\text{change in } y}{\text{change in } x} = \frac{6}{2} = 3\).
Answer: \(3\)
Cambridge IGCSE Maths (0580) · Topic 3: Coordinate geometry · 3.3
Cambridge IGCSE Maths 0580 Gradient of a Straight Line Questions
Gradient of a Straight Line 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.
- 9 questions
- 6 Core
- 3 Extended
- 7 non-calculator
- Free, no sign-in
What the syllabus asks
- 3.3 Gradient of linear graphs Core Extended
Find the gradient of a straight line from its graph.
Extended also: Calculate the gradient from the coordinates of two points.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
Gradient of a Straight Line questions: Core
For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).
Question 2
A straight line passes through \((0, 4)\) and \((4, 0)\).
Work out its gradient.
Show the worked answer
- From \((0, 4)\) to \((4, 0)\): \(y\) goes down \(4\) as \(x\) goes up \(4\).
- Gradient \(= \frac{-4}{4} = -1\).
Answer: \(-1\)
Question 3
A straight ramp rises 1.2 m over a horizontal distance of 4.8 m. Find the gradient of the ramp.
Show the answer and mark scheme
- M1 1.2 ÷ 4.8
- A1 0.25
Answer: \(0.25\)
Question 4
A ramp rises \(0.6\) m over a horizontal distance of \(4\) m.
Work out the gradient of the ramp.
Show the worked answer
- \(\frac{0.6}{4} = 0.15\)
Answer: \(0.15\)
Question 5
The graph of a straight line is drawn on a grid. The line passes through the grid points \((-2, 3)\) and \((4, 6)\). Use these points to find the gradient of the line.
Show the answer and mark scheme
- M1 (6 − 3) ÷ (4 − (−2))
- A1 1/2 oe
Answer: \(\frac{1}{2}\)
Question 6
A straight-line graph shows the cost of a phone call, in dollars, against its length in minutes. It passes through \((10, 4.50)\) and \((30, 10.50)\).
(a) Find the gradient of the line.
(b) What does the gradient represent?
Show the answer and mark scheme
- B1 (a) 0.3
- B1 (b) the cost per minute (30 cents a minute)
Answer: (a) \(0.3\) (b) the cost per minute, \(\$0.30\)
Gradient of a Straight Line questions: Extended
Extended content, for Papers 2 and 4. Core students can skip these.
Question 7
Work out the gradient of the line through \((2, 3)\) and \((6, 11)\).
Show the worked answer
- \(\frac{11 - 3}{6 - 2} = \frac{8}{4} = 2\)
Answer: \(2\)
Question 8
Work out the gradient of the line through \((-1, 5)\) and \((3, -3)\).
Show the worked answer
- \(\frac{-3 - 5}{3 - (-1)} = \frac{-8}{4} = -2\)
Answer: \(-2\)
Question 9
The line through \((2, k)\) and \((5, 13)\) has gradient \(3\).
Find \(k\).
Show the worked answer
- \(\frac{13 - k}{5 - 2} = 3\), so \(13 - k = 9\).
- \(k = 4\)
Answer: \(k = 4\)
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).
Keep going
- Coordinate geometry practice for 0580: more questions, each one marked, tagged Core or Extended
- My mistakes, then a Skill Builder on the skills you missed
- Common mistakes in 0580: what the Cambridge examiner reports say
- Coordinate geometry revision notes and the 0580 formula sheet
- Cambridge IGCSE Maths 0580 past papers, when you are ready for a full paper
Questions students ask
Which Cambridge 0580 papers can test gradient of a straight line?
Gradient of a Straight Line is on both tiers (syllabus 3.3), 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.
Are these Cambridge past-paper questions?
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.
Where can I practise more gradient of a straight line questions?
In the 0580 practice for topic 3 (Coordinate geometry), 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.