Gradient of Linear Graphs (Copy)
IGCSE Mathematics 0580 – CORE Practice Exam
Topic: Finding the Gradient of a Straight Line from a Grid
Includes Full Worked Solutions
Paper 1 – Non-Calculator Section
Q1.
On a grid, a straight line passes through the points (0, 2) and (4, 6).
Find the gradient of the line.
Solution:
- Rise = 6 – 2 = 4
- Run = 4 – 0 = 4
- Gradient = rise ÷ run = 4 ÷ 4 = 1
Answer: 1
Q2.
A line passes through the points (1, 5) and (4, 2).
Find the gradient.
Solution:
- Rise = 2 – 5 = –3
- Run = 4 – 1 = 3
- Gradient = rise ÷ run = –3 ÷ 3 = –1
Answer: –1
Q3.
On a graph, a straight line passes through (–2, –1) and (2, 3).
Find the gradient of the line.
Solution:
- Rise = 3 – (–1) = 3 + 1 = 4
- Run = 2 – (–2) = 2 + 2 = 4
- Gradient = 4 ÷ 4 = 1
Answer: 1
Q4.
A line passes through (–3, 2) and (1, –2).
Find the gradient.
Solution:
- Rise = –2 – 2 = –4
- Run = 1 – (–3) = 1 + 3 = 4
- Gradient = –4 ÷ 4 = –1
Answer: –1
Q5.
A line passes through (0, 5) and (5, 5).
Find the gradient.
Solution:
- Rise = 5 – 5 = 0
- Run = 5 – 0 = 5
- Gradient = 0 ÷ 5 = 0
(This is a horizontal line.)
Answer: 0
Paper 2 – Calculator Allowed Section
Q6.
A line passes through (–4, –2) and (2, 1).
Find the gradient.
Solution:
- Rise = 1 – (–2) = 1 + 2 = 3
- Run = 2 – (–4) = 2 + 4 = 6
- Gradient = 3 ÷ 6 = 0.5
Answer: 0.5
Q7.
A line passes through (2, 8) and (5, 8).
Find the gradient.
Solution:
- Rise = 8 – 8 = 0
- Run = 5 – 2 = 3
- Gradient = 0 ÷ 3 = 0
Answer: 0
Q8.
A line passes through (1, 2) and (1, 7).
What is the gradient?
Solution:
- Run = 1 – 1 = 0 → no run → vertical line
- Gradient is undefined.
Answer: Undefined
Q9.
Find the gradient between (–1, –3) and (3, –3).
Solution:
- Rise = –3 – (–3) = 0
- Run = 3 – (–1) = 4
- Gradient = 0 ÷ 4 = 0
Answer: 0
Q10.
Find the gradient between (–5, 2) and (0, –3).
Solution:
- Rise = –3 – 2 = –5
- Run = 0 – (–5) = 0 + 5 = 5
- Gradient = –5 ÷ 5 = –1
Answer: –1
This practice exam tests all CORE-level skills for finding the gradient directly from two points on a grid by carefully calculating rise ÷ run as required.