Formula m = (y₂-y₁)/(x₂-x₁): Challenge & Extension
Mathematics
Grade 6
19 questions
~38 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the gradient formula m = (y₂ - y₁)/(x₂ - x₁) through practice, problem solving, real-world contexts, and extension questions suitable for Grade 6 students.
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Formula m = (y₂-y₁)/(x₂-x₁): Challenge & Extension
Subject: MathematicsGrade: Grade 6
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Untitled Worksheet
Grade Grade 6
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the gradient (m) between the points (2, 3) and (5, 11).
[2 marks]2.
Find the gradient between the points (-1, 4) and (3, 10).
[2 marks]3.
Determine the gradient between (0, 0) and (4, 8).
[2 marks]4.
Calculate the gradient between (1, 2) and (4, 8).
[2 marks]5.
Find the gradient between points (6, 9) and (9, 15).
[2 marks]6.
A line passes through (3, 5) and (3, 12). What is the gradient?
[2 marks]7.
Calculate the gradient between (–2, –4) and (4, 8).
[2 marks]8.
Determine the gradient between (0, 7) and (8, 7).
[2 marks]B
Problem Solving & Reasoning
Use your understanding of the gradient formula to solve these multi-step problems.
1.
A car travels from point A (2, 4) to point B (6, 10). Find the gradient of its path. If the car continues on the same path, how far does it travel horizontally when it has moved 12 units vertically?
[4 marks]2.
A cyclist rides along a straight path from (1, 2) to (4, 8). The cyclist then continues on the same line. How far horizontally will the cyclist travel when they have moved 12 units vertically?
[4 marks]3.
A ladder leans against a wall, touching the ground at (3, 0) and the wall at (0, 4). Find the gradient of the ladder.
[3 marks]C
Real-world Applications
Solve these questions based on real-life situations involving gradients.
1.
A road rises from point (0 km, 0 m elevation) to (5 km, 250 m elevation). What is the gradient of the road?
[3 marks]2.
A river flows from (0 km, 100 m) to (10 km, 50 m). What is the gradient of the river flow?
[3 marks]D
Challenge & Extension
Tackle these more difficult questions for extension and deepening your understanding.
1.
Find the gradient between points (–3, 2) and (5, –6). Then, determine the equation of the line passing through these points.
[4 marks]2.
A train moves between two stations. At station A, the coordinates are (2, 3), and at station B, they are (8, 15). Find the gradient and the equation of the train's path.
[4 marks]E
Mixed Review
Answer the following to review your understanding of the gradient formula.
1.
Plot the graph of y = 2x for x from 0 to 5. Describe the gradient of this line.
[3 marks]2.
Construct a triangle with vertices at (1, 2), (4, 6), and (1, 6). Calculate the gradient between (1, 2) and (4, 6).
[3 marks]F
Error Analysis
Identify and correct the mistake in each of these common errors.
1.
A student calculates the gradient between (2, 5) and (6, 13) as 8. Find the error and correct it.
[3 marks]2.
A student says the gradient between (–1, 4) and (3, 10) is 3. Is this correct? If not, what is the correct gradient?
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet