Positive: Challenge & Extension
Mathematics
Grade 8
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on positive gradients from graphs, designed to challenge and extend understanding for Grade 8 students.
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Positive: Challenge & Extension
Subject: MathematicsGrade: Grade 8
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Date:
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Untitled Worksheet
Grade Grade 8
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the gradient of the line passing through points (2, 3) and (5, 9).
[2 marks]2.
Determine if the graph of a line passing through (1, 2) and (4, 5) has a positive gradient.
[1 mark]AYes
BNo
3.
Plot the graph of y=3x + 1. Describe the slope of this line.
[2 marks]B
Problem Solving & Reasoning
Answer all questions with detailed working.
1.
A line passes through points (0, 4) and (3, 10). Explain why the gradient is positive and calculate its value.
[3 marks]2.
A graph shows a line with a positive gradient. If the line passes through (1, 2) and (4, y), what is the value of y?
[2 marks]C
Real-world Applications
Use your understanding of positive gradients to solve the following.
1.
A car accelerates such that its speed graph has a positive gradient. If the graph shows a change in speed from 20 km/h to 60 km/h over 5 seconds, what is the acceleration?
[2 marks]2.
A company's profit increases steadily over months, represented by a line with a positive gradient. If the profit increased from $10,000 to $25,000 over 5 months, what is the average monthly increase?
[3 marks]D
Challenge & Extension
Attempt these advanced problems to extend your understanding.
1.
Construct a line on the grid with a positive gradient of 3 passing through (0, 2). Write its equation.
[3 marks]2.
A graph shows two lines with positive gradients. The first line has a gradient of 4, and the second has a gradient of 1.5. Describe how their steepness compares and what the gradients indicate about their slopes.
[3 marks]E
Mixed Review
Answer these questions to review positive gradients.
1.
Identify the mistake: A student claims the gradient of a rising line is negative because the line goes up from left to right.
[2 marks]2.
Calculate the gradient of the line passing through (2, 5) and (6, 17).
[2 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