y = aˣ: Problem Solving & Reasoning
Mathematics
Grade 8
14 questions
~28 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on understanding and applying the exponential function y = aˣ, designed for Grade 8 students to develop procedural fluency and problem-solving skills.
Topics covered:
Worksheet Preview
Full preview • 14 questions
y = aˣ: Problem Solving & Reasoning
Subject: MathematicsGrade: Grade 8
Name:
Date:
TeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizz
Untitled Worksheet
Grade Grade 8
A
Fluency & Practice
Answer the following questions to practice basic skills with y = aˣ. Show your working in the grid spaces provided.
1.
Calculate y when a = 3 and x = 4.
[2 marks]2.
Evaluate y = (1/2)ˣ for x = 3.
[2 marks]3.
Plot the graph of y = 2ˣ for x from -2 to 2 on the grid.
[3 marks]B
Targeted Practice
Solve these questions to strengthen your understanding of y = aˣ at different values of a and x.
1.
Find y when a = 5 and x = -2.
[2 marks]2.
Construct a graph of y = 0.5ˣ for x between -3 and 3.
[3 marks]3.
Explain why the graph of y = 2ˣ is increasing as x increases.
[3 marks]C
Real-world Applications
Solve these word problems involving y = aˣ in real-world contexts.
1.
A bacteria culture doubles in size every hour. If the initial size is 100 bacteria, write an expression for the number of bacteria after x hours and calculate the size after 3 hours.
[4 marks]2.
A radioactive substance decays so that its remaining amount after x days is given by y = 50 * (1/2)ˣ. How much remains after 4 days?
[2 marks]D
Challenge & Extension
Attempt these more challenging questions to extend your understanding of y = aˣ.
1.
Given the graph of y = 3ˣ, determine the approximate value of y when x = 2.5. (Estimate based on the graph.)
[3 marks]2.
Derive the formula for y = aˣ when a is between 0 and 1, and explain how its graph differs from y = aˣ when a > 1.
[4 marks]E
Mixed Review
Answer these questions to review different aspects of y = aˣ.
1.
Plot the graph of y = 4ˣ for x from -2 to 2.
[3 marks]2.
If y = 2ˣ and y = 8, find x.
[2 marks]F
Error Analysis
Review these common mistakes and identify what students might do incorrectly. Then, suggest corrections.
1.
A student calculates y = 2ˣ when x= -3 and gets 8 as the answer. Identify the mistake and correct it.
[3 marks]2.
A student claims that y = aˣ is decreasing for all a < 1. Explain whether this is true and give a reason.
[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