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.

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Full preview • 14 questions

y = aˣ: Problem Solving & Reasoning

Subject: MathematicsGrade: Grade 8
Name:
Date:
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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]

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Details

Created
1/1/2026
Updated
1/1/2026
Type
worksheet