Difference Method: Challenge & Extension
Mathematics
Year 9
15 questions
~30 mins
3 views0 downloads
About This Worksheet
A worksheet focusing on the Difference Method for quadratic sequences, designed to develop procedural skills and reasoning at a higher level.
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Difference Method: Challenge & Extension
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Introduction
Read the key concept below before attempting the questions.
1.
The Difference Method involves analyzing the successive differences of a sequence. For quadratic sequences, the second differences are constant. Use this property to find the nth term.
[4 marks]B
Fluency & Practice
Answer all questions to build your procedural mastery.
1.
Given the sequence 3, 8, 15, 24, find the second differences and determine if the sequence is quadratic.
[3 marks]2.
Find the second difference of the sequence: 2, 6, 12, 20, 30.
[2 marks]3.
Use the difference method to find the nth term of the sequence 1, 4, 9, 16, 25.
[4 marks]C
Targeted Practice
Apply the difference method to more complex sequences.
1.
The sequence 5, 14, 27, 44, ... is quadratic. Find the second differences and determine the general term formula.
[4 marks]2.
Given the sequence 7, 15, 27, 43, ... find the sequence's second difference and write the nth term.
[4 marks]3.
Construct the sequence where the second difference is constant at 6, starting with first term 2. Write the first four terms.
[3 marks]D
Problem Solving & Reasoning
Solve multi-step problems and explain your reasoning.
1.
The sequence of tickets sold over consecutive days is quadratic. The number of tickets sold are 10, 25, 44, 67. Use the difference method to find the nth term and predict the number of tickets sold on the 6th day.
[5 marks]2.
A ball is dropped from a height, and its height after t seconds follows a quadratic sequence. The heights after 1, 2, 3 seconds are 10, 18, 28 meters respectively. Find the general formula for height using the difference method.
[5 marks]E
Real-world Applications
Apply the difference method to practical scenarios.
1.
A car's distance covered over time follows a quadratic pattern. The distances in km after 1, 2, 3 hours are 5, 12, 21. Find the formula for distance and estimate the distance after 4 hours.
[4 marks]2.
In a farming experiment, the number of crops harvested each week follows a quadratic trend. The weekly harvests are 20, 35, 50, 65. Use the difference method to find the weekly harvest formula.
[4 marks]F
Challenge & Extension
Tackle these advanced problems for further mastery.
1.
Create a quadratic sequence where the second difference is 8 and the first term is 3. Write the first five terms.
[4 marks]2.
Given the sequence 2, 8, 18, 32, ... find the second difference and derive the nth term.
[4 marks]G
Mixed Review & Error Analysis
Review common mistakes and practice identifying errors.
1.
A student claims the sequence 4, 9, 16, 25 has a constant first difference. Identify and correct the mistake in their reasoning.
[3 marks]2.
A sequence has second differences that are not constant. Explain why it cannot be quadratic and suggest how to verify the sequence.
[4 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.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet