Algebraic Conjectures Worksheet
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Algebraic Conjectures Worksheet
🧮 Part 1: Making Conjectures from Patterns
The algebraic rule for this pattern is:
My conjecture: The 10th term is ____________
| x (position) | 1 | 2 | 3 | 5 | 10 |
| y (term value) | ____ | ____ | ____ | ____ | ____ |
🔍 Part 2: Testing Your Conjectures
She conjectures that the 8th square number is 64.
a) Test Maya's conjecture by showing your working:
b) Is Maya's conjecture correct? Circle one: YES / NO
a) Write an algebraic rule for the plant's height (h) after w weeks:
h = ________________
b) Make a conjecture: How tall will the plant be after 10 weeks?
My conjecture: ____________ cm
c) Test your conjecture by substituting into your rule:
a) What is the common difference? ________
b) Write the algebraic rule: Term n = ________________
c) Use your rule to find Term 20: ________________
📈 Part 3: Justifying with Evidence
Explain whether Sam's conjecture is correct and show your reasoning:
a) Write an algebraic rule for the total cost (C) for d kilometres:
C = ________________
b) If a journey costs $25.70, how many kilometres was it?
Show your working:
c) Explain how you could use a graph to check your answer:
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