MathsFreePrintable

Algebraic Conjectures Worksheet

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Algebraic Conjectures Worksheet

Use the patterns and rules to make conjectures, test them, and explain your reasoning. Show working where asked.

Making Conjectures from Patterns

1.The sequence 6, 10, 14, 18, 22, ... increases by the same amount each time. Which rule gives the value of term n?

n + 5
4n + 2
2n + 4
6n

2.For the sequence 6, 10, 14, 18, 22, ..., use the rule for term n to find the value of term 12.

3.Use the rule y = 5x - 2 to find y when x is 1, 3, 4, 6 and 9.

____

4.A community hall charges a fixed booking fee of $18 plus $9 for each ticket. Which expression gives the total cost C for n tickets?

C = 18n + 9
C = 9n
C = 18 + 9n
C = 27n

Testing Conjectures

5.Luca says the 9th square number is 81. Test this claim by calculating the 9th square number, then state whether Luca is correct.

6.A seedling is 8 cm tall at the start of a study and grows 4 cm each week. Write a rule for its height h after w weeks, then use the rule to find its height after 7 weeks.

7.A linear sequence begins 9, 15, 21, ... Find its common difference, write a rule for term n, and use the rule to calculate term 18.

Justifying with Evidence

8.Aria claims that the rule y = 3x - 4 gives y = -4 when x = 0. Decide whether the claim is true and justify your answer by substituting x = 0.

9.A shuttle ride costs $4.80 to start, plus $1.70 per kilometre. Write a rule for the fare C for d kilometres. Then find the distance travelled if the fare is $21.80. Finally, describe how a graph of the rule could confirm the distance.