Stage 8 - Q1 - 2 marks
How many dots are in Pattern 1?
Hint
Count the two groups separately.
Stage 8 - Q2 - 2 marks
How many dots are added at each step?
Hint
Compare the changing teal part.
Stage 8 - Q3 - 2 marks
Write a position rule for this pattern.
Hint
Separate the repeated and fixed parts.
Stage 8 - Q4 - 2 marks
Use the rule \(T_{n}=5n+4\) to find the number of dots in Pattern 12.
Hint
The position is the value of n.
Stage 8 - Q5 - 2 marks
A row of n joined squares uses \(3n+1\) matchsticks. Find the number for 17 squares.
Hint
Check that the shared-side rule gives four when \(n=1\).
Stage 8 - Q6 - 2 marks
A pattern consists of 2 fixed dots and n groups of 6. Which pattern has 74 dots?
Hint
Undo the fixed addition before dividing.
Stage 8 - Q7 - 3 marks
A pattern has rule \(4n+3\). Can it have exactly 66 dots? Explain.
Hint
A position number must be a positive integer.
Stage 8 - Q8 - 3 marks
Pattern A has \(2n+7\) tiles and Pattern B has \(5n+1\) tiles. At which shared position are their counts equal?
Hint
The same position n must be used in both rules.
Stage 8 - Q9 - 4 marks
A pupil proposes \(6n+2\) for a pattern with 8, 13, 18, 23 tiles. Identify the error and give the correct linear rule.
Hint
Test both the difference and the first term.
Stage 8 - Q10 - 5 marks
Challenge: a row of n joined squares uses \(3n+1\) sticks. A row of m joined triangles uses \(2m+1\) sticks. Find the greatest total below 50 sticks that can make either complete design, and give both row lengths.
Hint
Look for totals that leave remainder 1 on division by both 3 and 2.