Stage 9 - Q1 - 3 marks
Find first and second differences; classify the pattern.
Hint
Use the differences between consecutive first differences.
Stage 9 - Q2 - 3 marks
Find first and second differences; classify the pattern.
Hint
Use the differences between consecutive first differences.
Stage 9 - Q3 - 3 marks
Assuming a rule of the form \(n^2+c\), find the nth term.
Hint
Subtract 1,4,9,16 from the corresponding terms.
Stage 9 - Q4 - 3 marks
Assuming a rule of the form \(n^2+c\), find the nth term.
Hint
Subtract 1,4,9,16 from the corresponding terms.
Stage 9 - Q5 - 4 marks
Count each pattern and give a rule for the total dots in Pattern \(n\). Then find Pattern 10.
Hint
Separate the growing square from the fixed extra dots.
Stage 9 - Q6 - 4 marks
A sequence has rule \(n^2+c\). Its fifth term is 30. Find \(c\) and the first four terms.
Hint
The fifth square is 25.
Stage 9 - Q7 - 3 marks
A pupil says the pattern \(5,\ 8,\ 13,\ 20\) is linear because its second differences are constant. Correct the classification.
Hint
First and second differences are different tests.
Stage 9 - Q8 - 4 marks
A sequence follows \(n^2+c\) and starts -6, -3. Find \(c\) and the next three terms.
Hint
Negative early terms do not prevent a quadratic rule.
Stage 9 - Q9 - 4 marks
A pattern has an \(n\times n\) tile square and 6 extra tiles. Its total is 175. Find the pattern number.
Hint
The pattern number is a positive integer.
Stage 9 - Q10 - 5 marks
Challenge: A sequence has rule \(T_n=n^2+c\). Its sixth and eighth terms sum to 114. Find \(c\) and decide whether 176 is a term, giving its position if so.
Hint
Use the same unknown offset in both given terms.