Review practice
Choose a section to work through its questions and solutions. Your progress is shared across pages. Ranges follow collection order; original source labels are kept on each question.
Section 1 · Questions 1–6
Evaluate a sum with three different structures · Recover the square-sum formula from a cubic identity · +4 more
- Question 1 · Evaluate a sum with three different structures
- Question 2 · Recover the square-sum formula from a cubic identity
- Question 3 · Match the final odd square to its summation index
- Question 4 · Subtract the correct prefix from a finite sum
- Question 5 · Express consecutive pair products using square and linear sums
- Question 6 · Rationalise a radical sum and distinguish terms from partial sums
Section 2 · Questions 7–12
Shift both bounds before applying a prefix formula · Separate odd-index and even-index denominator terms · +4 more
- Question 7 · Shift both bounds before applying a prefix formula
- Question 8 · Separate odd-index and even-index denominator terms
- Question 9 · Compare positive denominators to prove a strict lower bound
- Question 10 · Sum the rows of a triangular labelled board
- Question 11 · Distinguish a sequence of geometric sums from its own sum
- Question 12 · Recognise factorial growth from the recurrence
Section 3 · Questions 13–18
Treat fixed points as candidate limits before proving decrease · Count elapsed updates separately from the week label · +4 more
- Question 13 · Treat fixed points as candidate limits before proving decrease
- Question 14 · Count elapsed updates separately from the week label
- Question 15 · Use an iteration to approximate the specified cubic root
- Question 16 · Unfold a loss-then-top-up recurrence in two directions
- Question 17 · Relate separated arithmetic terms to a geometric progression
- Question 18 · Recover terms from partial sums and compare a geometric tail
Section 4 · Questions 19–22
Combine geometric heights with a weighted class mean · Compare a geometric training total with an arithmetic total · +2 more