🏅 Top 10 in the last 30 days
No results yet. Be the first!
Test
Fibonacci sequence and golden ratio
This test explores the rule of the Fibonacci sequence and ratios of consecutive terms. Tasks require students to continue the sequence, find missing terms and explain how Fibonacci numbers relate to the golden ratio.
Questions: 10Estimated time: 15 minutes
Time left: 00:00:00
Best results on this test
Top 10 registered students. Only each student’s best result in the period counts.
Sample questions
- A Fibonacci sequence fragment is ___, ___, ___, ... Find the next term.
- What is term ___ of 1, 1, 2, 3, 5, ...?
- Insert the missing Fibonacci term: ___, X, ___.
- The shorter side of a golden rectangle is ___ cm. Approximate the longer side using 1.618.
- The longer side of a golden rectangle is ___ cm. Approximate the shorter side.
Fibonacci sequence and golden ratio
In the Fibonacci sequence, every term from the third onward is the sum of the two preceding terms: Fₙ = Fₙ₋₁ + Fₙ₋₂. Check the stated starting values and indexing convention.
The golden ratio
The golden ratio φ satisfies φ = 1 + 1/φ, giving φ = (1 + √5)/2. Ratios of consecutive Fibonacci numbers approach φ but are generally not exactly equal to it at a finite step. In geometry, match the ratio of the longer to shorter part with the ratio of the whole to the longer part.
Related mathematics tests
Unit circle and obtuse angles
This test uses the unit circle to determine trigonometric values. Tasks cover quadrants, signs of sine and cosine, obtuse and supplementary angles and checking whether a resulting value is reasonable.
Combinatorial rules
This test applies the addition and product rules of combinatorics. Students count possible selections and arrangements, organise a solution systematically and avoid including duplicate outcomes.
Proportional division, mixtures and solutions
This test covers proportional division and practical problems involving mixtures, alloys and solutions. Students calculate part ratios, quantities and concentrations and check whether the result satisfies the conditions of the problem.
Parabola and the graph of a quadratic function
Eight questions on a parabola’s vertex, axis of symmetry, zeros, intersections, extrema, transformations and a motion model.
