🏅 Top 10 in the last 30 days
No results yet. Be the first!
Test
Set properties and number representations
Dynamic advanced-course tasks on number sets, inclusion, intervals, recurring decimals and comparing number representations.
Questions: 6Estimated time: 18 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
- Which listed number set is the smallest by inclusion that contains ___? ℕ denotes positive integers, ℤ integers, ℚ rational numbers and ℝ real numbers.
- A is the set of all integers divisible by ___; B is the set of all integers divisible by ___. Which statement is true? The symbol ⊊ means a proper subset: every element is included, but the sets are unequal.||None of these
- A = [___; ___) and B = (___; ___]. Find A ___ B. The symbol ∩ means intersection, ∪ union, and A ∖ B means elements of A that do not belong to B.
- Write the recurring decimal ___.(___) as an ordinary fraction. The two digits in parentheses repeat forever, with no non-repeating decimal digits before them.
- Which sign completes √___ … ___? Both numbers are non-negative.||Unknown
Set properties and number representations
Natural numbers are integers, integers are rational, and rational numbers are real. Distinguish set inclusion from equality.
Intervals and comparing numbers
Intersection keeps common elements, union combines sets, and difference removes elements of the other set. Convert recurring decimals by subtracting shifted equations. Compare non-negative numbers exactly through their squares.
Related mathematics tests
Trigonometric functions and equations
This test covers graphs, periods, ranges and signs of sine, cosine and tangent functions. Tasks also develop solution of elementary trigonometric equations and selection of solutions within a stated interval.
Higher-degree inequalities
Dynamic advanced-course tasks: sign intervals, repeated roots, biquadratic inequalities, restrictions and integer solutions.
Logarithmic equations
This test focuses on solving several types of logarithmic equations. Tasks apply logarithm properties and the fundamental identity, establish domain restrictions and reject invalid solutions.
Logarithms and their properties
This test develops understanding of the definition of a logarithm and its relationship with exponents. Tasks apply product, quotient and power properties, transform expressions and check domain restrictions.
