🏅 Top 10 in the last 30 days
No results yet. Be the first!
Test
Number sets and real numbers
Dynamic tasks on natural, integer, rational, irrational and real number sets, intervals and subsets.
Questions: 10Estimated time: 14 minutes
Start a test→
Enable solution history?
Test results will be stored only on this device in your browser’s local storage. They will not be sent to the Catestia.com database. If you disable this feature, all saved history will be permanently deleted.
Disable and delete history?
Disabling solution history will permanently delete all test results saved on this device. Are you sure you want to continue?
Preparing the test…
Question 1out of 10
What is the smallest listed set containing √6?
The square root of a positive integer that is not a perfect square is irrational. It cannot be written as a ratio of integers. I denotes the irrational numbers in the choices.
Question 2out of 10
What is the smallest listed set containing the fraction 1/9?
Rational numbers Q are all numbers that can be written as a ratio p / q of two integers, where q ≠ 0.
- Check whether the number is written as a fraction of integers.
- Make sure that the denominator is not zero.
- If the question asks for the smallest set, compare it with the chain N ⊂ Z ⊂ Q ⊂ R.
A fraction may have a terminating or repeating decimal form; in both cases it is rational. An irrational number cannot be written in this form.
Question 3out of 10
Which statement about number sets is always true?
Natural numbers belong to the integers Z. Every integer is rational because it can be written n/1. Rational numbers Q belong to the real numbers R: N ⊂ Z ⊂ Q ⊂ R. For a negative integer, Z is the smallest of these sets.
Question 4out of 10
Which inclusion relationship between number sets is correct?
Natural numbers belong to the integers Z. Every integer is rational because it can be written n/1. Rational numbers Q belong to the real numbers R: N ⊂ Z ⊂ Q ⊂ R. For a negative integer, Z is the smallest of these sets.
Question 5out of 10
What is the smallest listed number set containing -19?
Natural numbers belong to the integers Z. Every integer is rational because it can be written n/1. Rational numbers Q belong to the real numbers R: N ⊂ Z ⊂ Q ⊂ R. For a negative integer, Z is the smallest of these sets.
Question 6out of 10
Does -1 belong to the interval [-2, 1)?
The interval [a, b) means a ≤ x < b. The left endpoint is included and the right one is excluded. Check both conditions.
Question 7out of 10
Which of the listed sets is finite?
A finite set has a limited number of elements. The integers from −5 to 5 can all be listed: there are 11. The sets of all natural numbers, rational numbers or points on a line are infinite.
Question 8out of 10
Given A = {3, 8} and B = {8, 10}, find their intersection A ∩ B.
The intersection A ∩ B contains only elements belonging to both sets. Compare the lists and keep the common elements; elements appearing in only one set do not qualify.
Question 9out of 10
What is the smallest listed number set containing -25?
Natural numbers belong to the integers Z. Every integer is rational because it can be written n/1. Rational numbers Q belong to the real numbers R: N ⊂ Z ⊂ Q ⊂ R. For a negative integer, Z is the smallest of these sets.
Question 10out of 10
What is the smallest listed set containing √5?
The square root of a positive integer that is not a perfect square is irrational. It cannot be written as a ratio of integers. I denotes the irrational numbers in the choices.
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
- What is the smallest listed number set containing ___?
- What is the smallest listed set containing √___?
- What is the smallest listed set containing the fraction ___/___?
- Which inclusion relationship between number sets is correct?
- Does ___ belong to the interval [___, ___)?
Number sets and real numbers
Natural numbers form a subset of the integers, integers form a subset of the rational numbers, and rational together with irrational numbers form the real numbers. A rational number can be written as a/b, where a and b are integers and b ≠ 0.
Sets and intervals
A terminating or recurring decimal is rational, while numbers such as √2 and π are irrational. Interval brackets show whether an endpoint is included. Choose the smallest set containing a number, and distinguish membership ∈ from the subset relation ⊂.
Related mathematics tests
Pythagoras in solids
Dynamic tasks on space diagonals, cone slant height, pyramid apothem, sphere area and volume.
The Pythagorean theorem
Dynamic tasks on legs, hypotenuse, rectangle diagonals, coordinate distance and practical applications.
Full Grade 8 test
Full Grade 8 mathematics test with mixed topics, dynamically selected questions and a choice of duration. Practise before an assessment or review the whole course at your own pace.
Square and cube roots
Dynamic tasks on exact and approximate square and cube roots, comparison and simplification.
The test is finished
Your test result is
????
We've marked wrong answers in red.
🏆
Congratulations! This is your personal best on this test!
Try the test again and aim to improve your score!
What's next?
Answered all questions ahead of schedule.
You can finish the test now or review your answers and complete the test later by pressing the appropriate button.