Real Number System
Math ⇒ Number and Operations
Real Number System starts at 8 and continues till grade 12.
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See sample questions for grade 11
Explain why the sum of two irrational numbers can be rational, giving an example.
Express √50 in simplest radical form.
Express 0.272727... as a fraction in simplest form.
If a real number x satisfies x³ = 27, what is the value of x?
If x = 2 + √3 and y = 2 - √3, what is the value of x × y?
If x is a real number such that x² = 9, what are the possible values of x?
Is the number 0.101001000100001... (where the number of zeros between ones increases by one each time) rational or irrational?
Consider the decimal 0.12345678910111213... formed by writing the natural numbers in order after the decimal point. Is this number rational or irrational?
Which of the following is an irrational number?
(1) 3/4
(2) 0.333...
(3) √5
(4) -2
Which of the following is not a property of real numbers?
(1) Commutative property
(2) Distributive property
(3) Transitive property
(4) Imaginary property
Which of the following is the correct order from smallest to largest?
(1) -√2, 0, 1, π
(2) 0, -√2, π, 1
(3) π, 1, 0, -√2
(4) 1, π, 0, -√2
Which of the following is the multiplicative inverse of 5 in the set of real numbers?
(1) 0
(2) 1/5
(3) -5
(4) 5
Fill in the blank: The decimal expansion of a rational number is either _______ or eventually repeating.
Fill in the blank: The product of a nonzero rational number and an irrational number is always _______.
Fill in the blank: The real number system is _______ because between any two real numbers, there exists another real number.
Fill in the blank: The set of real numbers is the union of the set of _______ numbers and the set of irrational numbers.
If a and b are real numbers, is (a + b) always a real number?
If a real number x satisfies x² = -1, does x exist in the set of real numbers?
If x is an irrational number, is x² always irrational?
Is the number π (pi) rational?
