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 12
Explain why the sum of two rational numbers is always rational.
Express √50 in simplest radical form.
Express 0.272727... as a fraction in simplest form.
If a real number x satisfies x² = 9, what are the possible values of x?
If x = √3 and y = √12, what is x × y?
If x = 2 + √3 and y = 2 - √3, what is the value of x × y?
If x = 2 + √5, find the value of (x - 2)².
If x = 3 + √7, what is the conjugate of x?
Which of the following is a property of real numbers?
(1) Commutative property of addition
(2) Distributive property
(3) Associative property of multiplication
(4) All of the above
Which of the following is NOT a real number?
(1) 0
(2) -7
(3) √-1
(4) 2/3
Which of the following is the correct classification for the number 0?
(1) Rational only
(2) Irrational only
(3) Both rational and irrational
(4) Neither rational nor irrational
Which of the following is the correct order from smallest to largest?
(1) -π, -2, 0, 1/2
(2) -2, -π, 0, 1/2
(3) -2, 0, -π, 1/2
(4) 0, -2, -π, 1/2
Fill in the blank: The decimal expansion of a rational number either terminates or ________.
Fill in the blank: The multiplicative inverse of a nonzero real number a is ________.
Fill in the blank: The product of a nonzero rational number and an irrational number is always ________.
Fill in the blank: The set of real numbers is the union of the set of rational numbers and the set of ________ numbers.
If a and b are both irrational numbers, is their sum always irrational?
Is the set of rational numbers dense in the set of real numbers?
Is the set of real numbers closed under division?
Is the set of real numbers closed under subtraction?
