ALGEBRA AND TRIGONOMETRY ACTUAL TEST QUESTIONS AND SOLUTIONS COMPREHENSIVE REVIEW PACKAGE

ALGEBRA AND TRIGONOMETRY ACTUAL
TEST QUESTIONS AND SOLUTIONS
COMPREHENSIVE REVIEW PACKAGE

●● Real Numbers
Answer: Have points on the number line (e.g., 3, -17.4, √5, π, 4/3)


●● Imaginary Numbers
Answer: Square roots of negative numbers, have NO points on the
number line (e.g., √-3, 5√-2, -√-9)


●● Rational Numbers
Answer: Can be expressed exactly as a ratio of two integers (e.g., 4/5, -
2/3, 7.31, -5, √9, 0.333)


●● Irrational Numbers
Answer: Cannot be expressed exactly as the ration of two integers, but
are real numbers (e.g., √5, -3√11, π)


●● Radicals
Answer: Involve square root, cube root, etc., of integers (e.g., √5, -√11)

, ●● Transcendental Numbers
Answer: Cannot be expressed as roots of integers (e.g., π)


●● The Field Axioms
Answer: Closure
Commutativity
Associativity
Distributivity
Identity Elements
Inverses


●● Closure under addition
Answer: If x and y are real numbers, then x + y is a unique, real number.
(field axiom)


●● Closure under multiplication
Answer: If x and y are real numbers, then xy is a unique, real number.
(field axiom)


●● Commutativity of addition
Answer: If x and y are real numbers then x + y and y + x are equal to
each other. (field axiom)