# Math Samplex

First Long Exam

Page 1 of 1

Math 17

First Long Exam: Answer Key

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Page 2 of 2

UP Engineering Society

Building bridges, breaking barriers

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Math 17

1 Long Exam Reviewer

Sets and Basic Notations A set is a collection of objects, and the objects in a set are called the elements of the set. Ex. {0, 1, 2, 3, 4, 5} A pair of braces, { }, is used with words or symbols to describe a set. In the set builder notation, the criteria for deciding whether an object belongs to a set are given. Ex. {x|x is greater than 5} where “|” is read as “such that.” Two sets A and B are said to be equal, written A = B, if and only if A and B have identical elements. Ex. {4, 5, 6} = {6, 4, 5} The union of two sets A and B, denoted by A B and read “A union B,” is the set of all elements that are in A or in B or in both A and B. The intersection of A and B, denoted by A B and read “A intersection B,” is the set of all elements that are in both A and B. An empty set is a set that contains no elements and is denoted by . Two sets that have no elements in common are called disjoint sets. If every element of a set S is also an element of a set T, then S is a subset of T, written S T.

The Set of Real Numbers

A prime number is a natural number greater than 1 that has no natural number factors other than itself and 1. The number “2” is the only prime number that is even. “0” and “1” are not prime numbers. A natural number greater than 1 that is not a prime number is a composite number. Factoring Polynomials

Polynomials: Basic Operations An algebraic expression involving only nonnegative-integer powers of one or more variable and containing no variable in a denominator is called a polynomial. The degree of a polynomial is the same as the degree of the term with the highest degree in the polynomial. Ex. (degree 4) (degree 5) (degree 4) 5 (zero degree) 0 (no degree)

Integer Exponents If n and m are positive integers and a and b are real numbers, then

The Fundamental Theorem of Arithmetic. The completely factored form of any composite number is unique except for the order of the factors. Page 1 of 2

UP Engineering Society

Building bridges, breaking barriers

st

Math 17

1 Long Exam Reviewer

Rational Exponents If n is a positive integer greater than 1 and a and b are real numbers such that , then b is an nth root of a. If n is a positive integer greater than 1, a is a real number, and denotes the principal nth root of a, then: (i) if , is the positive nth root of a; (ii) if , and n is odd, is the negative nth root of a; (iii) In the above definition, the symbol is called a radical sign. The entire expression is called a radical, where the number a is the radicand and the number n is the index that indicates the order of the radical. If no index appears, the order is understood to be 2. If n is a positive integer greater than 1, and a is a real number, then if is a real number

Rational Expressions: Basic Operations If the numerator and denominator of a fraction are polynomials, then the fraction is called a rational expression. A rational expression is said to be in lowest terms if the numerator and denominator have no common factor other than 1 and -1.

If m and n are positive integers that are relatively prime, and a is a real number, then if is a real number

The least common denominator (LCD) of a rational expression is the polynomial of smallest degree that has each of the given denominators as a factor. If a fraction contains a fraction in either the numerator or denominator, or both, it is called a complex fraction. Radicals If a and b are real numbers,

If m and n are...

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