Math Samplex
Math 17
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 st 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
First Long Exam
Page 1 of 1
Math 17
First Long Exam: Answer Key
=
= =
(
√ ) √
√
√
=
√
√
√
√
√
=
=
5.
√
√
(
)
=
√
√
=
(
)
7.
16
= 16
=
(
)
= 16
=
(
)
=16 = 16
=
=16 (= -1/2
= =
6.
√ √
=
√ √
√ √
√ √
Page 2 of 2
UP Engineering Society
Building bridges, breaking barriers st 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