Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

1. College Algebra > 1. Prerequisite > Flashcards

1. Prerequisite Flashcards

1
Q

A combination of numbers, variables, and operation symbols is called an algebraic ______.

A

expression

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

If n is a counting number, b^n, read ________, indicates that there are n factors of b. The number b is called the _____ and the number n is called the _____.

A

b to the nth power

base

exponent

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

An equation that expresses a relationship between two or more variables, such as H = 9/10(220 - a), is called a/an ______. The process of finding such equations to describe real-world phenomena is called mathematical ______. Such equations, together with the meaning assigned to the variables, are called mathematical _______.

A

formula

modeling

model

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

The set of elements common to both set A and set B is called the ______ of sets A and B, and is symbolized by ______.

A

intersection

a ∩ b

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

The set of elements that are members of set A or set B or of both sets is called the _____ of sets A and B and is symbolized by ______.

A

union

a ∪ b

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

The set {1, 2, 3, 4, 5, …} is called the set of _____ numbers.

A

natural

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

The set {0, 1, 2, 3, 4, 5, …} is called the set of _____ numbers.

A

whole

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

The set {…, –4, –3, –2, –1, 0, 1, 2, 3, 4, …} is called the set of _____.

A

integers

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

The set of numbers in the form a/b, where a and b belong to the set {…, –4, –3, –2, –1, 0, 1, 2, 3, 4, …} and b ≠ 0, is called the set of _____ numbers.

A

rational

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

The set of numbers whose decimal representations are neither terminating nor repeating is called the set of _____ numbers.

A

irrational

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Every real number is either a/an _____ number or a/an _____ number.

A

rational

irrational

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

The notation |x| is read the _____ of x. If x ≥ 0, then |x| = ______. If x < 0, then |x| = _____.

A

absolute value

x

–x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

The commutative properties state that a + b = _____ and ab = ______.

A

b + a

ba

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

The associative properties state that (a + b) + c = _____ and _____ = a(bc).

A

a + (b + c)

(ab)c

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

The distributive property states that a(b + c) = _____.

A

ab + ac

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

a + (–a) = _____: The sum of a real number and its additive _____ is _____, the additive _____.

A

0

inverse

0

identity

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

a ∙ 1/a = 1, a ≠ 0: The product of a nonzero real number and its multiplicative _____ is _____, the multiplicative _____.

A

inverse

1

identity

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

An algebraic expression is _____ when the parentheses have been removed and like terms have been combined.

A

simplified

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

–(–a) = _____.

A

a

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

The product rule for exponents states that b^m ∙ b^n = _____. When multiplying exponential expressions with the same base, _____ the exponents.

A

b^(m + n)

add

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

The quotient rule for exponents states that (b^m)/(b^n) = _____, b ≠ 0. When dividing exponential expressions with the same nonzero base, _____ the exponents.

A

b^(m – n)

subtract

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

If b ≠ 0, then b^0 = _____.

A

1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

The negative-exponent rule states that b^–n = ______, b ≠ 0.

A

1 / b^n

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

True or false: 5^–2 = –5^2

A

false

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

Negative exponents in denominators can be evaluated using 1/(b^–n) = _____, b ≠ 0.

A

b^n

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

True or false: 1/(8^–2) = 8²

A

true

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

A positive number is written in scientific notation when it is expressed in the form a × 10^n, where a is _____ and n is a/an _____.

A

a number greater than or equal to 1 and less than 10

integer

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

True or false: 4 × 10^3 is written in scientific notation.

A

true

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

True or false: 40 × 10² is written in scientific notation.

A

false

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

The symbol √ is used to denote the nonnegative or _____, square root of a number.

A

principal

31
Q

√64 = 8 because _____ = 64.

A

8²

32
Q

√a² = _____

A

|a|

33
Q

The product rule for square roots states that if a and b are nonnegative, then √ab = _____.

A

√a ∙ √b

34
Q

The quotient rule for square roots states that if a and b are nonnegative and b ≠ 0, then √(a/b) = ______.

A

√a / √b

35
Q

8√3 + 10√3 = _____

A

18√3

36
Q

√3 + √75 = √3 + √(25 ∙ 3) = √3 + _____√3 = ______

A

5

6√3

37
Q

The conjugate of 7 + √3 is _____

A

7 – √3

38
Q

We rationalize the denominator of 5 / (√10 – √2) by multiplying the numerator and denominator by _____.

A

√10 + √2

39
Q

In the expression ∛64, the number 3 is called the _____ and the number 64 is called the _____.

A

index

radicand

40
Q

^5√–32 = –2 because _____ = –32

A

(–2)^5

41
Q

If n is odd, ^n√(a^n) = _____

A

a

42
Q

if n is even, ^n√(a^n) = _____

A

|a|

43
Q

a^(1/n) = _____

A

^n√a

44
Q

A polynomial is a single term or the sum of two or

more terms containing variables with exponents that are ______ numbers.

A

whole

45
Q

It is customary to write the terms of a polynomial in

the order of descending powers of the variable. This is called the ______ form of a polynomial.

A

standard

46
Q

A simplified polynomial that has exactly one term is

called a/an ______.

A

monomial

47
Q

A simplified polynomial that has two terms is called

a/an ______.

A

binomial

48
Q

A simplified polynomial that has three terms is called

a/an ______.

A

trinomial

49
Q

If a ≠ 0, the degree of ax^n is ______.

A

n

50
Q

Polynomials are added by combining ______ terms.

A

like

51
Q

To multiply 7x^3(4x^5 – 8x² + 6), use the ______ property to multiply each term of the trinomial ______ by the monomial ______.

A

distributive

4x^5 – 8x² + 6

7x^3

52
Q

To multiply (5x + 3)(x² + 8x + 7), begin by multiplying each term of x² + 8x + 7 by ______. Then
multiply each term of x² + 8x + 7 by ______. Then
combine ______ terms.

A

5x

3

like

53
Q

When using the FOIL method to find (x + 7)(3x + 5), the product of the first terms is ______, the product of the outside terms is ______, the product of the inside
terms is ______, and the product of the last terms
is ______.

A

3x²

5x

21x

35

54
Q

(A + B)(A – B) = ______. The product of the

sum and difference of the same two terms is the square of the first term ______ the square of the second term.

A

A² – B²

minus

55
Q

(A + B)² = ______. The square of a binomial sum is the first term ______ plus 2 times the _______ plus the last term ______.

A

A² + 2AB + B²

squared

product of the terms

squared

56
Q

(A – B)² = ______. The square of a binomial
difference is the first term squared ______ 2 times
the ______ _______ the last term squared.

A

A² – 2AB + B²

minus

product of the terms

plus

57
Q

If a ≠ 0, the degree of (ax^n)(y^m) is _______.

A

n + m

58
Q

Which technique should we use for factoring the polynomial?

16x² – 25

A

Factoring the difference of two squares :

A² – B² = (A + B)(A – B)

59
Q

Which technique should we use for factoring the polynomial?

27x^3 – 1

A

Factoring the difference of two cubes

A^3 – B^3 = (A – B)(A² + AB + B²)

60
Q

Which technique should we use for factoring the polynomial?

x² + 7x + xy + 7y

A

Factoring by grouping

61
Q

Which technique should we use for factoring the polynomial?

4x² + 8x + 3

A

Factoring trinomials by trial and error

62
Q

Which technique should we use for factoring the polynomial?

9x² + 24x + 16

A

Factoring perfect square trinomials

A² + 2AB + B² = (A + B)²

A² – 2AB + B² = (A – B)²

63
Q

Which technique should we use for factoring the polynomial?

5x² + 10x

A

Factoring out the GCF

64
Q

Which technique should we use for factoring the polynomial?

x^3 + 1000

A

Factoring the sum of two cubes

A^3 + B^3 = (A + B)(A² – AB + B²)

65
Q

The algebraic expression (x + 1)^(1/2) – 1/3(x + 1)^(3/2) can be factored using ______ as the greatest denominator.

A

(x + 1)^(1/2)

66
Q

A rational expression is the quotient of two ______.

A

polynomials

67
Q

The set of real numbers for which a rational expression
is defined is the ______ of the expression. We must
exclude all numbers from this set that make the
denominator of the rational expression ______.

A

domain

0

68
Q

We simplify a rational expression by ______ the
numerator and the denominator completely. Then we divide the numerator and the denominator by
any ______.

A

factoring

common factors

69
Q

(x/5) ∙ (x/3) = _______

A

x²/15

70
Q

(x/5) ÷ (x/3) = _______, x ≠ 0

A

3/5

71
Q

x²/3 – (x – 2)/3 = ______

A

(x² – x + 2) / 3

72
Q

Consider the following subtraction problem:

(x – 1) / (x² + x – 6) – (x – 2) / (x² + 4x + 3)

The factors of the first denominator are ______.

The factors of the second denominator are ______.

The LCD is _______.

A

x + 3 and x – 2

x + 3 and x + 1

(x + 3)(x – 2)(x + 1)

73
Q

An equivalent expression for (3x + 2) / (x – 5) can be obtained by multiplying the numerator and denominator by _____.

A

3x + 4

74
Q

A rational expression whose numerator or denominator orboth contain rational expressions is called a/an ______ rational expression or a/an ______ fraction.

A

complex

complex

1. College Algebra (8 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions