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Precalc Exam 1 > Study > Flashcards

Study Flashcards

1
Q

Set of real numbers symbol

A

ℝ

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2
Q

ℝ

A

Set of real numbers symbol

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3
Q

If a and b are in ℝ so is

A

a+b and a•b

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4
Q

Commutative property

A

a+b = b+a / a•b = b•a

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5
Q

a+b = b+a / a•b = b•a

A

Commutative property

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6
Q

Associative property

A

(a+b)+c = a+(b+c) / (a•b)•c = a•(b•c)

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7
Q

(a+b)+c = a+(b+c) / (a•b)•c = a•(b•c)

A

Associative property

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8
Q

Additive identities

A

Real # 0 such that a+0=a for all a

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9
Q

Real # 0 such that a+0=a for all a

A

Additive identities

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10
Q

Multiplicative identitity

A

Real # 1 that a•1=a for all a

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11
Q

Real # 1 that a•1=a for all a

A

Multiplicative identitity

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12
Q

Additive inverses

A

For any a in ℝ, there is a # -a in ℝ that a+(-a)=0

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13
Q

For any a in ℝ, there is a # -a in ℝ that a+(-a)=0

A

Additive inverses

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14
Q

Multiplicative inverses

A

For any a≠0, there is a # 1/a in ℝ that a•1/a=1

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15
Q

For any a≠0, there is a # 1/a in ℝ that a•1/a=1

A

Multiplicative inverses

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16
Q

Distributive property

A

a•(b+c)=a•b+a•c for all a,b,c in ℝ

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17
Q

a•(b+c)=a•b+a•c for all a,b,c in ℝ

A

Distributive property

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18
Q

Term

A

Any number, constant, variable, or parenthetical group

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19
Q

Any number, constant, variable, or parenthetical group

A

Term

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20
Q

Expression

A

Combination of terms using additional, subtraction, multiplication, division, exponents, or roots

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21
Q

Combination of terms using additional, subtraction, multiplication, division, exponents, or roots

A

Expression

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22
Q

Equation

A

Statement that two expressions are equal

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23
Q

Statement that two expressions are equal

A

Equation

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24
Q

Define expression “a^n”

A

a^0=1 if a≠0 / a^-n=1/a^n

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25
Q

a^0=1 if a≠0 / a^-n=1/a^n

A

a^n

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26
Q

(a•b)^n =

A

a^n • b^n

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27
Q

a^n • b^n =

A

(a•b)^2

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28
Q

(a/b)^n =

A

a^n/b^n (b≠0)

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29
Q

Does zero have a degree?

A

No

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30
Q

Does not have a degree

A

Zero

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31
Q

Polynomial with one term

A

Monomial

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32
Q

Monomial

A

Polynomial with one term

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33
Q

Polynomial with two terms

A

Binomial

34
Q

Binomial

A

Polynomial with two terms

35
Q

Polynomial with three terms

A

Trinomial

36
Q

Trinomial

A

Polynomial with three terms

37
Q

5x^2 y^4

What is the degree of this term?

A

6

38
Q

A^2-B^2 =

A

(A-B)(A+B)

39
Q

(A-B)(A+B)

A

A^2-B^2

40
Q

(A-B)^2 =

A

A^2-2AB+B^2

41
Q

A^2-2AB+B^2

A

(A-B)^2

42
Q

A^3-B^3 =

A

(A-B)(A^2+AB+B^2)

43
Q

(A-B)(A^2+AB+B^2)

A

A^3-B^3

44
Q

A^3+B^3 =

A

(A+B)(A^2-AB+B^2)

45
Q

(A+B)(A^2-AB+B^2)

A

A^3+B^3

46
Q

Rational number is a

A

Ratio of integers like 3/4

47
Q

Ratio of integers

A

Rational number

48
Q

Rational expression

A

Ratio of polynomials like x+3/2

49
Q

Ratio of polynomials

A

Rational expression

50
Q

Let a>0. To say b= √ a means:

A
  1. ) b^2=a
  2. ) b>0

This is principal square root of a

51
Q

For any real x, √ x^2 =

A

|x|

52
Q

If a>0 , n√a = b if

A

b^2=a and b>0

53
Q

If a<0 and n is odd n√a=b if

A

b^n=a

54
Q

If a<0 and n is even n√a is

A

Not real

55
Q

n√x

What is index and what is radicand?

A

n is index and x is radicand

56
Q

How do you rationalize 3√9?

A

Multiply by 3√9^2 because 1/3 + 2/3 = 1

57
Q

Multiply by 3√9^2 because 1/3 + 2/3 = 1

A

Rationalizing 3√9

58
Q

An equation whose solutions set is all ℝ is an

A

Identity

59
Q

Identity

A

An equation whose solutions set is all of ℝ

60
Q

An equation whose solution set is empty is

A

Inconsistent

61
Q

Inconsistent

A

An equation whose solution set is empty

62
Q

An equation with non-empty solution set that is not all of ℝ is

A

Conditional

63
Q

Conditional

A

An equation with non-empty solution set that is not all of ℝ

64
Q

Quadratic equation standard form

A

ax^2+bx+c

65
Q

ax^2+bx+c

A

Quadratic equation standard form

66
Q

b^2-4ac > 0
b^2-4ac = 0
b^2-4ac < 0

A

Two real solutions
One real solution
No real solutions

67
Q

A combination of one or more inequalities is a

A

Compound inequality

68
Q

Compound inequality

A

A combination of one or more inequalities is a

69
Q

|2x-3| = 13

A

2x-3 = 13 or 2x-3 = -13

70
Q

2x-3 = 13 or 2x-3 = -13

A

|2x-3| = 13

71
Q

Distance formula

A

√(x1-x2)^2 + (y1-y2)^2

72
Q

√(x1-x2)^2 + (y1-y2)^2

A

Distance formula

73
Q

Midpoint formula

A

(x1+x2/2,y1+y2/2)

74
Q

(x1+x2/2,y1+y2/2)

A

Midpoint formula

75
Q

Circle standard equation

A

(x-h)^2 + (y-k)^2 = r^2 with center (h,k)

76
Q

(x-h)^2 + (y-k)^2 = r^2 with center (h,k)

A

Circle standard equation

77
Q

If (x1,y1) and (x2,y2) are the points on a line, then its slope is

A

m = y2-y1/x2-x1

78
Q

m = y2-y1/x2-x1

A

If (x1,y1) and (x2,y2) are the points on a line slope

79
Q

Point-slope formula

A

y-y1 = m(x-x1)

80
Q

y-y1 = m(x-x1)

A

Point-slope formula

81
Q

Negative reciprocal slopes formula

A

m1•m2=-1

82
Q

m1•m2=-1

A

Negative reciprocal slopes

Precalc Exam 1 (1 decks)

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