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Math Pentathlon 24-25 > Math Section III > Flashcards

Math Section III Flashcards

1
Q

What is a set?

A

a collection of numbers, ex: {1, 2, 3}

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2
Q

What is an element?

A

a member of a set, represented by ∈

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3
Q

What does ∈ mean?

A

“belongs to”, is used to show that an element belongs to a set

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4
Q

What are equal sets?

A

sets with the same elements

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5
Q

What are equivalent sets?

A

sets with the same number of elements

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6
Q

What is a union of sets?

A

a set with all the members found in both sets you are unioning

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7
Q

What is ∪?

A

the symbol for union

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8
Q

What is an intersection of sets?

A

a set with elements both sets have in common, represented by ∩

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9
Q

What is ∩?

A

the symbol for intersection

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10
Q

What are integers?

A

the counting numbers, their negative form, and zero

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11
Q

What are rational numbers?

A

numbers written as a ratio of 2 integers

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12
Q

What are irrational numbers?

A

numbers that can’t be written as a ratio of 2 integers

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13
Q

What is a prime number?

A

a number greater than one with only 2 whole factors

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14
Q

What is prime factorization?

A

the integers that are the product of all prime factors that can be divided into the number

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15
Q

What is GCF? (greatest common factor)

A

the greatest whole numbers will divide evenly into 2 numbers

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16
Q

What is a base in an exponent?

A

the whole number that is affected by the exponent

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17
Q

Any number above zero raised to the power of zero will always equal what?

A

1

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18
Q

How do you make the exponent in x^-1 positive?

A

use the reciprocal of the original power, ex: x^-1 = 1/x^1

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19
Q

How do you simplify this? (x^n)^p

A

multiply n and p, x^np

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20
Q

How do you distribute this? (c/d)^n

A

distribute it to the numerator and denominator, c^n/d^n

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21
Q

How do you simplify this? x^n * x^n

A

add the exponents, x^n+n

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22
Q

What is power in an exponent?

A

the base and exponent together, ex: 5^3

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23
Q

What is base in an exponent?

A

the number being affected by the exponent, ex: 5 in 5^3

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24
Q

What is exponent in an exponent?

A

the number that is raising the power of the base, ex: 3 in 5^3

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25
Q

How do you simplify this? x^m/x^n

A

subtract the exponents, ex: x^m-n

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26
Q

What is the name of the symbol used to square root a number?

A

the radical sign

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27
Q

What is a square root?

A

the number that makes the original number when squared

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28
Q

How do you simplify this? √xy

A

√x * √y

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29
Q

How do you simplify this? √a * √a

A

a

30
Q

How do you simplify this? √x/y

A

√x/√y

31
Q

How do you simplify this? √a^n

A

(√a)^n

32
Q

What is a cube root

A

the number that makes the original number when squared

33
Q

What is a variable?

A

a number used to represent an unknown number or value

34
Q

What does sum, greater than, increased by, or more than usually indicate?

A

to use addition

35
Q

What does difference, smaller than, decreased by, or less than usually indicate?

A

to use subtraction

36
Q

What does product, times, or multiplied by usually indicate?

A

to use multiplication

37
Q

What does quotient, halve, divided by, or ratio usually indicate?

A

to use division

38
Q

What is a ratio?

A

a method of comparing two or more numbers or variables, and can be written as a:b or a/b

39
Q

What are the 2 ways ratios can be written?

A

a:b or a/b

40
Q

How do you read ratios?

A

“a is to b”

41
Q

What is a proportion?

A

a relationship between 2 variables whose ratio is a constant

42
Q

What is a proportionality constant?

A

the number you get when diving 2 values in a proportion

43
Q

What is a monomial?

A

an algebraic expression that has only one term

44
Q

How do you add monomials?

A

combine the coefficients and combine like terms, leave variables the same if they are not alike

45
Q

How do you multiply monomials?

A

add the exponents of the same bases and multiply the coefficients

46
Q

How do you divide monomials?

A

subtract the exponents with the same bases and divide the coefficients

47
Q

What is a binomial?

A

an algebraic expression with 2 monomial terms

48
Q

What type of algebraic expression is x + y?

A

binomial

49
Q

What is a trinomial?

A

an algebraic expression with 3 terms

50
Q

What type of algebraic expression is x + y + z?

A

trinomial

51
Q

What type of algebraic expression is y^2 + 9y + 8?

A

trinomial

52
Q

What is a linear equation?

A

an equation whose solution(s) create a straight line

53
Q

What is the FOIL method?

A

a way two multiply 2 binomials

54
Q

What is slope?

A

the steepness of a line

55
Q

What is an equation?

A

a mathematical sentence, or a relationship between numbers and variables

56
Q

What is slope formula?

A

(y2-y1)/(x2-x1)

57
Q

What mnemonic device is used to remember the order of operations?

A

PEMDAS

58
Q

What does PEMDAS stand for?

A

P = Parenthesis
E = Exponents
M/D = * and /, left to right
A/S = + and -, left to right

59
Q

What does FOIL stand for?

A

F = first terms
O = outer terms
I = inner terms
L = last terms

60
Q

What is factoring?

A

a method to find the two or more polynomials whose product equals the original value

61
Q

What are the steps to factoring?

A

factor out the GCF, look for a factor pattern like binomial squares, differences of 2 squares, etc, and check your answer by multiplying them

62
Q

What is the difference of 2 squares strategy?

A

it works when you factor out common factors and have 2 perfect squares subtracted from each other, ex: a^2 - b^2 would be (a - b)(a + b)

63
Q

What is the binomial squares strategy?

A

when you have 2 positive perfect squares for the first and last terms and the middle term is 2x the square root of the first and last term, middle term can be positive or negative

64
Q

What is a quadratic equation?

A

an equation with a variable that is squared and is usually in this form: ax^2 + bx + c = 0

65
Q

What is an inequality?

A

a statement where the relationships between the numbers are not equal

66
Q

What does < mean?

A

less than

67
Q

What does > mean?

A

greater than

68
Q

What does ≤ mean?

A

less than or equal to

69
Q

What does ≥ mean?

A

greater than or equal to

70
Q

What does ≠ mean?

A

not equal to

Math Pentathlon 24-25 (4 decks)

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