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Math Algebra Flashcards

(102 cards)

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1
Q

Define algebra.

A

A branch of mathematics dealing with symbols and the rules for manipulating those symbols.

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2
Q

What is a variable in algebra?

A

A symbol used to represent an unknown value in mathematical expressions.

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3
Q

True or false: The commutative property applies to addition and multiplication.

A

TRUE

It states that changing the order of the numbers does not change the result.

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4
Q

Fill in the blank: The distributive property states a(b + c) = ______.

A

ab + ac

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5
Q

What is a coefficient?

A

A numerical factor in a term of an algebraic expression.

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6
Q

Define equation.

A

A mathematical statement that asserts the equality of two expressions.

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7
Q

What does it mean to solve an equation?

A

To find the value(s) of the variable(s) that make the equation true.

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8
Q

True or false: An inequality shows that two expressions are equal.

A

FALSE

Inequalities indicate a relationship where one expression is greater or less than another.

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9
Q

Fill in the blank: An expression does not contain an ______.

A

equals sign

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10
Q

What is a linear equation?

A

An equation that makes a straight line when graphed, typically in the form y = mx + b.

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11
Q

Define function.

A

A relation that assigns exactly one output for each input.

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12
Q

What is the slope of a line?

A

The measure of the steepness of the line, often represented as rise over run.

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13
Q

True or false: The y-intercept is where a line crosses the y-axis.

A

TRUE

It is the value of y when x is zero.

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14
Q

Fill in the blank: The quadratic formula is used to solve ______.

A

quadratic equations

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15
Q

What is a polynomial?

A

An algebraic expression made up of terms that are non-negative integer powers of variables.

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16
Q

Define factor in algebra.

A

A number or expression that divides another number or expression evenly.

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17
Q

What is the greatest common factor (GCF)?

A

The largest factor that two or more numbers share.

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18
Q

True or false: A monomial has more than one term.

A

FALSE

A monomial consists of a single term.

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19
Q

Fill in the blank: A binomial consists of ______.

A

two terms

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20
Q

What is a root of an equation?

A

A solution to the equation, where the equation equals zero.

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21
Q

Define exponent.

A

A number that indicates how many times to multiply the base by itself.

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22
Q

What is the order of operations?

A

A set of rules to determine the sequence in which calculations are performed.

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23
Q

True or false: The acronym PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

A

TRUE

This acronym helps remember the order of operations.

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24
Q

Fill in the blank: The absolute value of a number is its distance from ______.

A

zero

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25
What is a **system of equations**?
A set of two or more equations with the same variables.
26
Define **matrix**.
A rectangular array of numbers arranged in rows and columns.
27
What is a **determinant**?
A scalar value that can be computed from the elements of a square matrix.
28
True or false: A **function** can have multiple outputs for a single input.
FALSE ## Footnote Each input must correspond to exactly one output.
29
Fill in the blank: The **domain** of a function is the set of all possible ______.
input values
30
What is the **range** of a function?
The set of all possible output values from the function.
31
Define **asymptote**.
A line that a graph approaches but never touches.
32
What is a **rational number**?
Any number that can be expressed as a fraction of two integers.
33
True or false: **Irrational numbers** can be expressed as a simple fraction.
FALSE ## Footnote Examples include pi and the square root of 2.
34
Fill in the blank: A **function's** graph is a ______.
visual representation of its outputs based on inputs.
35
What is a **linear function**?
A function whose graph is a straight line, typically in the form y = mx + b.
36
Define **quadratic function**.
A function that can be expressed in the form f(x) = ax^2 + bx + c.
37
What is the **vertex** of a parabola?
The highest or lowest point of the parabola, depending on its orientation.
38
True or false: The **axis of symmetry** divides a parabola into two equal halves.
TRUE ## Footnote It passes through the vertex of the parabola.
39
Fill in the blank: The **x-intercept** is where a graph crosses the ______.
x-axis
40
What is a **y-intercept**?
The point where a graph crosses the y-axis.
41
Define **slope-intercept form**.
A linear equation written as y = mx + b, where m is the slope and b is the y-intercept.
42
What is the **point-slope form** of a line?
An equation of the form y - y1 = m(x - x1), where (x1, y1) is a point on the line.
43
True or false: The **Pythagorean theorem** applies only to right triangles.
TRUE ## Footnote It states that a^2 + b^2 = c^2 for right triangles.
44
Fill in the blank: The **hypotenuse** is the longest side of a ______.
right triangle
45
What is a **composite function**?
A function that is formed by combining two functions, denoted as (f ∘ g)(x) = f(g(x)).
46
Define **inverse function**.
A function that reverses the effect of the original function.
47
What is a **logarithm**?
The inverse operation to exponentiation, answering the question of how many times a base must be multiplied.
48
True or false: The **base** of a logarithm is always 10.
FALSE ## Footnote Common bases include 2, e, and 10.
49
Fill in the blank: The **product rule** for logarithms states log_b(mn) = ______.
log_b(m) + log_b(n)
50
What is the **quotient rule** for logarithms?
log_b(m/n) = log_b(m) - log_b(n).
51
Define **exponential function**.
A function of the form f(x) = a * b^x, where b is a positive constant.
52
What is the **binomial theorem**?
A formula for expanding expressions raised to a power, expressed as (a + b)^n.
53
True or false: The **factorial** of a number n is n! = n × (n-1)!
TRUE ## Footnote Factorials are used in permutations and combinations.
54
Fill in the blank: The **mean** is the ______ of a set of numbers.
average value
55
What is the **median**?
The middle value in a data set when arranged in order.
56
Define **mode**.
The value that appears most frequently in a data set.
57
What is **standard deviation**?
A measure of the amount of variation or dispersion in a set of values.
58
True or false: A **normal distribution** is symmetric about the mean.
TRUE ## Footnote It is often represented as a bell curve.
59
Fill in the blank: The **range** is the difference between the ______.
highest and lowest values
60
What is a **scatter plot**?
A graph that uses dots to represent values for two different variables.
61
Define **correlation**.
A statistical measure that describes the strength and direction of a relationship between two variables.
62
What is a **linear regression**?
A statistical method for modeling the relationship between a dependent variable and one or more independent variables.
63
True or false: A **positive correlation** means that as one variable increases, the other decreases.
FALSE ## Footnote In a positive correlation, both variables move in the same direction.
64
Fill in the blank: A **negative correlation** indicates that as one variable increases, the other ______.
decreases
65
Define **integer**.
A whole number that can be positive, negative, or zero.
66
What is the **square** of 5?
25
67
True or false: The **sum** of two even numbers is always even.
TRUE
68
Fill in the blank: The **product** of 7 and 8 is ______.
56
69
Define **algebraic expression**.
A combination of numbers, variables, and operations.
70
What is the **value** of x in 2x + 3 = 7?
2
71
True or false: A **prime number** has exactly two distinct positive divisors.
TRUE
72
Fill in the blank: The **mean** of 4, 8, and 10 is ______.
7.33
73
What is the **distributive property**?
a(b + c) = ab + ac
74
Define **variable**.
A symbol used to represent an unknown value.
75
What is the **greatest common divisor** of 12 and 16?
4
76
True or false: The **difference** of two odd numbers is even.
TRUE
77
Fill in the blank: The **area** of a rectangle is length times ______.
width
78
What is the **Pythagorean theorem**?
In a right triangle, a² + b² = c².
79
Define **coefficient**.
A numerical factor in a term of an algebraic expression.
80
What is the **slope** of the line y = 3x + 2?
3
81
True or false: The **sum** of angles in a triangle is 180 degrees.
TRUE
82
Fill in the blank: The **perimeter** of a square is 4 times ______.
the length of one side
83
What is the **quadratic formula**?
x = (-b ± √(b² - 4ac)) / 2a
84
Define **function**.
A relation that assigns exactly one output for each input.
85
What is the **median** of the set {3, 5, 7, 9}?
6
86
True or false: A **circle** has an infinite number of lines of symmetry.
TRUE
87
Fill in the blank: The **volume** of a cube is side cubed, or ______.
s³
88
What is the **mode** of the set {1, 2, 2, 3, 4}?
2
89
Define **ratio**.
A comparison of two quantities by division.
90
What is the **hypotenuse** in a right triangle?
The longest side opposite the right angle.
91
True or false: The **product** of two negative numbers is positive.
TRUE
92
Fill in the blank: The **circumference** of a circle is 2π times the ______.
radius
93
What is the **absolute value** of -7?
7
94
Define **exponent**.
A number that indicates how many times to multiply the base.
95
What is the **factorial** of 5?
120
96
True or false: The **sum** of an even and an odd number is odd.
TRUE
97
Fill in the blank: The **angle** formed by two rays is measured in ______.
degrees
98
What is the **distance formula**?
d = √((x2 - x1)² + (y2 - y1)²)
99
Define **composite number**.
A positive integer that has at least one positive divisor other than one and itself.
100
What is the **range** of the set {3, 7, 2, 9}?
7
101
True or false: A **triangle** can have two right angles.
FALSE
102
Fill in the blank: The **mean** is calculated by dividing the total by the number of ______.
values
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