Algebra 1 Final Exam Flashcards

Questions and Answers

What are positive numbers?

Numbers less than zero

Numbers that can be expressed as fractions

Numbers that are part of the set {0, 1, 2,...}

Numbers greater than zero (correct)

What are negative numbers?

Numbers that can be expressed as fractions

Numbers that are part of the set {1, 2, 3,...}

Numbers less than zero (correct)

Numbers greater than zero

Natural numbers are defined as which set?

The set of all rational numbers

The set {..., -3, -2, -1, 0, 1, 2, 3,...}

The set {0, 1, 2,...}

The set {1, 2, 3,...} (correct)

What are whole numbers?

Numbers that are part of the set {0, 1, 2,...} Signup and view all the answers

What are integers?

Numbers that are part of the set {..., -3, -2, -1, 0, 1, 2, 3,...} Signup and view all the answers

What are rational numbers?

Numbers that can be expressed in the form a/b, where a and b are integers and b is not zero. Signup and view all the answers

What is a square root?

One of two equal factors of a number. Signup and view all the answers

What is a perfect square?

A number that has a square root that is a rational number. Signup and view all the answers

What are irrational numbers?

Numbers that cannot be expressed as terminating or repeating decimals, or as a rational number. Signup and view all the answers

What are real numbers?

The set of all rational and irrational numbers. Signup and view all the answers

What is absolute value?

The distance of a number from zero. Signup and view all the answers

What are opposites?

Two numbers with the same absolute value but different signs. Signup and view all the answers

What are additive inverses?

A number and its opposite. Signup and view all the answers

The product of two positive numbers is a _____

positive Signup and view all the answers

The product of two negative numbers is a _____

positive Signup and view all the answers

The product of a positive and a negative is a ____

negative Signup and view all the answers

What are reciprocals?

Two numbers whose product is 1. Signup and view all the answers

What is the multiplicative inverse?

Also known as reciprocal. Signup and view all the answers

What is percent?

A ratio that compares a number to 100. Signup and view all the answers

What is the formula for the perimeter of a rectangle?

P = 2L + 2W Signup and view all the answers

What is the formula for the perimeter of a square?

P = 4s Signup and view all the answers

The perimeter of a triangle is _____

P = a + b + c Signup and view all the answers

What is the circumference of a circle?

The distance around a circle. Signup and view all the answers

What is the area of a rectangle?

A = L x W Signup and view all the answers

What is the area of a triangle?

A = 1/2 x b x h Signup and view all the answers

What is an algebraic expression?

A combination of numbers, variables, and operations. Signup and view all the answers

What are variables?

Symbols used to represent an unknown value. Signup and view all the answers

What are factors?

The quantities being multiplied in a multiplication expression. Signup and view all the answers

What is the product in mathematics?

The result of a multiplication expression. Signup and view all the answers

What is an exponent?

The number of times a number is used as a factor within a power. Signup and view all the answers

What is the base in an expression?

The factor within a power. Signup and view all the answers

What is the sum in mathematics?

Addition. Signup and view all the answers

What is the difference in mathematics?

Subtraction. Signup and view all the answers

What is quotient?

The result of division. Signup and view all the answers

What is the order of operations?

Parenthesis, exponent, multiplication, division, addition, subtraction. Signup and view all the answers

What are equivalent expressions?

Expressions that represent the same number. Signup and view all the answers

What is the additive identity?

The sum of any number and zero is equal to the number. Signup and view all the answers

What is the multiplicative identity?

The product of any number and one is equal to the number. Signup and view all the answers

What is the multiplicative property of zero?

The product of any number and zero is equal to zero. Signup and view all the answers

What is the commutative property of addition?

The order in which you add numbers does not change their sum. Signup and view all the answers

What is the commutative property of multiplication?

The order in which you multiply numbers does not change their product. Signup and view all the answers

What is the associative property of addition?

The way in which you group three or more numbers when adding does not change their sum. Signup and view all the answers

What is the associative property of multiplication?

The way in which you group three or more numbers when multiplying does not change their product. Signup and view all the answers

What is the distributive property?

a(b + c) = ab + ac. Signup and view all the answers

What are like terms?

Terms that contain the same variables, with corresponding variables having the same power. Signup and view all the answers

What is simplest form?

An expression that contains no like terms and no parenthesis. Signup and view all the answers

What is a coefficient?

The numerical factor of a term. Signup and view all the answers

What is a solution in algebra?

The value for a variable that makes an equation true. Signup and view all the answers

What is the coordinate plane?

A system formed by the intersection of two number lines. Signup and view all the answers

What is the y-axis?

The vertical number line in the coordinate plane. Signup and view all the answers

What is the x-axis?

The horizontal number line in the coordinate plane. Signup and view all the answers

What is the origin of the coordinate plane?

The point where the two number lines intersect in the coordinate plane. Signup and view all the answers

What is an ordered pair?

A set of numbers that represent a point on the coordinate plane. Signup and view all the answers

What is the x-coordinate?

The horizontal value of a point on the coordinate plane. Signup and view all the answers

What is the y-coordinate?

The vertical value of a point on the coordinate plane. Signup and view all the answers

What is a relation in mathematics?

A set of ordered pairs. Signup and view all the answers

What is the domain of a relation?

The set of x-coordinates in a relation. Signup and view all the answers

What is the range of a relation?

The set of y-coordinates in a relation. Signup and view all the answers

What is a function?

A relation in which each element of the domain is paired with exactly one element of the range. Signup and view all the answers

What is the y-intercept?

The point at which a graph intersects the y-axis. Signup and view all the answers

What is the x-intercept?

The point at which a graph intersects the x-axis. Signup and view all the answers

What is end behavior in mathematics?

Describes the values of a function at the positive and negative extremes in its domain. Signup and view all the answers

What are equivalent equations?

Two equations with the same solution. Signup and view all the answers

What is the addition property of equality?

Adding the same number to both sides of an equation results in an equivalent equation. Signup and view all the answers

What is the subtraction property of equality?

Subtracting the same number from both sides of an equation results in an equivalent equation. Signup and view all the answers

What is the multiplication property of equality?

Multiplying both sides of an equation by the same number results in an equivalent equation. Signup and view all the answers

What are consecutive integers?

Integers in counting order, such as 4, 5, 6. Signup and view all the answers

What is a ratio?

A comparison of two numbers by division. Signup and view all the answers

What is proportion?

An equation stating that two ratios are equal. Signup and view all the answers

What is a linear equation?

An equation that forms a line when it is graphed. Signup and view all the answers

What is slope?

The rate of change of a linear equation. Signup and view all the answers

What is the slope-intercept form of a linear equation?

y = mx + b Signup and view all the answers

What does 'm' represent in the slope-intercept form?

The slope of the line. Signup and view all the answers

What does 'b' represent in the slope-intercept form?

The y-intercept of the line. Signup and view all the answers

What is point-slope form?

y - y = m(x - x) Signup and view all the answers

What are parallel lines?

Lines with the same slope. Signup and view all the answers

What are perpendicular lines?

Lines with negative reciprocal slopes. Signup and view all the answers

What is inequality?

Two expressions compared by an inequality symbol. Signup and view all the answers

What does '<' represent?

Less than Signup and view all the answers

What does '>' represent?

Greater than Signup and view all the answers

A monomial has ______ term(s)

one Signup and view all the answers

What is a constant?

A monomial that is a real number with no variables. Signup and view all the answers

To multiply two powers that have the same bases, you _____ their exponents.

add Signup and view all the answers

To divide two powers that have the same bases, you _____ their exponents.

subtract Signup and view all the answers

To find the power of a power, you _____ the exponents.

multiply Signup and view all the answers

Study Notes

Types of Numbers

Positive Numbers: Greater than zero.
Negative Numbers: Less than zero.
Natural Numbers: Set of numbers {1, 2, 3,...}.
Whole Numbers: Set of numbers {0, 1, 2,...}.
Integers: Set including {..., -3, -2, -1, 0, 1, 2, 3,...}.
Rational Numbers: Can be expressed in the form a/b, with b ≠ 0.
Irrational Numbers: Cannot be expressed as terminating or repeating decimals.
Real Numbers: Combination of rational and irrational numbers.

Square Root: One of two equal factors of a number.
Perfect Square: A number with a rational square root.

Number Properties

Absolute Value: Distance of a number from zero.
Opposites: Two numbers with the same absolute value, different signs.
Additive Inverses: A number and its opposite.

Multiplication Properties

Product of two positive numbers: Positive.
Product of two negative numbers: Positive.
Product of a positive and a negative number: Negative.
Reciprocals: Two numbers whose product equals 1.

Geometry Formulas

Perimeter of a Rectangle: P = 2L + 2W.
Perimeter of a Square: P = 4s.
Perimeter of a Triangle: P = a + b + c.
Area of a Rectangle: A = L x W.
Area of a Triangle: A = 1/2 x b x h.

Algebra Basics

Algebraic Expression: Combination of numbers, variables, and operations.
Variables: Symbols representing unknown values.
Factors: Quantities multiplied in a multiplication expression.
Exponents: Indicate how many times a number is used as a factor.
Coefficients: Numerical factor of a term.

Operations and Properties

Sum: Result of addition.
Difference: Result of subtraction.
Quotient: Result of division.
Order of Operations: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction (PEMDAS).
Equivalent Expressions: Represent the same number.

Properties of Addition and Multiplication

Additive Identity: Any number plus zero equals the number.
Multiplicative Identity: Any number times one equals the number.
Multiplicative Property of Zero: Any number times zero equals zero.
Commutative Property: The sum/product remains the same regardless of the order.
Associative Property: Grouping does not change the sum/product.
Distributive Property: a(b + c) = ab + ac.

Coordinate Geometry

Coordinate Plane: Formed by the intersection of two number lines.
Axes: X-axis (horizontal), Y-axis (vertical).
Origin: Intersection point of the axes.
Ordered Pair: Represents a point (x, y).
Domain: Set of x-coordinates.
Range: Set of y-coordinates.

Functions and Slopes

Function: Each domain element paired with one range element.
Slope: Rate of change in linear equations.
Slope-Intercept Form: y = mx + b; "m" is slope, "b" is y-intercept.

Lines and Graphs

Parallel Lines: Same slope.
Perpendicular Lines: Negative reciprocal slopes.
Correlation in Scatter Plots: Positive, negative, or none indicate relationship strength.

Inequalities

Inequality: Two expressions compared using inequality symbols (<, >, ≤, ≥, ≠).

Algebraic Structures

Monomial: One term.
Constant: A real number with no variables.
Exponential Rules:
- Multiplying powers with same bases: Add exponents.
- Dividing powers with same bases: Subtract exponents.
- Power of a power: Multiply exponents.

Studying That Suits You

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Description

Prepare for your Algebra 1 final exam with these flashcards covering key concepts. This quiz focuses on different sets of numbers including positive, negative, natural, whole, and integers. Review each term and its definition to enhance your understanding and retention of the material.