OnRamps Algebra 2 Quiz & Flashcards for Units 1 & 2

Questions and Answers

What are natural numbers?

Numbers of the form a/b where a and b are integers and b ≠ 0.

-3, -2, -1, 0, 1, 2, 3,...

1, 2, 3, 4, 5,... (correct)

All rational and irrational numbers

What are integers?

1, 2, 3, 4, 5,...

All numbers that have points on a number line.

Numbers of the form a/b where a and b are integers and b ≠ 0.

-3, -2, -1, 0, 1, 2, 3,... (correct)

What are rational numbers?

1, 2, 3, 4, 5,...

Numbers that can be written as a fraction a/b where a and b are integers and b ≠ 0. (correct)

Everything that isn't rational.

-3, -2, -1, 0, 1, 2, 3,...

What are irrational numbers?

Numbers that cannot be expressed as a fraction. Signup and view all the answers

What are real numbers?

All rational and irrational numbers. Signup and view all the answers

What is a complex number?

In the form of x+yi where x and y are real numbers. Signup and view all the answers

The symbol for 'is an element of or belongs to' is ______.

∈ Signup and view all the answers

The symbol for 'there exists' is ______.

∃ Signup and view all the answers

The symbol for 'for all or for every' is ______.

∀ Signup and view all the answers

The symbol for 'such that' is ______.

: or | Signup and view all the answers

The symbol for 'an implication or mapping' is ______.

→ Signup and view all the answers

What is the closure addition operation?

x+y (where y is a real number) Signup and view all the answers

What is the identity addition property?

x+0=x Signup and view all the answers

What is the associative multiplication property?

(xy)z = x(yz) Signup and view all the answers

What is the inverse addition property?

x+(-x)=0 Signup and view all the answers

What is a linear function?

f(x)=x Signup and view all the answers

What is a quadratic function?

f(x)=x² Signup and view all the answers

What is the y-intercept?

What is y when x=0 Signup and view all the answers

What is the distribution rule?

x(y+z)=xy+xz Signup and view all the answers

What does a positive horizontal shift indicate?

The graph moves to the right Signup and view all the answers

What does a negative vertical shift indicate?

The graph moves down Signup and view all the answers

What does reflection across the x-axis represent?

-f(x) Signup and view all the answers

What does reflection across the y-axis represent?

f(-x) Signup and view all the answers

Study Notes

Number Types

Natural Numbers: The set of positive integers starting from 1 (1, 2, 3, ...).
Integers: Includes all positive and negative whole numbers, along with zero (-3, -2, -1, 0, 1, 2, 3, ...).
Rational Numbers: Numbers expressible as a fraction (a/b) where a and b are integers and b ≠ 0 (Q).
Irrational Numbers: Numbers that cannot be expressed as a fraction, existing outside the rational number category (Q^c).
Real Numbers: Comprised of both rational and irrational numbers, encompassing all numbers represented on the number line (R).
Complex Numbers: Formulated as x + yi, where x and y are real numbers and i represents the square root of -1 (C).

Mathematical Symbols

Element of: Symbolized by ∈, indicating membership in a set.
Existential Quantifier: Denoted by ∃, used to specify that there exists at least one element.
Universal Quantifier: Represented by ∀, used to indicate that a statement applies to all elements in a set.
Conditional Statement: Expressed with the symbol →, representing implications or mappings in functions.
Such That: Indicated by : or | to specify a condition.

Algebraic Properties

Closure Addition: States that the sum of any two real numbers x and y is still a real number.
Closure Multiplication: Establishes that the product of any two real numbers x and y remains a real number.
Commutative Addition: The order of addition does not affect the sum (x + y = y + x).
Commutative Multiplication: The order of multiplication does not affect the product (xy = yx).
Associative Addition: Grouping in addition does not change the result ((x + y) + z = x + (y + z)).
Associative Multiplication: Grouping in multiplication doesn't affect the product ((xy)z = x(yz)).
Identity Addition: Adding zero to a number does not change its value (x + 0 = x).
Identity Multiplication: Multiplying a number by one does not change its value (x * 1 = x).
Inverse Addition: Adding a number and its negative results in zero (x + (-x) = 0).
Inverse Multiplication: Multiplying a number by its reciprocal yields one, provided the number is not zero (x * (1/x) = 1 for x ≠ 0).
Distribution Rule: Distributing multiplication over addition (x(y + z) = xy + xz).

Functions and Graphs

X Intercept: The value of x when the function value (y) is zero.
Y Intercept: The value of y when the input (x) is zero.
Linear Function: Defined as f(x) = x, representing a straight line.
Quadratic Function: Denoted by f(x) = x², illustrating a parabolic curve.
Absolute Value Function: Given by f(x) = |x|, representing distances from zero.

Transformations

Horizontal Shift: A positive shift moves the graph to the left, while a negative shift moves it to the right.
Vertical Shift: A positive shift raises the graph, whereas a negative shift lowers it.
Reflection Across the X-Axis: Achieved by negating the function, expressed as -f(x).
Reflection Across the Y-Axis: Accomplished by replacing x with -x in the function, shown as f(-x).

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Description

This quiz provides flashcards covering essential concepts from Units 1 and 2 of the OnRamps Algebra II curriculum. Learn key definitions such as natural numbers, integers, rational numbers, and irrational numbers. Master these fundamental mathematical concepts to enhance your algebra skills.

OnRamps Algebra II Units 1 & 2 Flashcards