Algebra II Trig Placement Test Review

Questions and Answers

What is the result of factoring $10x^2 - 7x - 3$?

(2x + 3)(5x - 1)

(5x + 1)(2x - 3)

(10x - 3)(x + 1)

(10x + 3)(x - 1) (correct)

What is the domain of the function?

{-2, 0, 2}

What defines a function?

Each x value goes to only one y value.

What is a parabola?

A shape where the extreme point (max or min) is the vertex, and zeros are the x-intercepts. Signup and view all the answers

What does f(x) represent?

f(x) = y; f(2) is solved if x is 2. Signup and view all the answers

True or False: Any number raised to the power of 1 is itself.

True Signup and view all the answers

What is the product rule in exponents?

Add the exponents when multiplying with the same base. Signup and view all the answers

What is the power rule in exponents?

Multiply the exponents when raising a power to a power. Signup and view all the answers

What is the quotient rule in exponents?

Subtract the exponents when dividing with the same base. Signup and view all the answers

True or False: Any non-zero number raised to the zero power is 0.

False Signup and view all the answers

What do negative exponents represent?

A nonzero number raised to a negative power equals its reciprocal raised to the opposite positive power. Signup and view all the answers

Study Notes

Factoring

The expression (10x^2 - 7x - 3) can be factored into ((10x + 3)(x - 1)).

Domain

The domain is a set of x-values, which in this case is ({-2, 0, 2}).

Functions

A function uniquely maps each x-value to a single y-value, exemplified by pairs like ((2, 3), (3, 4), (4, 2)).

Parabola

A parabola has a vertex that represents its extreme point (maximum or minimum), while the x-intercepts are known as zeros.

Function Notation

(f(x)) denotes a function with output (y), where (f(2)) requires solving for y when (x = 2).

Rule of One

Any number raised to the power of 1 remains unchanged, while 1 raised to any power results in 1.

Product Rule

When multiplying two expressions with the same base, their exponents can be added together.

Power Rule

When raising a power to another power, multiply the exponents.

Quotient Rule

Dividing two expressions with the same base entails subtracting the exponents while retaining the base.

Zero Exponent Rule

Any non-zero number raised to the zero power equals 1.

Negative Exponents

A nonzero number with a negative exponent equals the reciprocal of that number raised to the opposite positive exponent (e.g., (4^{-2} = \frac{1}{4^2})).

Description

Prepare for your Algebra II Trigonometry placement test with this comprehensive set of flashcards. Each card covers key concepts including factoring, domain, functions, and more, designed to enhance your understanding and retention of crucial algebra topics.