Algebra I - 3rd Quarter Review

Properties of Exponents

100

(a^m)ⁿ = a^mn

An exponent raised to another power → multiply exponents

What is the Power of a Power Property?

200

a^-n = 1/aⁿ

To rewrite a negative exponent, take the reciprocal of the base raised to a positive exponent.

What is the Negative Exponent Property?

300

a^m * aⁿ = a^{m + n}

Multiplying terms with same base & different exponents → add the exponents

What is the Product Property?

400

a^m/aⁿ = a^{m - n}

Dividing terms with same base & different exponents → subtract the exponents

What is the Quotient Property?

500

(ab)^m = a^m * b^m

A product raised to a power → distribute the power to each term in the parentheses

What is the Power of a Product Property?

Radical Expressions

100

Add the radical expressions. Simplify.

3√75 + 2√3

What is 17√3?

200

Divide the radical expressions. Simplify.

√(845/5)

What is √169 or 13?

300

Multiply the radical expressions. Simplify.

2√30 * 3√70

What is 6√2100 or 60√21?

400

Divide the radical expressions. Simplify.

√640/√5

What is √128 or 8√2?

500

Multiply the radical expressions. Simplify.

x√2x⁵ * 2x√8x

What is 2x²√16x⁶?

Exponential Growth/Decay (Compound Interest & Geometric Sequence)

100

f(x) = a(1+r)^t is the formula of:

What is Exponential Growth?

200

f(x) = a(1-r)^t is the formula for:

What is Exponential Decay?

300

A=P(1+r/n)^nt is the formula for:

What is Compound Interest?

400

a_n=r(a_n-1) is the formula of: 

What is the Recursive Formula of a Geometric Sequence?

500

a_n=a₁(r)^n-1 is the formula of:

What is the Explicit Formula of a Geometric Sequence?

Polynomials

100

Monomial, Binomial, and Trinomial determines the _________ ___ ______ in a polynomial.

What is number of terms?

200

A polynomial written from highest to lowest according to degree/exponent.

What is the Standard Form of a Polynomial?

300

Simplify.

(2x²-4x-1) - (3x²+8x-4)

What is -x² - 12x + 3?

400

Multiply and simplify.

(2x+6)(x-4)

What is 2x² - 2x - 24?

500

Factor the polynomial.

6y⁵ - 42y⁴ + 18y³

What is 6y³(y² - 7y + 3)?

Quadratic Functions

100

(h, k) → the minimum and/or maximum of a point of a parabola

What is a Vertex?

200

f(x) = a(x-h)²+k is the formula of:

What is the Vertex Form of a Quadratic Function?

300

x = h of the quadratic function is the:

What is the Axis of Symmetry?

400

(x - h) and (x + h) determines the ______________ shift.

What is Horizontal?

500

+k and -k determines the ____________ shift.

What is Vertical?