🤩 Algebra II Pre-Teaching Review 🤩

Functions and Exponents

100

How can you tell if a relation is a function?

There must be one unique output for every input.

200

Expand 3x⁵ using multiplication.

3 • x • x • x • x • x

300

If f(x) = ¼x² + 5x - 6 and g(x) = 2x, calculate f(4) + g(1).

f(4) + g(1) = 20

400

Multiply (11a²b⁵c⁷d³)(2a⁵b⁸d⁹).

22a⁷b¹³c⁷d¹²

500

Evaluate (7w⁴x⁹y²z)².

49w⁸x¹⁸y⁴z²

Factor, FOIL, Quadratic Formula, Complete the Square

100

Multiply 2(3x+½)(x+2) by FOILing.

6x² + 13x + 2

200

Find the solutions to x²-24x+63 = 0 by Factoring.

x = 3 and 21

300

Find the solutions to f(x) = -4x²-9x+17 using the Quadratic Formula.

Round answers to three decimal places.

x = -3.474 and 1.224

400

Find the solutions to 10x³-10x²-900x = 0 by Factoring.

x = -9, 0, 10

500

Find the solutions to x²+10x+8 = 0 by Completing the Square.

Round answers to three decimal places.

x = -9.123 and -0.877

Rational Functions and Division of Polynomials

100

Simplify the rational function (x²-6x-16) / (x²+3x+2). 

Think FOCO... Factor Out, Cancel Out.

(x-8) / (x+1)

200

Use Synthetic Division or Long Division to calculate (x²-5x-9) ÷ (x+3).

x - 8 + 15/x+3

300

Simplify the rational function (2x²+10x+12) / 2(x² - 4).

(x+3) / (x-2)

400

Use Synthetic Division or Long Division to calculate (x⁴-3x³+1) ÷ (x-5).

x³ + 2x² + 10x + 50 + 251/x-5

500

Find the value(s) of x that make the rational function f(x) = (2x+1) / (x³-4x²-5x) undefined.

Undefined @ x = -1, 0, 5

Graphing Quadratic and Rational Functions

100

Explain whether the quadratic f(x) = -½x² - 10 will open up or down and how you know.

Opens down because the x² is negative.

200

Find the y-intercept of the quadratic f(x) = -3x² + 10.

y-intercept @ (0, 10)

300

Find the vertex of the quadratic f(x)=-2x²+12x+10.

Vertex @ (3, 28)

400

Find any hole(s) in the rational function (x²-7x+10) / (x²-25).

Hole @ x = 5

500

Find the horizontal asymptote of the rational function (3x²+2x+1) / (2x²-4).

HA @ y = 3/2

Logs and Compound Interest

100

Condense 2 log₄ 3 + log₄ x.

log₄ (9 + x)

200

Calculate the total cost of the following loan.
-Principle: $55,000
-Interest Rate: 2.09%
-Time: 12 Years
-Compounded Weekly

$70,674.36

300

Expand log₁₁ (x²y⁴/z³).

2 log₁₁ x + 4 log₁₁ y - 3 log₁₁ z

400

Condense 5 log₃ 2 + 6 log₃ a + 14 log₃ b + 42 log₃ c - 2 log₃ 4 - 2 log₃ a - 7 log₃ c.

log₃ (2a⁴b¹⁴c³⁵)  or  log₃ (32a⁶b¹⁴c⁴²/16a²c⁷)

500

Alissa can spend $600 per month for a car payment.
She wants to purchase a car for $26,000 and will use a 4-year loan at 2.67% compounded monthly.

Can Alissa afford this monthly payment?  If so, how much money per month will she have left?  If not, how much is she short by?

Short by $2.65 per month.