Algebra 2 Sem2 Final REVIEW Notes

Rational Exponents

Simplify the expression 9^{3/2}

Radical Expressions

Simplify the radical expression \sqrt{242}

Solving Radical Equations

Solve the radical equation \sqrt{15x + 61} = 11

Solving for x in terms of y

Solve for x in terms of y: y = f(x) = \frac{7}{3}x - 9

Inverse of a Nonlinear Function

Find the inverse of the function f(x) = (x - 1)^3

Rewriting Exponential Functions

Rewrite the exponential function y = a(9)^{t/12} in the form y = ab^t

Compound Interest

Calculate the balance after 8 years for a principal of $9000 compounded monthly at an annual interest rate of 6.3%

Simplifying Exponential Expressions

Simplify the exponential expression \frac{66e^{11}}{11e^6}

Rewriting Exponential Equations

Rewrite 49^{5/2} = 16807 in logarithmic form

Expanding Logarithmic Expressions

Expand the logarithmic expression \log_2 \frac{x^7}{3z}

Condensing Logarithmic Expressions

Condense the logarithmic expression \log6 8 + 5\log6 2 - \log_6 4

Solving Exponential Equations

Solve the exponential equation 9^x = 84

Solving Logarithmic Equations

Solve the logarithmic equation \log5 3x + \log5 (x + 2) = 1

Newton's Law of Cooling

If T0 = 390°F, TR = 70°F, and T = 150°F at t = 20 minutes, find T after 30 minutes using Newton's Law of Cooling.

Writing Exponential Functions

Given points (2, 5) and (4, 125), write the exponential function in the form y = ab^x

Inverse Variation

If y = 8 when x = 5, find y when x = 2 in an inverse variation.

Graphing Rational Functions

Identify the domain and range for the rational function g(x) = -\frac{5}{x + 3} - 8

Simplifying Rational Expressions

Simplify the rational expression \frac{x^2 - 3x - 28}{x^2 + 2x + 1}

Multiplying Rational Expressions

Multiply the rational expressions \frac{7x^7y^5}{9x^4y^2} \cdot \frac{3x^5y^3}{14x^2y^6}

Dividing Rational Expressions

Divide the rational expressions \frac{5x}{-6x - 30} \div \frac{x^2 + 7x}{x^2 + 12x + 35}

Solving Rational Equations

Solve the rational equation \frac{x + 3}{4x} = \frac{9 + x}{4x + 5}

Trigonometric Functions

If \cot \theta = \frac{5}{4}, find the values of the other trigonometric functions.

Solving Right Triangles

In a right triangle, if \angle A = 34° and c = 9, find the lengths of sides a and b and the measure of angle B.

Radian Conversion

Convert 290° to radians.

Unit Circle

Evaluate \tan(-630°).

Reference Angles

Evaluate \sin \frac{4\pi}{3} using reference angles.

Period of Cosine

Find the period of the cosine function g(x) = \cos 5x

Transformations of Sine Functions

Identify the amplitude, period, and vertical shift for the sine function g(x) = 3\sin 4x + 2

Trigonometric Functions and Graphs

If \cos \theta = -\frac{7}{25} and \frac{\pi}{2} < \theta < \pi, find the values of the other trigonometric functions.