Algebra 2 Final Exam Preparation

Overview

• Focus on solving 10 problems featuring important concepts for Algebra 2 exam.
• Covers inequality solving, systems of equations, graphing, imaginary numbers, quadratic equations, polynomial division, functions, cube roots, and logarithms.

Inequality Solving

• Problem: Solve for x in -2(4x - 3) < -2.
• Method: Apply distributive property, isolate x, and remember to flip the inequality sign when dividing by a negative.
• Solution: x > -1.

Solving Systems of Equations

• Problem: Solve two equations for x and y.
• Methods: Substitution and Elimination.
• Example: Use substitution if y is isolated or easily isolated.
• Solution: x = 1, y = 5 (or as coordinates: (1, 5)).

Graphing

• Problem: Graph y = |x + 3|.
• Concepts: Recognize absolute value as "V" shape and perform transformations.
• Transformation: Moves the graph left by 3 units.

Imaginary Numbers

• Problem: Simplify (3 + 2i)(5 - 4i).
• Concepts: Use FOIL method to multiply complex numbers.
• Key Point: i^2 = -1.
• Solution: 23 - 2i.

Quadratic Equations

• Problem: Solve x^2 + 2x - 8 = 0.
• Method: Quadratic formula: x = [-b ± sqrt(b^2 - 4ac)] / 2a.
• Solutions: x = 2, x = -4/3.

Domain and Range

• Concept: Domain is all x-values; range is all y-values that function can take.
• Example: Domain is all real numbers, range is from y ≥ 1 to infinity.

Polynomial Division

• Problem: Divide 2x^3 + 5x^2 - 11x + 6 by 2x - 1.
• Methods: Long division or synthetic division (under certain conditions).
• Solution: x^2 + 3x - 4 + 2/(2x - 1).

Functions

• Problem: Find f(g(x)) where f(x) = 3x - 2 and g(x) = x^2 + 1.
• Method: Substitute entire g(x) into f(x).
• Solution: 3x^2 + 1.

Cube Roots

• Problem: Solve for x in cube root equation.
• Method: Undo operations by cubing both sides.
• Solution: x = 14.

Logarithms

• Problem: Solve log base 3 of 243.
• Concepts: Logarithms as exponents.
• Method: Trial and error or calculator method (log big number/log small number).
• Solution: 5.

Additional Resources

• Full videos on each topic available in description.
• Midterm video with additional problems covering other concepts.

Good luck with studying and finals preparations! For any questions, refer to comments section in the video.