Semester 2 Mastery Answer Key
Answer Key: Mastery Final
Algebra 2 Semester 2 // Teacher Resource
Ref: CR-A2-S2-AK-V5
01: Simplifying Radicals
\( 6x^2y^3\sqrt{2x} \)
02: Operations
\( \sqrt{5} \)
03: Conversions
A: \( \sqrt[3]{(5x)^2} = \sqrt[3]{25x^2} \)
B: \( 10^{1/4}y^{3/4} \)
04: Radical Equations
\( x = 21 \)
05: Complex Numbers
A: \( 23 + 14i \)
B: \( i=i, i^2=-1, i^3=-i, i^4=1 \)
C: \( i^{23} = -i \)
06-09: Factoring Toolbox
06: \( 6x^2y^2(2x^2 - 3y) \)
07: \( (x-4)(x-3) \)
08: \( (3x-2)(x+4) \)
09: \( (2x+3)(4x^2 - 6x + 9) \)
Page 1 of 3
Answer Key: Mastery Final (Cont.)
Part II: Functions & Solving
10: Parent Identification
| Icon | Solution Name / Eq | Deg | EB (\(\infty\)) | EB (\(-\infty\)) |
|---|
| Linear / \( x \) | 1 | \( \infty \) | \( -\infty \) |
| Quadratic / \( x^2 \) | 2 | \( \infty \) | \( \infty \) |
| Cubic / \( x^3 \) | 3 | \( \infty \) | \( -\infty \) |
| Abs Val / \( | x | \) | N/A |
| Quartic / \( x^4 \) | 4 | \( \infty \) | \( \infty \) |
| Quintic / \( x^5 \) | 5 | \( \infty \) | \( -\infty \) |
11: Graph Analysis (\( y = x^2 - 2x - 3 \))
Vertex: (1, -4)
Axis of Sym: x = 1
Zeros: (3, 0), (-1, 0)
Min Value: y = -4
12: Factoring Solve
\( x = -2, -3 \)
13: Quad Formula
\( \frac{2 \pm \sqrt{6}}{2} \)
Page 2 of 3
Answer Key: Mastery Final (Cont.)
Part III: Rationals & Reference Practice
14-15: Rationals
14: \( \frac{x-3}{x+2} \)
15: \( \frac{x+1}{3x} \)
Reference Guide Practice Solutions
Complex: \( i^{38} \)
\( (i^4)^9 \cdot i^2 = -1 \)
Factor Squares: \( x^2 - 49 \)
\( (x-7)(x+7) \)
Factor Cubes: \( x^3 + 27 \)
\( (x+3)(x^2-3x+9) \)
Rational Simplify
\( x \)
Page 3 of 3
Semester 2 Mastery Final Exam Packet
Algebra 2: Semester 2 Final
Mastery Assessment Packet
Ref: CR-A2-S2-V5
Student Name
Date
Period
01
Simplifying Radicals
Simplify completely:
\( \sqrt{72x^5y^6} \)
02
Operations
Simplify & combine:
\( 3\sqrt{20} + \sqrt{45} - 2\sqrt{80} \)
03
Conversions
A. To Radical Form:
\( (5x)^{2/3} \)
B. To Rational Exponent:
\( \sqrt[4]{10y^3} \)
04
Radical Equations
Solve for \( x \):
\( \sqrt{2x + 7} - 5 = 2 \)
05
Complex Numbers
A. Multiply & simplify:
\( (4 - 3i)(2 + 5i) \)
B. List the values for:
\( i, i^2, i^3, i^4 \)
C. Evaluate Power:
\( i^{23} \)
Algebra 2 Semester 2Page 1 of 4
Part II: Factoring & Functions
Blueprint CR-2
06-09
Factoring Toolbox
06: GCF\( 12x^4y^2 - 18x^2y^3 \)
07: Quad \( (a=1) \)\( x^2 - 7x + 12 \)
08: Quad \( (a>1) \)\( 3x^2 + 10x - 8 \)
09: Cubes\( 8x^3 + 27 \)
10
Parent Function Identification
Identify each parent function graph. Provide Eq, Deg, and End Behaviors.
Eq:
Deg:
\(x \to \infty\):
\(x \to -\infty\):
Eq:
Deg:
\(x \to \infty\):
\(x \to -\infty\):
Eq:
Deg:
\(x \to \infty\):
\(x \to -\infty\):
Eq:
Deg:
\(x \to \infty\):
\(x \to -\infty\):
Eq:
Deg:
\(x \to \infty\):
\(x \to -\infty\):
Eq:
Deg:
\(x \to \infty\):
\(x \to -\infty\):
Algebra 2 Semester 2Page 2 of 4
Part III: Solving & Rationals
Blueprint CR-3
11
Graphing Analysis
Analyze the quadratic equation and its graph:
\( y = x^2 - 2x - 3 \)
Vertex:
Axis of Symmetry:
Zeros:
Min/Max Value:
