Algebra II, Semester 2 Topics
Chapter 6 Irrational and Complex Numbers
1. I can simplify binomials containing radicals.
ex) (4 + √7)(3 + 2√7)
ex) (√7 + 1)2
2. I can rationalize the denominator of a radical expression.
ex)
3+√5
ex)
3−√5
2√3
√4
3. I can solve equations containing radicals.
ex) √2𝑥 − 1 = 3
ex) 2 √𝑥 − 1 = 3
3
4. I can classify each number as real or a complex/imaginary number or rational or irrational number.
ex)
22
7
ex) √3
ex) 3 + 2𝑖
ex) 3√−6
5. I can simplify radicals that contain a negative number, and express in simplest radical form.
ex) √−32
ex)
6
√−2
6. I can multiply radicals.
ex) √30 ∙ √42
2
ex) (2√5)
7. I can add and multiply complex numbers.
ex) (3 + 6𝑖) + (4 − 2𝑖)
ex) (2 + 4𝑖)(5 − 2𝑖)
Chapter 7 Quadratic Equations and Functions
1. I can solve quadratic equations by completing the square.
ex) 𝑥 2 − 6𝑥 − 3 = 0
ex) 𝑥 2 − 5𝑥 = 4
2. I can solve quadratic equations by the quadratic formula.
ex) 5𝑥 2 + 4𝑥 − 2 = 0
ex) 𝑥 2 + 6𝑥 = −2
3. I can find the discriminant and use the discriminant to determine the nature of the roots of a quadratic
equation.
ex) 𝑥 2 − 8𝑥 + 5 = 0
ex) 𝑥 2 − 4𝑥 + 13 = 0
ex) 𝑥 2 + 10𝑥 + 25 = 0
4. I can find the vertex of a quadratic function (min or max).
ex) 𝑦 + 2 = (𝑥 + 3)2
ex) 𝑦 = −(𝑥 − 1)2
5. I can find the axis of symmetry of a quadratic function.
ex) 𝑦 − 5 = 2(𝑥 − 2)2
1
ex) 𝑦 + 1 = − (𝑥 − 3)2
3
6. I can graph quadratic equations and label the axis of symmetry and the vertex.
ex) 𝑦 + 4 = (𝑥 − 3)2
ex) 𝑦 − 2 = −2(𝑥 − 4)2
7. I can find all intercepts of a quadratic equation.
1
ex) 𝑦 − 7 = − (𝑥 + 6)2
2
ex) 𝑦 + 8 = −3(𝑥 − 1)2
8. I can write quadratic equations given its roots.
ex) 2, 5
ex) 1 + √3, 1 − √3
Chapter 10 Exponential and Logarithmic Functions
1. I can write expressions as a single logarithm.
ex) 5 log 4 𝑝 + log 4 𝑞
1
ex) 4 log 3 𝑎 − log 3 𝑏
2
2. I can expand a single logarithm into multiple logs.
ex) log 2 𝑀6 𝑁 3
ex) log 3 𝑀√𝑁
3. I can change base to be the same to solve exponential equations.
ex) log 4 7
ex) log 3 5
4. I can multiply each side by log when I cannot change the base to be the same to solve exponential
equations.
ex) 3𝑥 = 7
ex) 4𝑥 = 16
5. I can solve logarithmic expressions.
ex) log 8 𝑥 = −
1
3
ex) log 2 8√2 = 𝑥
6. I can solve compound interest problems.
ex)
7. I can simplify natural log expressions. (ln and e)
ex) ln 𝑒 2
ex) ln
1
𝑒3
8. I can solve natural log problems. (ln and e)
ex) ln 𝑥 = 3
ex) 𝑒 𝑥 = 2
ex) √𝑒 2𝑥 =4