```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) √2 − 1 = 3
ex) 2 √ − 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 + 2
ex) 3√−6
5. I can simplify radicals that contain a negative number, and express in simplest radical form.
ex) √−32
ex)
6
√−2
ex) √30 ∙ √42
2
ex) (2√5)
7. I can add and multiply complex numbers.
ex) (3 + 6) + (4 − 2)
ex) (2 + 4)(5 − 2)
Chapter 7 Quadratic Equations and Functions
1. I can solve quadratic equations by completing the square.
ex)  2 − 6 − 3 = 0
ex)  2 − 5 = 4
ex) 5 2 + 4 − 2 = 0
ex)  2 + 6 = −2
3. I can find the discriminant and use the discriminant to determine the nature of the roots of a quadratic
equation.
ex)  2 − 8 + 5 = 0
ex)  2 − 4 + 13 = 0
ex)  2 + 10 + 25 = 0
4. I can find the vertex of a quadratic function (min or max).
ex)  + 2 = ( + 3)2
ex)  = −( − 1)2
5. I can find the axis of symmetry of a quadratic function.
ex)  − 5 = 2( − 2)2
1
ex)  + 1 = − ( − 3)2
3
6. I can graph quadratic equations and label the axis of symmetry and the vertex.
ex)  + 4 = ( − 3)2
ex)  − 2 = −2( − 4)2
7. I can find all intercepts of a quadratic equation.
1
ex)  − 7 = − ( + 6)2
2
ex)  + 8 = −3( − 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  + log 4
1
ex) 4 log 3  − log 3
2
2. I can expand a single logarithm into multiple logs.
ex) log 2 6  3
ex) log 3 √
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) 3 = 7
ex) 4 = 16
5. I can solve logarithmic expressions.
ex) log 8  = −
1
3
ex) log 2 8√2 =
6. I can solve compound interest problems.
ex)
7. I can simplify natural log expressions. (ln and e)
ex) ln  2
ex) ln
1
3
8. I can solve natural log problems. (ln and e)
ex) ln  = 3
ex)   = 2
ex) √ 2 =4
```