Download WS--Semester1 Review - Liberty Union High School District

Semester 1 FINAL Review
Algebra II
Chapters 1 and 2
1. Describe the transformation of each
a.)
f ( x) = x + 2
2. Solve the system (1.4)
b.)
f ( x) = x − 4
c.)
f ( x) = −
a.) 3 x + 5 y + 4 z = 13
1
x−2
2
d.)
f ( x) = 3( x − 1) 2 + 2
b.) x − y − z = − 9
5 x + 2 y + 3z = − 9
2 x + 2 y + z = 19
6 x + 3 y + 4 z = −8
x + y − z = −1
3. Write an equation of a line and interpret the slope. (1.3)
a.) Find the equation of the line that fits the data.
b.) How many calories will you burn after walking 45 minutes?
Minutes walking, x
1
6 11 16
Calories burned, y
6 27 48 69
4. Interpreting a parabola on a graph (Ch 2)
a.) Interpret what the vertex means.
b.) When is the flu epidemic increasing and decreasing?
c.) What does the point (0, 1) mean?
5. Graph the function. Label the vertex and axis of symmetry. Determine if there is a minimum or maximum value of f.
Then describe where it is increasing and decreasing.
a.) f(x) = (x + 3)2 – 4
b.) f(x) = 1/2x2 – 2x – 1
c.) f(x) = -2(x – 1)(x – 3)
6. Write an equation of the parabola.
a.) passes through (5,
c.) passes through (8,
-4) and vertex (-2, 5)
14), (3, 4) and (6, -2)
b.) x-intercepts of 12 and 8, passes through (9,
5)
Chapter 3
7. Simplifying complex numbers
8. Solving quadratic equations
a.) x2 + x – 20 = 0
a.)
(12 + 3i) + (7 – 6i)
b.)
(4 – 2i) – (5 – 8i)
c.)
(2 + 5i)(3 – 2i)
d.)
(3 + 4i)(3 – 4i)
b.)
x2 – 6x = 8
c.)
3x2 + 4 = -2x
f.)
x2 + 10x + 25 = 64
c.)
x2 – 14x = -2
d.)
-2x2 + 4x – 4 = 0
e.)
3x2 – 48 = 0
g.)
36x2 + 49 = 0
h.)
3x2 + 13x + 4 = 0
9. Solve for x using the “complete the square” method?”
b.) x2 – 6x
a.) x2 – 2x – 63 = 0
= -17
10. Write as a complex number in standard form.
a)
(1 – i) – (4 – 5i)
b)
(-4 + 5i)(5 – i)
11. What does it mean to be a solution to a system of equations?
a) What is the solution to the system graphed?
b) Solve the non-linear system algebraically?
y = x–4
y = x2 – 4x
c) Solve the non-linear system algebraically?
y = x+6
y = x2 + 5x + 10
Chapter 4
12. Simplifying polynomials….perform the operation indicated.
a.) (18x + 2 x − 21) + (13x + 8 − 11)
d.)
(6 x 3 − x 2
g.)
( x2
+ 12 x) ÷ ( x 2 + 2)
(x
− 8 x + 11)( x 2 + 4 x − 9)
13. Factor completely:
a) 4x2 – 12x
e)
e.)
(
+8
5x2 + 15x – 90
14. Show that
x+3
is a factor of
)
c.)
− 9 ) − ( − x 2 − 19 x + 6 )
f.)
b.) (12 x + 2) x 2 − 12 x + 7
h.)
(2 x 4
( x − 1)( x − 2)
(3 x 2
− 11x − 4) ÷ ( x − 1)
− 40 x 2 − 28) ÷ ( x 2 − 5 x − 2)
b)
18 – 2x2
c)
x3 – 125
f)
3x3 + 375
g)
4x2 – 40x + 64
f(x) = 3x4 – 3x3 – 36x2
d)
3x3 – 12x2 – x + 4
h)
5x4 – 80
Then factor f(x) completely.
15. Write a polynomial function f of least degree that has a leading rational coefficient of 1, and the given zeros.
a)
7, -3, 0
b)
4, 3i
c)
Multiple Select (Choose ALL of the answers that are correct.)
16. Joey claims that more than one of the polynomials below have a factor of x+1.
Select each polynomial that supports Joey’s claim:
3
a. f(x) = x3 + x2 – 17x + 15
c. f(x) = x –
b.
f(x) = x3 – 10x2 + 19x + 30
17. Which is a graph of an even function with a positive
Leading coefficient?
d.
-5, 1 – √2
16x2 + 55x + 72
f(x) = x3 + 4x2 – 11x – 30
18. Which are terms in the expansion of
4
4
a. 8x
b. 16x
c.
125
d.
(2x + 5)4?
5
19. What are all of the zeros for the function
2
f(x) = x – 2x – 8
a.
-2
b.
2
c.
-4
d.
4
20. What are the zeros for the graph shown?
Describe the degree and leading coefficient
of the graph.
Semester 1 Need to Know
Algebra II
Chapter 1
* Parent Functions
* Transformation Rules (writing them and graphing)
*Equation of a line
y = mx + b
m=
*Slope of a line
y 2 − y1
x 2 − x1
* Solving 3 equations with 3 variables.
Chapter 2
*Vertex Form verses
*Standard Form
verses
*Intercept Form
(find the vertex and Axis of Symmetry from all three forms)
*Maximums and Minimums
(find it, interpret it, and know it is an overall or a “local”)
* Transformation Rules (writing them and graphing)
* Where a Function -- increasing or decreasing -- f(x) > 0 f(x) < 0
Chapter 3
* Solving Quadratic Equations
-Factoring
- Square rooting
- Quadratic Formula .
- Completing the Square
* Complex Numbers and Imaginary numbers are in the form
Chapter 4
* Factoring completely
- GCF
- Grouping
- Difference of Two Squares
- Sum of Two Cubes
- Trinomial Square
- Difference of Two Cubes
* Solving or Finding the zeros
- by Factoring
- using the Rational Root Theorem
* Performing operations on polynomials
- Addition
- Subtraction
- Long Division
- Synthetic Division
* Graphs
- Using zeros
- End behavior
- Using the degree and leading coefficients
- Evaluating functions
-- using Synthetic Division
- Multiplication
- Pascal’s Triangle