Algebra 2 Semester 1 ReviewDO ALL WORK ON YOUR OWN PAPER FOR CREDIT!
1.Which polynomial has a greatest common factor of 5x?
a.b.c.d.
2.One factor of the expression is is.Which of the following is another factor?
a.b.c.d.
3.Which equation could you solve to find the solution of equation ?
a.c.
b.d.
4.Factor the expression completely :
5.Factor the expression completely:
6.When the trinomial is is factored completely, which of the following is one of the factors?
a.b.c.d.
7.Given the expression Write an equivalent expression.
8.Simplify:
9.Simplify:
10.Consider the equation . What are the solutions?
11.What are the zeros of the equation ?
12.Which of the following expressions could be used to find the area of the square below?
a.b.
c.d.
13.What is simplified form of the expression ?
14.Consider the expression . Write an equivalent expression.
15.The graph of the function is shown. Between which two consecutive integers does one of the solutions of the equation fall?
a.2 and 3b.1 and 2c.-1 and 0d.-3 and -2
16.Consider the end behavior of the graph shown
Which of the following functions could be graphed?
a.c.
b.d.
17.What is the minimum or maximum value of the quadratic ?
18.What are the x-intercepts of the graph of the function ?
19.A company predicts it monthly profit P with the equation , where x is the amount spent on advertising, in thousands of dollars. What amount should the company spend on advertising to maximize its profit?
Find the discriminant of the quadratic equation and give the number and type of solutions of the equation.
20.
21.
22.
23.What value must be added to both sides of the equation to complete the square
24.What is the value of y in the system?
25. You ride an express bus from the center of town to your street. You have two payment options. Option A is to buy a monthly pass and pay $1 per ride. Option B is to pay $2.50 per ride. A monthly pass costs $30. What does a solution of 20 rides mean in the context of the problem.
26.Solve the system of equations by graphing:
27.From 1990 to 1999, the per person consumption B of bottled water (in gallons) and the population P of the United States (in thousands) can be modeled by
wheret is the number of years since 1990. Write a model for the total consumption C of bottled water (in thousands of gallons).
Consider the functions
Perform the indicated operation
28.
29.
30.
31.
32.Given the figure, write an expression for the total area.
The area of each triangle piece is given by the function
The area of rectangle piece is given by the function
Given the following zeros, state the least degree of the polynomial.
33.-1, 3, 4
34.
35.
36.Consider each of the following graphs with given degree. State the number of real zeros and imaginary zeros for each graph.
Consider the graph
37.What are the real roots of the function?
38.What are possible factors of the function?
39.Is the sign of the leading coefficient positive or negative?
Justify your response.
40.Is the degree of the function even or odd?
Justify your response.
41.What are the local maximums and local minimums?
42.State the intervals of increase.
43.State the intervals of decrease.
44.State the domain and range of the function.
45.The graph of the parabola has a vertex at (3, 4). If this parabola is shifted 5 units to the left and 3 units down, what is the equation of the new parabola?
46.What are the solutions to ?
a. x = 1 and x = 5b.x = 1c. x = 5d. no solution
47.Find the inverse of each of the following:
a.
b.
Perform the indicated operations.
48.49.
50.51.
Solve for x and y.
52.53.