Download Algebra 2 – Semester Review

Algebra 2 – Semester Review
Units 1 and 2
Unit 1:
 Solving equations and inequalities
 Interval notation
 Multiply, simplify, evaluate
 Absolute value – Dos Solutions!
Unit 2:
 Writing equations of lines
 Word problems
 Function notation and composites
 Domain and range
1. Solve the following equations and inequalities. If you are given an inequality,
write your final answer in interval notation.
a. 5x +19 = 5
d. x + 8  6
g. x + 2  19
b. x 2 = 64
e. 7x - 8 < 13
c. x +1 = 5 - 4(x + 2)
f. (9x - 3)(x + 13) = 0
2. Use the following functions to answer the questions below.
f(x) = 5x2 + x
g(x) = 3x - 10
h(x)= x - 9
a. f(g(5))
b. Find x when h(x) = 15
c. g(f(x))
d. f(-5)
e. h(-7)
f. h(g(x))
3. The manager of a restaurant found that the cost to produce 50 cups of coffee
is $15.45, while the cost to produce 400 cups is $65.95. Assume the cost C(x) is
a linear function of x, the number of cups produced. Find the formula for C(x).
4. Assume that the time it takes to construct a road varies linearly with the
number of workers on the job. If there are 100 people working, the job will be
finished in 14 weeks. If there are 200 men working, the job will be finished in 7
weeks. The equation that predicts time on the job when given the number of
-7
t + 21
workers is: J(t) =
100
a. How long will it take a crew of 250 to complete the job?
b. What does the slope mean in the real world?
c. Give an appropriate domain and range and justify your answer.
d. If you have only 4 weeks to complete the job, how many will make up
your work crew?
5. Find the slope of each line.
b. Through (-14, 6) and (0, 2)
c. x = 8
b. y = 2x + 7
d. 5x – y = 11
6. Given equation, find slope, y-intercept, and x-intercept. Please write the
intercepts as ordered pairs: 2x – 4y = 18