Algebra Sample Problems
1. Add/subtract fractions
Example:
Answer:
2. Absolute Value
Examples
b. Solve the equation for x.
(Answer: x= -4, x=7)
3. Exponents
Examples
4. Factor a quadratic equation
Example: Factor the following expression.
Answer :
5. Simplify a radical function
Example: Simplify the following expression.
Answer :
6. Simplify a complex fraction.
Example: Simplify.
Answer :
7. Simplify radical expressions.
Example: Simplify.
Answer :
8. Given an equation, solve for x.
Examples
9. Solve an inequality
Example: Solve the inequality and write the solution set in interval
notation.
Graph the solution set.
10. Find coordinates of a point
Example: Find the coordinates of the point C.
11. Read data from graph.
Example: Suppose the following graph represents sales of DVD players (in
dollars) for Locke Industries in 2007.
a. What was the sales amount on June 1? (Answer: $3500.
00)
b. What was the maximum sales amount? (Answer: $4500. 00)
c. In what month did the maximum sales occur? (Answer: August)
d. In what months was sales equal to $3000. 00?
(Answer: April, November, December)
12. Find x and y intercepts.
Example: Find the x-and y-intercepts of the graph of the equation
Answer: x-intercept is (12,0), y-intercept is (0,-4)
13. Lines
Examples
a. Find the slope of the line.
b. Find the equation of the line that passes through the points (4,-1) and (-6,14).
Answer:
14. Domain and range of a function.
Example: Find the domain and range of
Answer:
domain is [-7,∞], range is [0,∞]
15. Graph a function by making a table of values and plotting points.
16. Find values of a function by looking at a graph.
Example: Given below is the graph of y=g(x) .
a. What is the value of g(2)?
Answer: -5
b. What are the values of x such that g(x)=0?
Answer:-3. 5, 3. 1
17. Function Values
Example: If f(x)=2x+8 what is the value of f(z+2)?
Answer:2z+12
18. Composition of functions
Example: If f(x)=x^2 and g(x)=x+4, what is 
?
Answer:
