Practice Problems for Exam 1
1
1. Given the numbers {.2, ,3, 2 , | 4 |} .
2
a) List the numbers that are:
Natural Numbers:
Integers:
Rational Numbers:
Irrational Numbers:
b) Draw all the numbers on a number line.
2. Evaluate
2 2
a)
3 15
3 2 2
b)
8 3 15
c) 8 3[6 2 2(7 4)]
x
d)
, x 2, y 1
|2 y|
3. Simplify
a) 2 x[8 (6 x)] 5 x
b) 15 7( x 2)
4. Write an algebraic expression:
a) One hundred increased by the product of 15 and a number.
b) The area of a rectangle whose length is L and width is 5 units less than the
length.
5. Solve for x
a) 4 x 64 0
b) 3(2 x 1) 9 3 x
4x 1 3
c)
5 10 2
d) | 4 3 x | 8
e) | x 2 | 2 4
6. Solve for x . Draw each solution on a number line and write it as an interval.
a) 6 2 x 8 4
x
3x
b)
2
5
4
8
c) | x 3 | 2
d) | 5(1 x) | 25
7. You accepted a summer job that pays $200 per week plus a one-time bonus of
$350. How many weeks would you have to work at this job to earn $2750?
8. A real estate agent receives a commission of $9000 for the sale of a $150,000
house. What percent commission is this?
9. Solve for the missing side:
10. Ticket sales for a play total $2200. There are 3 times as many adult tickets sold as
children’s tickets. The prices are $6 and $4 respectively. Find the number of
adult and children tickets sold.
11. You can mow a lawn in 3 hours and your friend can mow in 4 hours.
a) What fractional part of the lawn can each person of you mow in 1 hour?
b) How long will it take both of you to mow the lawn working together?
12. Consider the two points (-5,-1) and (1,2)
a) Find the distance between the two points.
b) Find the midpoint between the two points.
c) Find the line passing through the two points
d) Sketch the line
13. Consider the equation 2 x 4 y 1
a) Find the x-intercept and y-intercept.
b) Find the equation of the line that is parallel and goes through the point (-1,5).
c) Find the equation of the line that is perpendicular and goes through the (-1,5).
14. Sketch 3 x 4 y 2
15. Consider the function f ( x) 4 5 x . Evaluate
a) f (10)
2
b) f
5
c) f (a 1)
d) f ( x) f (10)
16. Find the domain
a) y x 2
1
b) y
( x 1)( x 2)
c) y 5 x
3 x, x 0
17. Let f ( x)
. Evaluate
2
1 x , x 0
a) f (2)
b) f 1
c) f 0
18. Let y | x 1 | . Fill in the table below, sketch the points and connect to get a
rough sketch of the graph.
x
-1
0
1
2
3
y
0
