Precalculus
Name:________________________
Chapter 1 Test Review
Show all you work for full credit. Read the questions carefully.
1. Solve for n:
1
1
(n  8)  2  (n  6)
4
2
Answer ______________
2. Solve for y:
2 x  3 y  15
Answer ______________
3. Solve for g:
1
s  gt 2  vt
2
Answer ______________
4. Solve: 5( x  2)  3  3 x  11
Solution in set notation ____________
Graph
Solution in interval notation ____________
5. How many pound of cheese worth $0.81/lb must be mixed with 10 lb cheese
worth $1.29 to make a mixture worth $1.11/lb?
6. Express the compound inequality x  4 and x  3 graphically and in interval
notation.
Graph
interval notation: _______________
7. Solve the compound inequalities (interval notation) and graph the solution set.
2x x
  2 or x  3  2
5 10
Graph
interval notation: _______________
8. Determine the domain for each expression:
a. 4 x  20
b. 12  2x
2
9. Solve and express the answer in set notation: 5  x  9  8
3
Hint: set notation is  
Answer ______________
g ( x) 
1
2x  3
10. Solve and express the answer in interval notation. If there is no solution , write  .
3x  2
a.
b. 3x  4  12
1
4
Answer ______________
Answer ______________
11. Multiply and express answers in a  bi form.
a. (5  2i)(7  3i)
b. (2  3i)2
c. The product of (1  2i 3) and its conjugate.
12. Simplify each expression and write the result in standard form:
a. 72
b. i 57
c. i 74
Answer ______________
d.
10  50
5
Answer ______________
Answer ______________
Answer ______________
13. Perform the operation. Express answers in a  bi form.
5i
2  3i
a.
b.
c 3  4i)  (4  5i)
1  2i
1  2i
Answer ______________
Answer ______________
Answer ______________
14. Use substitution to verify that the given complex number and its conjugate are
solutions to the equation shown:
2
x  4 x  9  0; x  2  i 5
15. A ski lift carried Matt up a slope at the rate of 6 km/h, and he skied back down
parallel to the lift at 34 km/h. The round trip took 30 min. How far did he ski and for
how long?
16. The volume of an inflatable hot air balloon can be approximated using the formulas
2
1
for a hemisphere and a cone: V   r 3   r 2 h . Assume the conical portion has height
3
3
h = 24 ft. During inflation, what is the radius of the balloon at the moment the volume of
air is numerically equal to 126 times the radius?
17. Solve. Write the answers in exact form. If there are no real solutions write  .
a. 2 x 2  4 x  30
b. 3v 2  v  2
c. ( x  3) 2  7  2
_______________
_____________
_______________
18. Solve. Write the answer in exact form.
a. ( x  5) 2 
12
25
_______________
b. 6 w2  w  2
c. 8 x 2  5 x  1
_____________
_______________
19. Solve by completing the square: Write the answer in exact form
a. x 2  2 x  15
b. 4 x  2 x 2  3
20. Use the Discriminant to determine whether the equation has real (rational or
irrational), repeated or complex roots. Hint: Discriminant = b 2  4ac
a. 4 x  x 2  13  0
b. 15 x 2  x  6  0
Discriminant
______________
Discriminant _____________
Type of root
______________
Type of root
______________
Solve each equation. Identify any extraneous roots (include them in your answer but
state that they are extraneous.) Show all your work.
21. x 
14
2x
 1
x7
x7
Answer _____________________
22.
a
2a 2  5
3
 2

2a  1 2a  5a  3 a  3
Answer _____________________
23.
2 x  31  x  2
Answer _____________________
2
25. 2( x  5) 3  11  7
Answer _____________________
24. 3x  4  7 x  2
Answer _____________________
26. x 2  3x 1  4  0
Hint: Use a u-substitution. Identify the u.
Answer _____________________
27. Solve for h: S   r r 2  h2 Show all the steps.