The Man
Precalculus—
1-75
Practice Test
MIXED REVIEW
1. Find the allowable values for each expression. Write your response in interval notation.
10
Ϫ5
a.
b.
3x ϩ 4
1x Ϫ 8
2. Perform the operations indicated.
a. 1Ϫ18 ϩ 1Ϫ50
b. 11 Ϫ 2i2 2
3i
c.
d. 12 ϩ i132 12 Ϫ i132
1ϩi
3. Solve each equation or inequality.
a. Ϫ2x3 ϩ 4x2 ϭ 50x Ϫ 100
b. Ϫ3x4 Ϫ 375x ϭ 0 c. Ϫ2Ϳ3x ϩ 1Ϳ ϭ Ϫ12
4
x
d. Ϫ3 ` Ϫ 5 ` Յ Ϫ12 e. v3 ϭ 81
3
1
f. Ϫ21x ϩ 12 4 ϭ Ϫ6
Solve for the variable indicated.
2
1
4. V ϭ r2h ϩ r3; for h 5. 3x ϩ 4y ϭ Ϫ12; for y
3
3
Solve as indicated, using the method of your choice.
6. a. Ϫ20 Յ 4x ϩ 8 6 56
b. Ϫ2x ϩ 7 Յ 12 and 3 Ϫ 4x 7 Ϫ5
7. a. 5x Ϫ 12x Ϫ 32 ϩ 3x ϭ Ϫ415 ϩ x2 ϩ 3 n 5
4
b. Ϫ 2 ϭ 2 Ϫ Ϫ n
5
3
15
8. 5x1x Ϫ 102 1x ϩ 12 ϭ 0
9. x2 Ϫ 18x ϩ 77 ϭ 0
17. a. 12v Ϫ 3 ϩ 3 ϭ v
3
3
b. 2 x2 Ϫ 9 ϩ 1 x Ϫ 11 ϭ 0
c. 1x ϩ 7 Ϫ 12x ϭ 1
75
18. The local Lion’s Club rents out two banquet halls for large meetings and other events. The records show that when they charge $250 per day for use of the halls, there are an average of 156 bookings per year.
For every increase of $20 per day, there will be three less bookings. (a) What price per day will bring in
$61,950 for the year? (b) How many bookings will there be at the price from part (a)?
19. The Jefferson College basketball team has two guards who are 6¿3– tall and two forwards who are
6¿7– tall. How tall must their center be to ensure the
“starting five” will have an average height of at least
6¿6–?
20. The volume of an inflatable hot-air balloon can be approximated using the formulas for a hemisphere and a cone: V ϭ 2r3 ϩ 1r2h. Assume the conical
3
3 portion has height h ϭ 24 ft. During inflation, what is the radius of the balloon at the moment the volume of air is numerically equal to 126 times this radius?
10. 3x2 Ϫ 10 ϭ 5 Ϫ x ϩ x2
11. 4x2 Ϫ 5 ϭ 19
12. 31x ϩ 52 2 Ϫ 3 ϭ 30
13. 25x2 ϩ 16 ϭ 40x
14. 3x2 Ϫ 7x ϩ 3 ϭ 0
15. 2x4 Ϫ 50 ϭ 0 x 1
2
1-75
Practice Test
MIXED REVIEW
1. Find the allowable values for each expression. Write your response in interval notation.
10
Ϫ5
a.
b.
3x ϩ 4
1x Ϫ 8
2. Perform the operations indicated.
a. 1Ϫ18 ϩ 1Ϫ50
b. 11 Ϫ 2i2 2
3i
c.
d. 12 ϩ i132 12 Ϫ i132
1ϩi
3. Solve each equation or inequality.
a. Ϫ2x3 ϩ 4x2 ϭ 50x Ϫ 100
b. Ϫ3x4 Ϫ 375x ϭ 0 c. Ϫ2Ϳ3x ϩ 1Ϳ ϭ Ϫ12
4
x
d. Ϫ3 ` Ϫ 5 ` Յ Ϫ12 e. v3 ϭ 81
3
1
f. Ϫ21x ϩ 12 4 ϭ Ϫ6
Solve for the variable indicated.
2
1
4. V ϭ r2h ϩ r3; for h 5. 3x ϩ 4y ϭ Ϫ12; for y
3
3
Solve as indicated, using the method of your choice.
6. a. Ϫ20 Յ 4x ϩ 8 6 56
b. Ϫ2x ϩ 7 Յ 12 and 3 Ϫ 4x 7 Ϫ5
7. a. 5x Ϫ 12x Ϫ 32 ϩ 3x ϭ Ϫ415 ϩ x2 ϩ 3 n 5
4
b. Ϫ 2 ϭ 2 Ϫ Ϫ n
5
3
15
8. 5x1x Ϫ 102 1x ϩ 12 ϭ 0
9. x2 Ϫ 18x ϩ 77 ϭ 0
17. a. 12v Ϫ 3 ϩ 3 ϭ v
3
3
b. 2 x2 Ϫ 9 ϩ 1 x Ϫ 11 ϭ 0
c. 1x ϩ 7 Ϫ 12x ϭ 1
75
18. The local Lion’s Club rents out two banquet halls for large meetings and other events. The records show that when they charge $250 per day for use of the halls, there are an average of 156 bookings per year.
For every increase of $20 per day, there will be three less bookings. (a) What price per day will bring in
$61,950 for the year? (b) How many bookings will there be at the price from part (a)?
19. The Jefferson College basketball team has two guards who are 6¿3– tall and two forwards who are
6¿7– tall. How tall must their center be to ensure the
“starting five” will have an average height of at least
6¿6–?
20. The volume of an inflatable hot-air balloon can be approximated using the formulas for a hemisphere and a cone: V ϭ 2r3 ϩ 1r2h. Assume the conical
3
3 portion has height h ϭ 24 ft. During inflation, what is the radius of the balloon at the moment the volume of air is numerically equal to 126 times this radius?
10. 3x2 Ϫ 10 ϭ 5 Ϫ x ϩ x2
11. 4x2 Ϫ 5 ϭ 19
12. 31x ϩ 52 2 Ϫ 3 ϭ 30
13. 25x2 ϩ 16 ϭ 40x
14. 3x2 Ϫ 7x ϩ 3 ϭ 0
15. 2x4 Ϫ 50 ϭ 0 x 1
2