Table Of ContentTEST BANK
for
PRECALCULUS: FUNCTIONS & GRAPHS
Bernard Kolman & Arnold Shapiro
by
MICHAEL L. LEVITAN
Villanova University
Academic Press, Inc.
(Harcourt Brace Jovanovich, Publishers)
Orlando San Diego San Francisco New York London
Toronto Montreal Sydney Toyko Säo Paulo
Copyright © 1984 by Academic Press, Inc.
All rights reserved.
No part of this publication may be reproduced
or transmitted in any form or by any means,
electronic or mechanical, including photocopy,
recording, or any information storage and retrie
val system, without permission in writing from
the publisher.
Academic Press, Inc.
Orlando, Florida 32887
United Kingdom Edition Published by
Academic Press, Inc. (London) Ltd.
24/28 Oval Road, London NW1 7DX
ISBN: 0-12-417896-0
Printed in the United States of America
This book is dedicated to my parents ... who
made it possible ... to my children, Eric and
Cheryl ... who made it necessary ... and
finally to my Australian friends (now more
insufferable than ever with the America's Cup
temporarily residing in Perth) ... who
taught me a foreign language.
CHAPTER TEST 1A
1. Write explicitly the elements of the set of all integers
73 such that -2 < n £ 3.
2. On the real number line, draw the graph of the set of
real numbers x satisfying -2 < x £ 3.
In Problems 3-5 evaluate the following:
3. '* " y* when x = -3 and y = 2
4. 4 - 52 + 7(3 + 1)
I 1
5 ^JU
5 6
In Problems 6-7 perform the indicated operations and simplify:
6. (x - 4x2 + 3) - (2 - 5x + 8x2)
7. (x - 3y) (y - 3x)
In Problems 8-9 factor completely using only integer coefficients.
8. 4x3 - 9*
9. 16(y + 1) - x2(y + 1)3
In Problems 10-13 simplify:
sL·• 6y - 7 Λ Iy72 -Ja JiL
10. ■ 2y - 8 16
y2-
3 5
11. 2x + 1 x - "5
2
3 +
12. X
2_ _
2
X
13. Write the following as the ratio of two polynomials:
4(x + 1)2 - 3x~2
In Problems 14 - 15 simplify:
14. 8 /3
»· Φ*
16. Rationalize the denominator:
5
1
CHAPTER TEST 1A
17. Simplify and combine:
/TF + Λ8" - 2 V§T
18. Write the following in the form a + bi:
(3 + li) (2 - i)
19. Find the values of x satisfying the inequality
2x + 3 < 5
and draw the solution set on the real line.
20. Find the set of x such that:
x2 - 6x + 8 ^ 0
2
CHAPTER TEST 1B
1. Write explicitly the elements of the set of all integers
n such that n > 4.1 and x ^ 7.5.
2. On the real number line, draw the graph of the set of real
numbers x satisfying x > 4.1 and x ^ 7.5.
->
In Problems 3-5 evaluate the following:
3. \xy\ when x = 2 and y = -1
Ixl - M
4. 9 + 4(32 - 5)
5. ^ —i
1-i
In Problems 6-7 perform the indicated operations and simplify:
6. 2(3xy + 4t - 5) + 3(7 - xy + t)
7. (x2 + 2x + 3) Cx - 1]
In Problems 8-9 factor completely using only integer coefficients.
8. xk - 6x2 + 5
9. 3(3z + 6) - z2(z + 2)
In Problems 10-13 simplify:
a2 + 2ab + b2 a2 - 2?2
A
2a2 - a£ - b2 ' 2a2 + 3a2> + b2
2x . 4x + 1
n
x - 1 x + 1
12. 2Χ+Γ4Τ
i 3x
x - 1
13. Write the following as the ratio of two polynomials:
x2 - 5x~3 + Ar
3
CHAPTER TEST 1B
In Problems 14-15 simplify:
M "3/2
15. (8)
16. Rationalize the denominator:
Λ- 2
17. Simplify and combine:
-2/32 - /Ϊ8" + ι/ξδ"
18. Write the following in the form a + bi:
(4 - 7i) (2 + i)
19. Find the values of x satisfying the inequality
-3x + 2 > 1
and draw the solution set on the real line.
20. Find the set of x such that:
x2 - 8x + 15 < 0
4
CHAPTER TEST IC
1. Write explicitly the elements of the set of all positive
integers n such that n. ^ A.
2. On the real number line, draw the graph of the set of positive
numbers x satisfying x ^ A.
1 , >
In Problems 3-5 evaluate the following:
3. .lffc ~ 5l when s = 3 and t = 2
\s\ - |-A|
A. 7 v 4 + 9(52)
li - I
'5 10
In Problems 6-7 perform the indicated operations and simplify:
6. (9t - 5t2 + s - st) - (125 + st2 - i* - st + 9t)
s
7. (z + 1)2(2z + 3)
In Problems 8-9 factor completely using only integer coefficients.
8. 3x2 + Ax - 20
9. w2x2(y + 3) + 8t2(-6 - 2y)
In Problems 10-13 simplify:
m g2 " z " 6 · z2 * z " 2
lu# z* - 1 T z2 + Az + 3
11 * + 1 2(x - 1)
11 . , + r-
x - A 3 - x
1 1
12. x " x + 1
3 _ 1
x + 1 x
13. Write the following as the ratio of two polynomials:
5
CHAPTER TEST 1C
In Problems 14 - 15 simplify
14. (64) k
»· UP
16. Rationalize the denominator:
6
3/Γ+ 5
17. Simplify and combine:
21/3 + 2Va 2?/3
+
18. Write the following in the form a + bi:
(3 - i) (2 + i)
19. Find the values of x satisfying the inequality
5x - 1 * -2
and draw the solution set on the real line.
>
20. Find the set of x such that
x2 + 3x - 4 > 0
6
CHAPTER TEST 1D
1. Write explicitly the elements of the set of all natural
numbers n such that 1.4 < n < 3.8.
2. On the real number line, draw the graph of the set of real
numbers x such that 1.4 < x ^ 3.8.
>
In Problems 3-5 evaluate the following:
\st\ - \t\ _ 5
3# when s = 3 and t =
t\ t - s I
4. 6 - 4 T (2 + 2 · 3)
JL 1
5. 10 " 7
_L 1
14 + 5
In Problems 6-7 perform the indicated operations and simplify:
6. (x + 9x2 + 5x3 - 4) - 2(4 + 8x - 9y)
7. (-3w - 1) (-2* + 1)
In Problems 8-9 factor completely using only integer coefficients.
8. 2x2 - 3x - 9
9. 4x yz3 + 3yz x - yz
In Problems 10-13 simplify:
4z2 + 3z - 1 4z2 - z
A
z + 2z + 1 z - z - 2
11. 2 3x_
2x2 + 3x x + 1
A x
12. * + x2 - 1
7
