1.1 Real Numbers
1. State the property of real numbers being used
(a) Commutative Property for addition
(b) Commutative Property for multiplication
(c) Associative Property for addition
(d) Associative Property for multiplication
(e) Distributive Property
Answer: (a)
2. State the property of real numbers being used.
(a) Commutative Property for addition
(b) Commutative Property for multiplication
(c) Associative Property for addition
(d) Associative Property for multiplication
(e) Distributive Property
Answer: (e)
3. State the property of real numbers being used.
(a) Commutative Property for addition
(b) Commutative Property for multiplication
(c) Associative Property for addition
(d) Associative Property for multiplication
(e) Distributive Property
Answer: (b)
4. Use properties of real numbers to write without parentheses.
1 FUNDAMENTALS
[1]
(a) (b) (c) (d) (e) Answer: (d)
of
12/4 z
parentheses. (a) (b) (c) (d) (e) Answer: (e)
properties of
parentheses. (a) (b) (c) (d) (e) Answer: (d) 44 xx 25210 xyxy 33 xyyx 3(2) ab 66ab 32ab 6ab 63ab 63ab 1 4 z 1 12 z 48z 12z 3z (2)rs 22rs 2 rs 2 rsr 2 rsr 2 rsr Precalculus Mathematics for Calculus 6th Edition Stewart Test Bank Full Download: http://testbanktip.com/download/precalculus-mathematics-for-calculus-6th-edition-stewart-test-bank/ Download all pages and all chapters at: TestBankTip.com
5. Use properties
real numbers to write
without
6. Use
real numbers to write without
1 FUNDAMENTALS
7. Use the properties of real numbers to write the expression without parentheses.
8. Perform the indicated operation.
9. Perform the indicated operation.
[2]
1.1 Real Numbers
(a) (b) (c) (d) (e) Answer: (d)
(a)
Answer: (d)
(b) (c) (d) (e)
(a) (b) (c) (d) (e) Answer: (e)
21 32 13 105 Answer: 5/3
Perform the indicated operations. 21 52 13 105 Answer: 9/7 22 2 d xabc 2 xaxbxcxd 224 xaxbxcxd 24 xaxbxcxd 224xaxbxcxd 222 xaxbxcxd 11 412 1 16 1 48 1 4 1 3 3 12 63 1 2 2 18 1 18 1 3 1 4
10. Perform the indicated operations.
11.
1 FUNDAMENTALS
1.1 Real Numbers
12. Perform the indicated operations.
Answer: 2
13. Perform the indicated operations.
Answer: 3/4
14. Perform the indicated operation(s) and simplify.
Answer: (d)
15. Perform the indicated operation(s) and simplify.
(c) (d) (e)
Answer: (e)
16. State whether the inequality is true or false. Answer: True
17. State whether the inequality is true or false.
[3]
1 12 11 812
1 10 11 35
(a) (b) (c) (d) (e)
(a)
(b)
11 10100
1113 5 4454 3 4 3 4 1 25 1 4 1 4 1111 5423 3 2 25 24 1 2 3 24 25 21.41
Answer: False
18. State whether the inequality is true or false. Answer: True
19. Write the following statement in terms of inequalities. is negative.
(b) (c) (d) (e) Answer: (b)
20. Write the following statement in terms of inequalities. is greater than or equal to
21. Write the statement in terms of inequalities. The distance from x to 3 is at most .
22. Find the set AB
if and
23. Find the set ABC
if and and
[4]
1 FUNDAMENTALS 1.1 Real Numbers
(a)
(a)
(b) (c) (d) (e) Answer: (b)
(a) (b) (c) (d) (e) Answer: (a)
(a) (b) (c) (d) (e) Answer: (a)
. (a) (b) (c) (d) (e) Answer: (e) 22 7 x 0 x 0 x 0 x 0 x 0 x z 1 1 z 1 z 1 z 1 z 0 z 6 36 x 36 x 36 x 63 x 63 x 12 33 3,2,0,,,6,9 A 12 33 0,,. B 12 330,2,3,6,9,, 12 330,2,3,6,9,, 12 330,2,3,6,9,, 0,2,3,6,9 2 3 0,2,3,6,9, 0 A 1,2 B 1,0,1,2 C 0,2 1,2 1,2 1,0,1,2 0,1,2
1 FUNDAMENTALS 1.1 Real Numbers [5] 24. Find AC if and (a) (b) (c) (d) (e) Answer: (a) 25. Find if and . (a) (b) (c) (d) (e) Answer: (b) 26. Evaluate the expression. Answer: 27. Evaluate the expression. Answer: 28. Evaluate the expression Answer: 29. Find the distance between 1/15 and 3/25 . Answer: |4Axx |26Cxx |24xx |26xx |46xx |26xx AB | Axx |1 Bxx |1 and xxx |1 xx |1xx | xx 233 23323344 22 222244 2552 5225 255227 11 522527 1344 15257575
1 FUNDAMENTALS
1.1 Real Numbers
30. Find the distance between and . 1
Answer:
31. Express the repeating decimal as a fraction. 0.8 Answer: 8/9
32. Express the repeating decimal as a fraction. Answer:
33. Express the repeating decimal as a fraction.
[6]
1.135 Answer:
111 2.45 27 2.45 11
562/495
1 FUNDAMENTALS
1.2
Exponents and Radicals [7] 1. Evaluate 32 (a) 16 (b) 8 (c) 4 (d) 8 (e) 16 Answer: (b) 33 2(2)8
Evaluate the expression. 3 4 (a) 1 256 (b) 1 64 (c) 1 64 (d) 1 256 (e) 1 512 Answer: (c) 3 3 11 4 64 4 3. Evaluate 2 2 3 (a) 9 4 (b) 4 9 (c) 9 4 (d) 1 4 (e) 1 Answer: (a) 2 9 2 34 4. Evaluate 2 36 9 (a) 9 2 (b) 2 9 (c) 3 4 (d) 1 4 (e) 1 12 Answer: (d) 2 36 1 94 5. Evaluate 1124 42 (a) 1 64 (b) 1 256 (c) 64 (d) 1 4 (e) 256 Answer: (e) 1124 42 256 6. Evaluate each expression. (a) 0 1 7 2 3 (b) 3 0 3 4 (c) 2 1 5 Answer: (a) 0 1 71 2 32 (b) 3 0 31 27 4 (c) 2 1 25 5
2.
7. Evaluate each expression.
Exponents and Radicals [8]
1 FUNDAMENTALS 1.2
(a) 0 1 5 3 3 (b) 3 0 3 5 (c) 2 1 3 Answer: (a) 0 1 51 3 33 (b) 3 0 31 27 5 (c) 2 1 9 3 8. Evaluate 1 9 512 (a) 1 4 (b) 1 2 (c) 16 (d) 1 16 (e) 256 Answer: (b) 1/9 11 9 5122 512 9. Evaluate 0.2 32 (a) 2 (b) 1 2 (c) 16 (d) 1 4 (e) 1 1024 Answer: (b) 5 0.21/5 11 2 32 3232
2748
(a) 21 (b) 1 (c) 43 (d) 33 (e) 3 Answer: (e) 274833433 11. Simplify 1/31/3 2/3 xy xy and eliminate any negative exponents. (a) xy (b) 2/3 xy (c) 1/3 xy (d) y (e) 1/3 xy Answer: (a) 1/3 1/31/3 1/32/3 2/32/3 xy xy xyxy xyxy 12. Simplify 2/5 255 xyz and eliminate any negative exponents. (a) 2 5 2 y zx (b) 2 4 2 5 y zx (c) 4 2 4 y zx (d) 2 2 y zx (e) 4 2 5 y zx Answer: (b) 2 2/5 2554/522 4 2 5 y xyzxyz zx
10. Simplify the expression
.
15. Simplify the expression 33
16. Simplify the expression. Assume the letters denote any real numbers.
17. Simplify the expression. Assume the letters denote any real numbers.
Answer: 55672
18. Simplify the expression. Assume the letters denote any real numbers.
Answer: 6633366abab
FUNDAMENTALS 1.2 Exponents and Radicals [9]
Simplify 1 2 32 4 2ab abc c and eliminate any negative exponents. (a) 26bc (b) 62 2 2 bc a (c) 26 2 3 bc a (d) 26 2 bc a (e) 26 2bc Answer: (d) 1 2426 3232 42 2 2 2 abcbc abcabc a cab
Simplify 2 2 3 3421 abcabbc and eliminate any negative exponents. Answer: 2 2 2 68346 2 3 3421 433268 34 3 11 abcabc abcabbc b ccab ab ab c
1
13.
14.
Answer: 3 33 3 3 64644 yz yzyz
3 64 yz
44 4 xy
44 4 xyxy
Answer:
5 67 uv
uvuvuv
66 36
ab
1 FUNDAMENTALS
1.2 Exponents and Radicals
19. Simplify the expression. Assume the letters denote any real numbers. 66 3 64xy
Answer: 66 3 642xyxy
20. Simplify the expression and eliminate any negative exponents(s). Assume that all letters denote positive numbers.
21. Simplify the expression and eliminate any negative exponents(s). Assume that all letters denote positive numbers.
33242 64 rsrs
Answer: 2 4rs
22. Simplify the expression and eliminate any negative exponents(s). Assume that all letters denote positive numbers.
33242 81 rsrs
Answer: 2 3 33 rs
23. Write 0.000101010 in scientific notation.
Answer: 4 0.0001010101.010110
24. Write 1,010,100,000,000 in scientific notation.
Answer: 121,010,100,000,0001.010110
25. Write the number in the statement in scientific notation:
The mass of a proton is 0.0000000000000000000000000016726231 kg.
Answer: 27 0.00000000000000000000000000167262311.672610
kg
26. Write the number in the statement in scientific notation. The distance to the edge of the observable universe is about 100,000,000,000,000,000,000,000,000m.
Answer: 100,000,000,000,000,000,000,000,000 26110 m
[10]
3 uu Answer: 1/31/31/3 3 2/21/23/21/2 uuuuuuuuu
27. Use scientific notation, laws of exponents, and a calculator to perform the indicated operations. State your answer correct to the number of significant digits indicated by the data.
1610 (4.0110)(8.1110)
28. A sealed warehouse measuring 12 m wide, 18 m long and 6 m high, is filled with pure oxygen. One cubic meter contains 1000 L, and 22.4 L of any gas contains 236.0210 molecules. How many molecules of oxygen are there in the room?
29. Which of the numbers 10 0.001 and 10
is smaller?
30. Which of the numbers
31. Rationalize the denominator.
32. Rationalize the denominator.
1 FUNDAMENTALS
[11]
1.2 Exponents and Radicals
Answer: 1610161027 (4.0110)(8.1110)4.018.11103.2510
Answer: Volume 1218610001 ,296,000 L 2328 1,296,000 6.02103.48310 22.4 molecules
Answer: 10 0.01
3 2 1010 101000 0.01 10 , whereas 4 3 1010 1010 0.001 10 ,000
0.01
is smaller because
1 10 0.001 and 2 10 0.01 is larger? Answer: 2 10 0.01 is larger because 2 6 101 10 0.011,000,000 , 1 4 101 10 0.00110,000 .
6 x Answer:
6 66 xx
3/7 1 s Answer: 3/7 7 4 1 s s s
1.3 Algebraic Expressions
1. Perform the indicated operations and simplify. 3(34)5(1) xx
(a) 413 x (b) 213 x (c) 47 x (d) 213 x
Answer: (c) 3(34)5(1)9125547 xxxxx
2. Perform the indicated operations and simplify.
(a) 32 2635 xxx
(b) 32 26312 xxx
(c) 32 2631 xxx
(d) 32634xxx
(e) 32634xxx
(e) 229 x
32332 264834634
3. Find the sum, difference, or product. 24 2(25)(1)(1) tttt Answer: 243242(25)(1)(1)310tttttttt
4. Find the sum, difference, or product.
2(25)(2)(1) tttt Answer: 243242(25)(2)(1)3102tttttttt
5. Multiply the algebraic expressions using the FOIL method and simplify.
xyxy
Answer: 22(45)(24)82620 xyxyxxyy
6. Multiply the algebraic expressions using a Special Product Formula and simplify.
Answer: 2 223492416 xyxxyy
1 FUNDAMENTALS
[12]
323 264834 xxxxx
Answer:
xxxxxxxx
(e)
24
(45)(24)
2 34xy
1 FUNDAMENTALS
1.3 Algebraic Expressions
7. Multiply the algebraic expressions using a Special Product Formula and simplify.
2 222542025 xyxxyy
Answer: 2 222542025 xyxxyy
8. Multiply the algebraic expressions using a Special Product Formula and simplify.
33yy
Answer: 333yyy
9. Multiply the algebraic expressions using a Special Product Formula and simplify.
55yy
Answer: 55 5 yyy
10. Perform the indicated operations and simplify.
2222 axyaxy
axyaxyaxy
11. Perform the indicated operations and simplify.
22222 xbyxcxyay
(a) 43222222324 xcxyaxybyxbcyxaby
(b) 43222324 xxcyxaybycxbya
(c) 23222324 xxyxaybycxaby
(d) 24224 axaxyy
(e) 4322324 xcxyaxycyxaby
Answer: (a) 2222243222222324 xbyxcxyayxcxyaxybyxbcyxaby
[13]
(a) 222 axy (b) 24224 axaxyy (c) 244 axy (d) 24224 axaxyy (e) 244 axy
(c)
Answer:
2222244
1 FUNDAMENTALS
1.3 Algebraic Expressions
12. Perform the indicated operations and simplify. 3 2 1
13. Perform the indicated operations and simplify.
14. Perform the indicated operations and simplify.
[14]
x y
(a) 2 3 246 331 xx x yyy
(b) 2 3 226 31 xx x yyy
yy
Answer: (a) 3 2 3 2246 1331 xx xx yyyy
(c) 22 3 43 333 xx x y
(d) 2 3 6 31 x x y y
(e) 3 6 1 x y
2/31/312xx (a) 3 3322xxx (b) 2 33 1 xxx (c) 2 33 2 xxx (d) 2 3322xxx
Answer: (d) 2 2/31/3 331222xxxxx
(e)
2 3322xx
(3)(21)3(2) ttt (a) 2 264 tt (b) 2 229 tt (c) 2 2210 tt (d) 2 235 tt (e) 2 254 tt Answer: (b) 22 (3)(21)3(2)26336229 ttttttttt
1 FUNDAMENTALS
1.3 Algebraic Expressions
15. Perform the indicated operations and simplify.
(2)(2) uvuv
16. Factor the expression.
22 2 yxyx
(a) 22 xxyyx
(b) 2xyxy
(c) 2xyxy
(d) 2xyxy
(e) 22xyxy
Answer: (b) 2222 yxyxxyxy
17. Factor the expression.
2 6136 xx
(a) 2 23 x
(b) 362xx
(c) 2136 xx
(d) 616 xx
(e) 2332 xx
Answer: (e) 2 61362332 xxxx
18. Factor the expression.
1 xnyxyn
(a) xny
(b) 1 xxyn
(c) ny
(d) xy
(e) xy
Answer: (c) 1 xnyxynny
[15]
(c) 22164uv (d) 22162uv (e) 22164uv
(a) 22 4uv (b) 2284uv
Answer: (a) 2222(2)(2)4224 uvuvuuvuvvuv
1 FUNDAMENTALS
1.3 Algebraic Expressions
19. Factor the expression.
2332 55xxxx (a)
(b)
(c)
(d)
2 255xxx
2 2 255xxx
22255xxx
2 5525xxx
(e)
2 2 255xxx
20. Factor the expression.
21. Factor the expression.
2 815(3)(5)xxxx
22. Factor the expression.
23.
[16]
Answer: (e) 232322
55255 xxxxxxx
2
(a) (4)(2) xx (b) 42xx (c) (8)(1) xx (d) (8)(1) xx (e) (4)(2) xx Answer: (d) 2
78xx
78(8)(1)xxxx
2 815xx (a) (3)(5) xx (b) (3)(5) xx (c) (3)(5) xx (d) (3)(5) xx (e) 35xx Answer:
(a)
32
(a) 3 2 x (b) 3 8 x (c) 3 2 x (d) 2 2224 xxx (e) 2 24 x Answer: (a) 3
6128xxx
3261282xxxx
Answer: 322
Factor the expression completely. 32 263 xxx
263321 xxxxx
1 FUNDAMENTALS
1.3 Algebraic Expressions
24. Factor the expression completely.
32 2105 xxx Answer:
322 2105521 xxxxx
25. Factor out the common factor. 423414721 xyxyx Answer:
42343233 14721723 xyxyxxxyyx
26. Use a Factoring Formula to factor the expression.
2 165649 xx Answer:
2 2 16564947 xxx
27. Use a Factoring Formula to factor the expression.
33125216 st
2256253036 stsstt
28. Factor the expression. 22 64sy
29. Factor the expression. 22254sr
22 2545252 srsrsr
30. Factor the expression.
3 641 x
32 641411641 xxxx
[17]
Answer:
Answer:
22 6488sysysy
Answer:
Answer:
1.3 Algebraic
31. Factor the expression completely.
2221251xxx
32. Factor the expression completely.
2224164xxx
33. Factor the expression. 222510 yxxyyy
35. Factor the expression completely. Begin by factoring out the lowest power of each common factor.
1112 xxxx
1 FUNDAMENTALS
[18]
Expressions
Answer:
22212511155 xxxxxxx
Answer: 222
xxxxxxx
41642244
(a) 215xyyx (b) 2 155yyx (c) 215yyx (d) 251yyx (e) 2 15yx Answer: (c) 22
7/23/2
xx (a) 2 213xxx (b) 213xxx (c) 3/2 213xxx (d) 1/2 213xxx (e) 3/2 213xxx Answer: (e) 3/2 213xxx
2510215 yxxyyyyyx
34. Factor the expression.
22
5/23/2
xx Answer:
11
5/23/23/2
36.
1.3
37. Factor the expression.
1 FUNDAMENTALS
Algebraic Expressions [19]
2 22115150nn (a) 2332nnnn (b) 2 233nnn (c) 2 133nnn (d) 112nnn (e) 4 2 n Answer: (a) 2 221151502332 nnnnnn
Factor the expression.
1132 22xxyx Answer: 32 1111 2 2 22 2 2 xx x yx xxy
1.4
1 FUNDAMENTALS
Fractional Expressions [20]
Simplify the expression. 2 2 2 23 xx xx (a) 1 2 x x (b) 2 3 x x (c) 3 2 x x (d) 3 2 x x (e) 2 2 x x Answer: (b) 2 2 2(1)(2)2 (1)(3)3 23 xxxxx xxx xx
Simplify the expression 2 2 25 2430 y yy (a) 23 5 y y (b) 6 25 y y (c) 6 26 y y (d) 5 26 y y (e) 3 6 y y Answer: (d) 2 2 25(5)(5)5 (5)(26)26 2430 yyyy yyy yy 3. Simplify the expression. 2 3 1 1 x xx (a) 2 1 1 x xx (b) 2 1 1 x xx (c) 2 1 21 x xx (d) 2 1 1 x xx (e) 2 1 1 x xx Answer: (a) 2 322 1(1)(1)1 1(1)(1)1 xxxx xxxxxxx 4. Simplify the expression. 22 22 6 223 xxxx xxxx (a) 2 2 x x (b) 2 x x (c) 1 (d) x (e) 2 x Answer: (c) 22 22 6(2)(3)(1) 1 (2)(3)(1) 223 xxxxxxxx xxxx xxxx Precalculus Mathematics for Calculus 6th Edition Stewart Test Bank Full Download: http://testbanktip.com/download/precalculus-mathematics-for-calculus-6th-edition-stewart-test-bank/ Download all pages and all chapters at: TestBankTip.com
1.
2.
