Download BM1 ( Intermediate Algebra) Part 1

United Arab Emirates University
University General Requirements Unit
Mathematics Department
Chapters: 1 and 2
Basic Math 1
Instructor: M. Zalzali
Student’s name:
Student’s ID:
Date: 7 / 11 / 2010
Section:
Midterm Revision
BM1
Chapters
1 and 2
Multiple Choice
Questions
1
Chapter 1: The Real Numbers
Circle the correct answer.
1. Evaluate
− 5 2 − (− 13)
42 − 5 * 2
a) 25
2. Evaluate
b) – 2
− − 8 +
a) 6
(−
3 − − 5
a) -20
4.
–
d) undefined
c) 0
d) – 10
)
b) - 6
3. The additive inverse ( opposite ) of
c) 0
0.05 is
b) 20
c) 0.05
d) 2
The reciprocal ( multiplicative inverse ) of
- 0.125
a) 0.8
b) 8
c)
b) 6
c) 8
d) 16
b) 1
c) undefined
d) 9
is
–8
d) – 0.8
5. Evaluate
a) 4
6. Evaluate
4
− 9 − (−9)
a) 0
7.
3 – 4 [ 6( 3 – 10) – 9]
a) 207
b) – 3
c) 204
d) 177
a) 34
b) -12
c) 20
d) 25
8.
For question 9-13 , state the property that satisfies the equation
9. 0 + 4 = 4
a) Distributive property
b) Additive identity
c) Multiplicative identity
d) Commutative property of addition
2
10.
−2 5
•
=1
5 −2
a) Multiplication inverse
b) Additive identity
c) Multiplicative identity
d) Commutative property of addition
11. 3(2 x − 5) = 6 x − 15
a) Distributive property
b) Additive identity
c) Multiplicative identity
d) Commutative property of addition
12. 3 x + ( 2 x + 6) = (3 x + 2 x) + 6
a) Distributive property
b) Additive identity
c) Associative property of addition
d) Commutative property of addition
13. 12 + ( −12) = 0
a) Distributive property
b) Additive identity
c) Multiplicative identity
d) Additive inverse
14. On November 23, the temperature in Siberia is − 13 o C and in Al Ain is 25 o C . How much warmer
was it in Al Ain?
a) 10
b) 38
15. Evaluate the arithmetic expression
a) 3
b) 14
(
16. 3 x 5 y − 4 z 2
)
0
(
a) 0.5
)
−1
d) 26
(36 − 4) ÷ 8 + 5 − 2(− 3) − − 5
c) – 8
d) 4
=
a) 1
17. 4 −1 + 4 −1
c) 24
b) – 1
c) 3 x 5 y −4 z 2
d) 4
b) 2
c) – 4
d) 4
=
3
(
)(
)
18. − 2 x 4 3 xy −2 =
a) − x 4 y −2
b) − 6 x 5 y 2
c)
− 6x5
y2
d) 1
19. Given a = −1, b = −5, c = 4 . Evaluate b 2 − 4ac
a) – 11
b) 31
c) – 4
d) 41
20. Simplify the algebraic expression 5 − 3(2 x − 5) + 2 x(3 x − 5)
a) 6 x 2 + 16 x − 20
21. If
b) 6 x 2 − 16 x + 20
, then
22. The value of
d) 6 x 2 − 16 x − 20
is equal to:
b) 2
a) 6
c) 6 x 2 − 4 x − 5
c) -2
d) 4
equals:
a)
b)
c) –
d)
a)
b) undefined
c) 1
d)
23.
24. The expression
is not a real number when
a) -1
b) 0
c) 1
d) -2
25. The standard notation of the real number 2.36 × 10 −5 is
a) 236000
b) 0.00236
c) 0.000236
d) 0.0000236
26. The scientific notation of the real number 542600000 is
a) 5.426 × 10 3
(
27. − 3a 5 b − 2
a)
) (2a b )
2
− 72a 19
b
3
3
b) 5.426 × 10 8
c) 5.426
b) 27 a 13b
c)
d) 54.26 × 10 7
=
72a 19
b
d)
b
72a 19
4
Chapter 2: Linear Equations and Inequalities in One
Variable
28. Find x: 5 − 3( x − 4 ) = −2 x + 14
a) – 3
29. Find y:
a) – 2
b) 3
y y − 4 23
−
=
2
5
10
b) 2
c) – 7
d) 7
c) – 5
d) 5
30. Find (n + 1) if n + (n + 1) + (n + 2) = 39
a) 12
b) 13
c) 14
d) 15
31. Find m: 0.52m − 0.07( m + 200) = 0.03m + 28
a) 42
b) 100
c) 1000
d) 4200
32. The linear equation 3( x − 2) + x + 5 = 4 x + 1 is
a) conditional
b) inconsistent
c) identity
d) none
33. The linear equation 3( x − 2) + x + 5 = 4 x − 1 is
a) conditional
34. Solve for x:
a) – 6
b) inconsistent
d) none
c) – 8
d) 5
x − 1 4x − 2 1
−
=
2
6
3
b) – 3
35. Find m so that the equation
a) – 2
c) identity
5 − 4mx + x = 9 x + 8 is inconsistent
b) 3
c) 9
d) 4
36. Find a so that the equation 5 − 4ax + x = 11x + 5 is an identity
a) – 2.5
b) 3.5
c) – 4.5
d) 6.5
37. Find the solution set in interval notation: 3 x − 2 < 4 x + 1
a) (−∞, − 3]
b) (−∞, − 3)
c) ( −3, 3]
d) ( −3, + ∞)
5
38. Find the solution set in interval notation:
10

b)  , + ∞ 
3


10 

a)  − ∞, 
3

6x − 5
≤ −5
−3
c) (−10, 3]
d) ( −5, + ∞)
39. Find the compound inequality that corresponds to the graph below
–2
a)
b)
c)
d)
4
x > 4 and x < −2
x > 4 or x < −2
x ≥ 4 or x < −2
x > 4 and x > −2
40. Find the compound inequality that corresponds to the graph below
-3
a)
b)
c)
d)
5
x > 5 and x < −3
x ≥ −3 and x < 5
x ≥ −3 or x < 5
x ≥ −3 and x > 5
41. Find the compound inequality that corresponds to the graph below
-3
a) − 3 ≤
b) − 3 <
c) − 3 <
d) − 3 ≤
x
x
x
x
≤
<
≤
<
5
5
5
5
5
42. Find the solution in interval notation that corresponds to the graph below
-7
a)
b)
c)
d)
3
(− ∞, − 7 ) U (3, + ∞ )
(− ∞, − 7 ) U [3, + ∞ )
(− 7, 3]
(− ∞, + ∞ )
6
43. Which value is not in the solution set for the inequality 3 x − 1 < 11 ?
a) 2.5
b) 3
c) 3.5
d) 6
44. Which value is not in the solution set for the inequality − 2 x + 5 ≤ 11 ?
a) –3
b) –5
c) – 1
d) – 2
45. The length of a rectangle is twice its width. If the perimeter is 60 m. Find its length.
a) 10 m
b) 20 m
c) 30 m
d) 40 m
46. The length of a rectangle is 3 meters more than its width. If the perimeter is 58 m. Find its length.
a) 13 m
b) 14 m
c) 17 m
d) 16 m
47. The length of a rectangle is 4 meters less than twice the width. If the perimeter is 58 m. Find its
length.
a) 11 m
b) 18 m
c) 17 m
d) 34 m
For Questions 48-50. Motion Problem: Hussein walked for one hour and biked for 2 hours. He bikes 4
times faster than he walks. If the total distance is 36 miles.
48. Find the speed of his bike?
a) 4 mph
b) 8 mph
c) 16 mph
d) 14 mph
c) 16 miles
d) 14 miles
c) 16 miles
d) 32 miles
49. Find the distance he walked?
a) 4 miles
b) 8 miles
50. Find the distance he biked?
a) 4 miles
b) 8 miles
7
Choose the correct answer for each of the following questions.
51. The……………… of 9 and 3 is equal to 3. .
a. addition
d. quotient
c. difference
b. product
52. The………………….. of −17 is 17.
d. absolute value
c. square
b. exponent
a. square root
b. −12
a. 12
c. 0
b. 5
a. 3
55. The scientific notation of 0.0001008 is
d. 1.008 × 10 −3
c. 1.008 × 10 −4
b. 1.8 × 10 −4
53. The result of −9 subtracted from 3 is equal to
d. −6
c. 6
54. The expression 3 ÷ (k − 5) is not a real number when k =
d. −5
a. 1.8 × 10 6
56. The multiplicative inverse of 0.125 is …………
d. 100
(
c. – 1000
b.
1
0.125
a. 0.125
b. 3x 6
a. − 40x 8
)( )
57. − 5 x 2 8 x 4 =
d. − 40x 6
c. − 40x 9
58. The additive inverse of – 1.25 is ………..
a. –1.25
59.
− 52 − 3
2 − (− 3)
2
b. 1.25
c.
−1
1.25
1
d. 1.25
=
a. 4
b. – 4
c. 5
d. –5
60. Simplify the algebraic expression 3 − 2( 4 x − 5 y ) + 8 x − 7 =
a. 10 y − 3 x − 4
b. − 10 y + 8 x − 4
c. 10 y + 3 x − 4
d. 10 y − 4
8
Choose the correct answer for each of the following questions.
61.
(− 2 x
3
y −2
10 x 6 y
)
2
d.
−4
5 xy 5
c.
4x 6
5y5
b.
2
5y5
a.
−2
5y5
4 x − 3( x − 5) + 2 = 0 is ………….
62. The equation
d. None of the others
c. identity b. inconsistent
a. conditional
63. Find m so that the equation 3x − 5( x + 1) = (2m + 4)x − 8 is inconsistent
d. −3
c. 3
b. −4
a.
−1
7
64. The solution of the equation 0.08 x − 0.01( x + 200 ) = 5
d. x = 100
b. x = –7
a. x = 7
b. − 18xz 3
a. 18xz 3
66. Find m and n so that the equation 2mx + 3 = −6 x + n + 1 is an identity
d. m = −3, n = 2
c. m = 2, n = −3
b. m = −2, n = −3
a. m = 2, n = −3
(
65. − 3 x 5 y 2 z −1
) (2 x
2
−9
c. x = –100
)
y − 4 z −1 =
18 x
d. − 3
z
c.
18 x
z3
9
(
67. − 5 x 2
) (20 x ) =
−1
7
d. 1000x 6
c. − 4x 5
b. − 100 x 5
a. − 4 x −14
68. The length of a rectangle is 9 meters more than its width. If the perimeter of the rectangle is 58 meters.
What is its length?
b. Length = 12 m
b. Length = 10 m
c. Length = 19 m
d. Length = 91 m
69. Ahmad drove for 5 hours before lunch. After lunch he drove 4 more hours and averaged 20 mph more than
before lunch. If his total distance was 890 miles, then what was his average speed after lunch?
b. 90 mph
70. The solution to the equation
a.
t = 5
b. 110 mph
c. 24 mph
d. 15 mph
t +1 t −1
−
=t +5
4
6
b.
t = 4
c.
t = −5
d.
t = −4
10