Download EXERCISES FROM OLD EXAMS FOR CHAPTER P

EXERCISES FROM OLD EXAMS FOR CHAPTER P
1) Factor y 4  64
 ( x  y ) 2 (2 z 4 ) 

2) Simplify t he expression 
3
 [ z ( x  y )] 
2
3) If a  3, then | 5  2a | is equal to ?
4) Conjugate of the complex number (6  3i)(3  i) 2 is
1
2
1
3 3
5) If x  y , then the expression ( x - 2 xy  y )  [( x  y) ] simplifies to
2
2
6) Simplify the expression 2[3(4a  b)  2(5a  3b)]  {5[3a  (b  4a)]  b}
7) The coefficient of x 2 y in the product (2 x  y) 2 ( x  y 
8) If A  Bi 
9)
3
23 2

3
3x
) is
y
 125  i 11   4  1
, then A and B are
i6
2 1
2
?
10) Simplify the expression
x  y x 1  y 1

x  y x 1  y 1
11) TRUE /FALSE For all real numbers a and b
3
a 3  b 3  a  b , a  b  a  b , 6 a12b 6  a 2 | b | , (a 1  b 1 ) 1  a  b , 4 a16b 4  a 4 b
12) One factor of 2  4 x  10 x 4  5 x 3 is?
13)
14)
2
3
54
3
4
16
3
16)
2
?
8  (2)( 4)  (10) 1.44
(32)
15)
1
3
3
5
?
64  5 0.00032  ?
p2
2 p 1
 2
?
3p  4p  4 3p  5p  2
2
17) Write the complex number Z 
i 19
in standard form
 2  3i
18) If Z1  x  4i , Z 2  5  2 yi and Z 2  3Z1  5 , then find x and y
19) Write the expression
 2x  2
without absolute value notation if 0  x  1 .
| x|| x2|
20) Rationalize the denominator of
20
3 5
and write it in the form A  B 5
21) Simplify the expression 3x3 8 x 3 y 4  4 y 3 64 x 6 y
22) Evaluate
5
0.00032
 ( x 2 y ) 1 (5 3 x 3 y  2 ) 2 
23) Simplify the expression  2
3
5  2 1 
 5 ( xy) ( x y ) 
24) Expand (2 x  3 y) 3

1
4
where x  0 and y  0
25) A square of side x cm is cut from a rectangle sheet of aluminum as shown below. Write the
remaining area of the shaded portion of the following figure in terms of x and y .
2y
y
x
x
26) Factor x 3  3x 2 y  3xy 2  y 3  ( x  y) 3
27) Factor 15 y  3x  10 y 2  2 xy
28) Find the number k for which the expression 36 x 2  kxy  100 y 2 is a perfect square.
3
2
1
29) Simplify the expression
4
3
x
1
2
1
x
 a 1b  ab 1 

30) Simplify the expression 
2
2
 a b 
31) Simplify the expression
1
n 2  3n n  3

n
n
32) Simplify the expression (  3  4)(  3  4)
33) Which one of the following statements is TRUE?
a)
b)
c)
d)
e)
The smallest odd composite number is 9
The set of irrational numbers is closed under addition
The sum of two composite numbers is a composite
a 2  a for all real numbers
(a  6)  2 y  (6  a)  2 y illustrates the associative property.
34) What is the decimal form of 5.62  10 4 ?
35) TRUE / FALSE
a)
b)
c)
d)
e)
The product of a complex number and its conjugate is a real number.
If m  0 then | m |  m
1 is the only integer that is not prime and not composite.
|  y | y for all real numbers
Every real number is either rational or irrational.
36) The distance between   and 3 is
 3
|   3 |
| 3|
 (  3)
37) TRUE / FALSE
3
 x3  x
16 x 2  4 x
(2 x) 2  2 x
3
64 x 3  4 | x |
38) i 50  i 51  i 52  ?
39) Do the multiplication and write it in the standard form. (3x  5)( 2 x 2  4 x  6)
|x
1
40) Given that 0  x  , write the expression
8
1
|
4
1
1
|x ||x |
8
8
without absolute value
notation.
 (2 y ) y (2 y ) 
41) Simplify t he expression 

 2 1  4
 (2 y ) y

1
0
3
1
2
42) Factor the polynomial 9 x 2  24 xy  16 y 2  100 z 2
2 3
43) Rationalize the denominator
2 3
44) Simplify  3x3 54 x 4  23 16 x 7
45) Simplify the expression
x
1
x3
 2
 2
2 x  1 2 x  7 x  4 x  x  12
46) Conjugate of the complex number
1
(2  i ) 2  8i
47) Which property of equality the following statement illustrates?
If 2x-y = z and z=13, then 2x-y = 13
1 
1
48) Find the coefficient of x y in the expression  x  y 
3 
2
2
49) Simplify the expression
10  2 x
, x0
| x||2 x|
(25) x y
50) Simplify the expression
(125)
1
4
2
1
51) Rationalize the denominator
5 5
2 5
( xy 2 ) 0
x 9 y 3


1
3


1
2
3
52) Simplify the expression (4 x  5 y )( 4 x  5 y )  (2 x  3 y )(3x  2 y )
53) Factor y 6  7 y 3  8
3i 90  9i 92
54) Simplify 89
2i  4i 91
55) Factor x 2  z 2  14 xy  49 y 2
56) Write the complex number in standard form
4  5i
2  3i
xy 1  yx 1
57) Simplify the expression 2 1
x y  y 2 x 1
58) Simplify the expression 123 4  3
59) Simplify the expression
20
16
5
3
 2
2 x  3x  2 2 x  x  1
2
60) Which one is irrational?

22
7
(0.23) 2
2 8
0.73
25
61) Write the expression without absolute value notation. | 2 x |  | 4 x |  || 6 x || x  1
62) Calculate 8  5[3x  4(2 x  3)] 
5
6
5
2
63) Simplify the expression
2 x y
1
3
4x y
1
5
7
10
64) If A  {x | x  1}  {x | x  2} and B  {x | 1  x  3}  {x | 1  x  5} , then
the set A  B is equal to
65) Imaginary part of the complex number
5  3i
is
4  2i
66) Find the coefficients of y 2 and y 3 in the multiplica tion (5y 3  3 y  4)(3 y 2  4 y  7)
67) Factor 4 x 3  4 x 2 y  9 xy2  9 y 3
68) Write the complex number (3  2  32 )( 2  3  8 ) in the standard form.
69) Simplify the expression
x 2  y 2
x 1  y 1
70) Simplify the expression
5
10
 2
x  x x 1
2
6x 2
4x 2  4x  1 2x  1
71) Simplify the expression


3x  6
x2
x3
72) Factor 36 x 3 (9 x 3  8) 3  (9 x 3  8) 4
73)
4
32  4
2
8
74) Calculate
?
(0.93  10 8 )(5.2  10 7 )
and write it in scientific notation.
(2.6  10 10 )(3  1015 )
75) Write the complex number (i ) 47   9  4 in standard form.
76) Calculate
 3 2  6  (3) 2  | 3 |
2  5 (3) 5
77) Write without absolute value | x  4 |  | 2x  3 |
 3  x  2
78) Find the coefficient of a 2 b in the expression (a  2b) 2 (3a  b)
79) Rationalize the denominator
3 2
2 3 3 2
 (ab) 1 c 2
80) Simplify the expression 
 2 1 2
 (ac ) b



2
81) Simplify the expression
y2  6y  9
y3
 3
3
y  27
y  3y 2  9 y
82) Simplify the expression
1  (1  x) 1
x 1  ( x  1) 1
83) Factorize x 4 n  1 completely.
84) Factorize 5 xy  20 y  15 x  60
85) Write the complex number
4i
1

in standard form
3i 3i
86) Calculate | 2   |  (3) 2  | 6  2 | 3 (3) 3
87) Simplify
5
3
8x 2
88) Write the number 0.000002015 in scientific notation
89) Simplify the expression 3x 2  5[4 x 2  6(3x  1)]
90) If A  {x | x is a composite numer  11} and
B  {z | z  2 y  1 , where y is an integer wi th  1  y  5}, then A  B  ?

( 2 ) 0 9  2 x  2 y
91) Simplify the expression 
10

 (81)  2 x  4 y 3
2
3
92) Factor 18 x 2  24 xy  8 y 2  6 x  4 y
93) Factor completely x 6  63 x 3  64
94) Simplify  3x3 54 x 4  23 16 x 7
95) Calculate (23 3  3 2 )( 43 9  23 6  3 4 )
96) Rationalize the denominator
97) Simplify
2 3 3 2
6( x  3) 1  2( x  1) 1
x( x  1) 1  3( x  3) 1
3 2




1
2
(21  10 8 )(160  10 3 )
in the scientific notation.
(4  10 4 )(700  10 6 )
98) Write the number
99) If  3  x  1 , then write the expression | 3  x |  | 2  2 x |  ||  x || without absolute value
2
100) Simplify
1
1
1
(2 x 3 y 2 )(3 x 6 y 3 )
17
6
x y

7
6
101) Rationalize the denominator
102) Simplify
3 5  2 10
3 5  2 10
x
x 2  2 x ( x  2)( x  3)


x5
x5
( x  3) 2
5
3
1
103) Factor 3x 2  9 x 2  6 x 2
104) Factor x 3 y 2  9 x 3  8 y 2  72
105) Write the complex number
106) Simplify
xy 1  x 1 y
xy 1  1  2 x 1 y
 2  8  i7
in standard form.
1 i