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1.) Find the domain of f(x): f(x) =
x2
x  25
2
2.) f(x) = x3  2 x 2  3x  5 find the average rate of change between x = 0 and x = 2
3.) f(x) = x  10 and g(x) = x + 9. Find the domain of g (f(x)) and the range of f (g(x))
4.) f(x) = 2, g(x) = x 3  x 2  4 , and h(x) =
x 3
find f (g (h(x)).
5.) f(x) and g(x) are inverse of each other.
f (2) = -3, f (4) = 6 find g (-3), g (6), and f (g (10))
6.) f(x) = 2 x  1 , find the inverse of f(x)
7.) f(x) = ( x  3) 2 , and the slope of f(x) at any point is given by 2x + 6.
a) find the slope of f(x) at x = -3
b.) Write an equation of a line that is tangent to f(x) at x = -3
8.) Find the quadratic function that satisfy the given conditions:
The graph is obtained by translating y = x 2 four units in the negative x-direction and three
units in the positive y-direction.
9.) If -2 is a zero of p(x) = x3  2 x 2  k  5 , find the value of k.
10.) Find a function whose graph is a parabola with vertex (3, 4) and that passes through
the point (1,-8)
x
1

11.) Simplify the expression: x  1 x  1
5
2

x 1 x 1
2
3x  7
3x  7
x  2x 1
x2  2 x  1
x2  2 x  1
(a)
(b) 2
(c)
(d)
(e)
x  2x 1
x 1
x 1
x 1
3x  7
2y
1
12.) Simplify the expression: 2

y 1 y 1
3y 1
(3 y  1)( y  1)
3y 1
y 1
3y 1
(a)
(b)
(c)
(d)
(e)
2
( y  1)
y 1
( y  1)( y  1)
( y  1)( y  1)
(3 y  1)(3 y  1)
13.) Solve the equation:
(a)
10
7
(b) 17
14.) the expression:
1 1
1
5



y 5y y 1 2 y
17
(c) 7 (d)
7
(e)
7
17
7
is equivalent to
2 3
2 3
14  3
14  3
(d)
(e)
7
7
7
15.) Find an equation of the circle that passes through (-2,-4) and has center (-1, 2).
(a) ( x  1) 2  ( y  2) 2  2
(b) ( x  1)2  ( y  2)2  36
(c) x 2  y 2  37
(a) 14  7 3
(b) 14  7 3
(c)
(d) ( x  1)2  ( y  2)2  37
(e) ( x  1)2  y 2  36
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16.)
(a) 16
(b) 20
(c) 32
(d) 4 10
(e) 4 8
17.) Find an equation of the line that is perpendicular to the line 2x – 3y =1 and passes
1 3
through ( , )
4 5
(a) 6x + 4y -1 = 0
(b) 6x – 4y – 1 = 0
(c) 3x + 2y – 9 = 0
(d) 8x + y – 3 = 0
(e) 60x + 40y +9 = 0
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18.) If f ( x)  x3  2 x 2 , then f(i) is equal to
(a) -2 + i
(b) - 2 – i (c) 2 + i
(d) 2 – i
(e) 2i
19.) The slope of f(x) at any given point is found by x 3 , find the slope of f(x) when x = 2
1
1
1
(a) -6 (b) 6 (c)
(d) 
(e) 
8
8
2
2
1
20.) If f ( x) 
and g ( x)  , then ( g ( f ( x))) is equal to
x3
x
1  3x
2x
x3
x3
2
(a)
(b)
(c)
(d)
(e) 2
x  3x
2x
1  3x
2
2x
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21.) For which positive value of m will the equation 4 x 2  mx  9  0 have roots that are
real, equal and rational?
(a) 12
(b) 9
(c) 3
(d) 4
(e) 0
22.) The solution set of the equation x  6  x is
(a) {-2, 3}
(b) {-2}
(c) {3}
(d) { }
23.) The solution set of 2 x  3  5 contains
(a) only negative real numbers
(b) only positive real numbers
(c) both positive and negative real numbers
(d) No real solutions
24.) A function is defined by the equation y = 5x – 5 which equation defines the inverse
of this function?
1
1
(a) y 
(b) y = 5x + 5
(c) x = 5y – 5 (d) x 
5x  5
5y  5
25.)
(a) HL  HL
(b) AAA  AAA
(c) AAS  AAS
(d) SSA  SSA
26.) In a given rectangle, the length varies inversely as the width. If the length is
doubled, the width will
(a) be divided by 2 (b) be multiplied by 2
(c) remain the same
(d) increased by 2
(e) decreased by 2
27.) Find the area of a triangle formed by the x-axis, y –axis and the line 2x + 3y -8 = 0
28.) Find a value of K that will make x = -2 a solution of the equation:
9x – k + 4 = 2kx – k + 4.
29.) Find the remainder when x1001  x579  4 x31  5 x12  3 is divided by x + 1.
30.) If 3x  8 and 3 y  3 find the value of 3x  y .
31.) Find the horizontal, vertical and or slant asymptotes. Find the holes in the graph if
( x  3)(2 x  4)( x  1)
there are any: y 
( x  2)( x  3)
32.) The vertex of a parabola is (-3,-1) and passes through the point (-3, -1) find a
quadratic equation.
33.) f ( x)  x 2  2 x  3 find the value of f(x + h)
34.)
35.)
36)
37.)
38.)
39)
40)
41)
42.)
43)
44.)
45.)
46.)
47.)
48.)
49.)
50.)
51.)
52.)
(b 2 n 1 )3
b n  b 4 n 3
x
54) simplify the expression: x  2
x
1
x2
x
y
55.)If 2  3 and 2  5 Find the value of 2x y
56) Find an equation of a circle that contains the points P(2,3) and Q(-1,8) and has the
midpoint of PQ as the center of a circle. Find the equation of a line PQ
57.) Write an equation of a line that is perpendicular to the line 2x + 3y = -6, and
passes through the point (3,1)
53.)simplify the expression:
58.) Find the x and the y intercept y  4  x 2
59.) Find the area of a triangle formed by the coordinate axes and the line y = 4x – 4
x
2
3


60.) Solve for x:
2
4x  x x 1 4x 1
1
1
1
(7  3 x) 2  x(7  3x) 2
2
61.) Simplify the expression
(7  3 x)
62.) The medians of a triangle are the line segments from each vertex to the midpoint
of the opposite side. Find the lengths of the medians of the triangle with vertices at
A(0,0) B(6,0) and C(4,4)
63.) Find the center, radius and the area of a circle whose equation is given by
x 2  4 x  12  y 2
64.) Find the point D that is located on AB, and is 3/5th of the way on AB from B.
A(-2,3) and B(8, -2)
2
3
65.) Solve for x: 2 x  5  55
66.) solve for x: x  2  3  7
67.) Solve for x: 2  x  3  4
68.) solve for x: 3x 2  12 x  6  0
69.)
70.)
71.)
72.) Find an equation of a line tangent to the y  x 2  2 x at x = 1
73.) Find an equation of a line tangent to the y  x 2  4 x  8 at x = 3
74.)If the roots of a quadratic equations are 2 and –3, and the constant term is –2 find the
equation.
75.)If the roots of a 4th degree equations are 2 +3i and 3 + 2i and the constant term is 1
find the equation.
76.)Find all the solution of x3  64
77.)Find all the solution of x 4  64
78.)Find all the solution of (x - 2)(x + 3)(x - 8)(x + 5) = 0
79.)Find all the solution of (x – 3)(x + 4) = -2
80.)Find an equation of a circle that contain the points (2,5), (3,- 4) and (0,0)
81.)Express the area of a square in terms of its diagonal z.
82.) f ( x)  x 2  2 x  3 . find the average rate of change between x = -2 and x = -2.
83.)The inverse function of f(x) is g(x). Domain of f(x) and g(x) are all real numbers.
f(2) = 3 and g(4) = 6.
Find: g(3) =
f(6) =
g(f(2)) =
f(g(6) =
84.)The pressure p of a sample of gas is directly proportional to the temperature T and
inversely proportional to the volume V.
a.) Write an equation that expresses this variation.
b.) Find the constant of proportionality if 100 L of gas exerts a pressure of 33.2 kpa
at a temperature of 400 K
c.) If the temperature is increased to 500 k and the volume is decreased to 80 L, what
is the pressure of gas?
85.)How many possible positive and negative real roots the polynomial can have. Then
determine the possible total number of real zeros. P(x) = x8  x5  x 4  x3  x 2  x  1
86.)Find all rational zeros of p(x) = 2 x 4  3x3  4 x 2  3x  2
87.)Show that polynomial p(x) has no real rational roots. 2 x50  6 x 22  8 x10  4 x 2  1 .
Show that p(x) has no real roots.
88.)f(x) = 2 x 3  x 2  4 find the average rate of change between x = 0 and x = 2
89.)The equation of a function is given by f(x) = x 2 + c, slope of f(x) is given by 2x. The
line
y = - 4x + 3 is tangent to f(x) at some point (x,y). Find the value of x, y and c.
90.)Consider the quadratic equation f ( x)  2 x 2  12 x  12 .
a.)Complete the square to write the function in the standard form, f ( x)  a( x  h)2  k
b.) Find the vertex of f(x)
c.) find the domain and the range of the f(x)
d.) find the roots of f(x)
e.) Find the sum of the roots and the product of the roots.
91.)A rectangular enclosure, is subdivided in to three congruent pens as shown, is to be
made using a barn as one side and 120 meter of fencing for the rest of enclosure. Find the
value of x that gives the maximum area for the enclosure. ( side with a barn doesn’t need
any fencing.)