Math 56/60
Print Name ________________________________
Final Exam #1, Fall 2005
Instructions:
Unless otherwise stated, (1) find exact values (nondecimal values), and (2) solve all problems algebraically (i.e. as if you
did not have the graphing and regression capabilities of your
calculator). Circle all non-graphing answers. Label and scale all axes.
1.
Solve (exact solution)
6x 2 + 13x = 5
2.
Solve (exact solution)
3x 2 - 5x + 1 = 0
3.
Solve (to the nearest thousandth) 2b - 3 = 51
4.
Solve (exact solution)
7
log 6 (3x) + log 6 (x - 1) = 1
Show all work and circle all answers (Page 2 of 9)
6.
Solve (exact solution)
7.
Solve (exact solution)
1
x
x-2
=
x2 - x - 6 x + 2 x - 3
x + 1 - 2x - 5 = 1
Show all work and circle all answers (Page 3 of 9)
8.
9.
Solve the system by elimination or substitution
Simplify
8b1/ 2 c -4/3
10b3/ 4 c -7/3
10. Simplify
3 8x 3 - 2x 18x
11. Simplify
3
4
x
2x + 4 y = 0
5x + 3y = 7
Show all work and circle all answers (Page 4 of 9)
12. Simplify
5 x -4
3 x +2
13. Perform the indicated operation and simplify.
3x
x+2
x 2 - 10x + 25 x 2 - 7x + 10
4x 3 - 8x 2 - 25x + 50
14.
Factor
15.
Find the equation of the line ( y = mx + b ) that contains the points
(-3, 2) and (2, -5). Write m and b in fractional form.
Show all work and circle all answers (Page 5 of 9)
16.
a.
Let f (x) = -x + 2x + 8 .
Find the x-intercepts of f .
b.
Find the y-intercept of f and its symmetric point.
c.
Find the vertex of f.
d.
Plot the points from parts a-c and sketch the graph of
f. Label and scale the axes.
17.
Find the equation of the exponential curve that contains the points
(3, 95) and (6, 12). Write the constants to the nearest thousandth.
2
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18.
Find the equation of the parabola that contains the points (2, 1), (3, 6)
and (4, 15).
19.
Evaluate
20.
Find the inverse function of f (x) = -4x - 7
21.
Find the inverse function of g(x) = log 2 (x)
log b ( 4 b )
Show all work and circle all answers (Page 7 of 9)
You may use the graphing and regression capabilities of your calculators
on problem 22 and 23 – you do not have to show your work.
22. Let f (t) represent the percentage of
passenger vehicles sold in the United States
that are light trucks since 1979.
a. Find the appropriate (linear, quadratic or
exponential) regression equation for f.
b.
Estimate the percentage of passenger
vehicles sold in 2002 that were light trucks.
c.
Find f
-1
Percentage of Vehicles
Sold that Are Light Trucks
Year
Percent
1979
9.4
1984
24.0
1989
30.2
1994
40.6
1998
44.8
2000
46.0
(49) . Explain its meaning in this application.
y
23. The graph of f is shown to the right.
a. Find f (2)
b.
Find x when f (x) = 5
c.
Find the equation for f in vertex form f (x) = a(x - h)2 + k .
4
-2
2
x
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24.
Solve (for exact solutions)
2x + 9 = -6
25. Graph the solution set to the system. Label and scale
the axes.
y £ -3x + 9
y ≥ 2x - 3
x≥0
y≥0
26. Solve (for exact solutions)
2x 2 + x + 1 = 0
x2 y2
27. Sketch the graph of
+
= 1 . Label and scale the
4
9
axes.
Show all work and circle all answers (Page 9 of 9)
28. (3 points each)
Circle TRUE if the statement is always true,
otherwise circle FALSE.
TRUE
FALSE All horizontal lines have an undefined slope.
TRUE
FALSE In a graph the independent variable is represented on the
horizontal axis.
TRUE
FALSE A graph is a graph of a function if every horizontal line
intersects the graph at most once.
TRUE
FALSE The domain of a function is the set of all values of the
independent variable.
TRUE
FALSE If a and b are positive,
TRUE
FALSE The range of a function is the set of all output values of
the function.
TRUE
FALSE A system of two linear equations that have the same
slope and same y-intercept is called a dependent system.
TRUE
FALSE For positive integer n, (a + b)n = a n + b n
TRUE
FALSE A negative exponent means to take the reciprocal.
TRUE
FALSE -9 2 = -81
TRUE
FALSE For an exponential function in the form y = ab x , if the
value of x is increased by one, then the value of the y is
multiplied by the base b.
TRUE
FALSE Every line perpendicular to the line 2x + y = 1 has a
slope of 1/2.
TRUE
FALSE The exponential function f (t) = 40(1.122)t has a 12.5%
decay rate.
a+b = a + b.