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Math 70 : Intermediate Algebra
Test 2 :
Please show your work as clear as possible.
You will not receive credit if no work is shown.
Use appropriate method in algebra to solve these problems.
CIRCLE YOUR ANSWERS. Use a ruler when you graph.
Name: ______________________________
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Points
6
5
5
6
4
4
5
3
6
6
6
9
7
6
6
6
Total
90
Your score
Comments
Your test score is ________________
Your current course grade is _______________
** Remember you can always get help at the MSC(SC300), or come to visit me during my
office hours.
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Fall 2010
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1. [6] (a) Find the midpoint of the line segment with endpoints (-2,4) and (6,8).
(b) Find the distance between the midpoint you obtained in part (a) and
the point (3,-5). (Present your answer in exact form.)
2. [5] For the equation 4 x  3 y  15 ,
Write the equation in slope-intercept form and find the slope.
3. [5] Use the slope-intercept form to find the equation of the line containing the
points (3,-5) and (5,2). (Present your answer in slope-intercept form.)
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4. [6] Find the equation of the line that contains the point (1,2) and is
perpendicular to the line 2 x  3 y  6 .
(a) Present your answer in slope-intercept form. ____________________
(b) Present your answer in standard form.
5. [4] Find the domain and range of the function
{(3,10) , (4,13) , (5, 16), (8,13)}.
6. [4] Evaluate g (n)  2n2  3n  5 when n  2 .
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7. [5] Given f ( x)  9  2 x , write f (3  h)  f (3) in simplest form.
8. [3] What values, if any, are excluded from the domain of the function
g ( x) 
x2
?
x2
9. [6] Use the point-slope formula to find the equation of the line that passes
through two points (2,3) and (1,2) .
(a) Present your answer in slope-intercept form.
(b) Present your answer in standard form. (That is, ax+by=c.)
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10. [6] Find the equation of the line that contains the point (2, -5) and is parallel
to the line 5 x  2 y  4 . Present your answer in slope-intercept form.
11.[6] Graph the solution set for 3x  4 y  12 (Find x-intercept and y-intercept.
Use them to graph the line. Choose a point to check which part of the graph
should be shaded. Use a ruler.)
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12. At sea level, the boiling point of water is 100ºC. At an altitude of 3 km,
the boiling point of water is 89ºC.
(i) [4] Write a linear equation for the boiling point of water in terms of the
altitude above sea level.
(ii) [3] What is the slope you found in (ii)? Use one sentence to explain the
meaning of your slope in this application.
(iii) [2] Use your equation to predict the boiling point of water on the top of
Mount Everest, which is approximately 8.85 km above sea level.
Round your answer to the nearest degree.
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13.[7] The director of a baseball camp estimates that 100 students will enroll if
the tuition is $250. For each $20 increase, 6 fewer students will enroll.
(c) Determine a linear function that will predict the number of students who
will enroll at a given tuition. (First try to obtain two points from the above
information.)
Tuition
$250
$270
$290
Number of students
100
(b)Use this equation to predict enrollment when the tuition is $315.
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14. [6] Population of California:
Year
1950
1960 1970 1980 1990
Population (in millions) 10.6
15.7 20.0 23.7 29.8
2000
33.9
(a) Find the average rate of change in California’s population from 1960 to
2000.
(b) Use one sentence to describe the number you get in part(a).
15. [6] Graph the solution set for y  2 x . (Show your work.)
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16.[6] There are approximately 126 calories in a 2-ounce serving of lean
hamburger and approximated 189 calories in a 3-ounce serving.
(d) Write a linear equation for the number of calories in lean hamburger in
terms of the size of the serving.
Serving
Calories
(e) Use your equation to estimate the number of calories in a 5-ounce serving
of lean hamburger.