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MATH 1101 Test #1

For partial credit show work.
1. The table below shows the relationship between the speed of a certain car and the number of miles per

Speed x 25 30 35 40 50 60 80
Mpg y 27 28 27 26 24 22 21

(5 points each)

(a) What is the average rate of change in miles per gallon between the speeds of 35 and 60? Show work.

(b) What is the meaning of your answer in part a?

(c) Find the slope and y-intercept of a “line of best fit” for the data in the table. Do not round off.

(d) Use your slope and y-intercept in part b to predict the miles per gallon when the speed is 85. Give the
answer correct to the nearest tenth (one decimal place after the point).

(e) Is your prediction in part c interpolation or extrapolation?

2. The data in the table below shows five points which almost lie on a straight line. Show work.

x 0 3 5 7 9
y 2 5 9 12 16

(5 points each)

(a) Use the first and last points in the table to calculate a slope of a line through those two points.

(b) What is the y-intercept for this line?

(c) Write an equation of this line using your answers in parts a and b.

3. According to the U.S. Bureau of Labor Statistics, the percentage of women in the civilian labor force
has changed between the years 1955 to 2000 according to the data in the table below.

Year 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
% W 35.7 37.7 39.3 43.3 46.3 51.5 54.5 57.5 58.9 60.0

(5 points each)

(a) What is the increase in the percent of women in the workforce between years 1965 and 1990?

(b) Between the years 1965 and 1990, what is the average rate of change per year in the percent of
women in the workforce?

4. Suppose g(x) = x2 − 5x − 36 . Choose a good
WINDOW for the y values in order to see the
complete graph of this if –5 < x < 10 and
you wanted to sketch the graph and label
the y-axis on the axes at right. (HINT: Let Ymin= –50)
Sketch the graph as accurately as possible,
Be sure to show the exact x- and y-intercepts.
Also show both coordinates of the minimum.

Label the axes!!! (10 points)

5. Solve the following equations for x. If you show work, I can give partial credit. If you use a calculator
method, it’s either right or wrong, but you can still show some work for partial credit OR explain what
you are doing with your calculator. (5 points each)

    Answer correct to 2 decimal places.

6. The percentage of the population voting in presidential elections has been estimated to be
p = 65.4042 − 0.3552x where x is the number of years after 1950 with 0 ≤ x ≤ 50 . (5 points each)
(a) When does this model predict that the percentage of people voting will be 50% ? Show or explain
your work. (HINT: let p = 50…….. don’t use 50% in your work)

(b) What percent does this model predict voted in the year 1977?

(c) Is your answer in part b interpolation or extrapolation?

7. The equation of a line is given by

(a) What is the slope of this line?
(1 point)

(b) What is the vertical axis intercept
of this line? (1 point)

(c) Graph this line at right labeling
the graph “completely.” (8 points)