Math 100A Fall 2012 Practice Exam #3
Name:
(12 points)
1. Find an equation of the line containing the given points. Express your answer in slope-intercept form,
if possible.
(a) (0, 0), (4, −3)
(a)
(b) (1, 3), (−3, −7)
(b)
(8 points)
2. Let v(t) give the market value in thousands of dollars of a house t years after 1995. Write a complete
sentence about what the following expressions tell you about the price of the house.
(a) g(5) − g(0) = 25
(b)
g(10) − g(5)
=4
5
Page 1
Math 100A
(8 points)
Practice Exam #3 (Continued)
3. Write the following equation in slope-intercept form.
3x + 8y = 10 − 2x
3.
(12 points)
4. The cost of denim fabric is directly proportional to the amount that you buy. Let C be the cost, in
dollars, of x yards of denim fabric.
(a) Denim costs $28.50 for 3 yards. Find the constant of proportionality and give its units.
(a)
(b) Write a formula expressing C as a function of x.
(b)
(c) How much does 5.5 yards of denim cost?
(c)
(8 points)
5. After a rain storm, the water in a trough begins to evaporate. The amount in gallons remaining after
t days is given by V = 50 − 1.2t. Identify the initial value and the rate of change, and explain their
meanings (and units) in practical terms.
Page 2
Math 100A
(12 points)
Practice Exam #3 (Continued)
6. Consider the function f (x) = 12 (x − 1) + 3.
(a) Without evaluating f (x) at any point or performing any algebraic manipulations, give the slope of
the graph and a point on the graph.
(a)
(b) Sketch the graph.
y
✻
5
✲
−10
−5
5
x
−5
(8 points)
−10
7. Find a possible formula for the linear function g(x) if g(8) = 20 and g(1) = −8.
7.
(8 points)
8. How many times do the graphs of the functions f (x) = 2(x + 1) − 3x + 6 and g(x) = 5x + 8 − 6x
intersect? Show your work.
8.
Page 3
Math 100A
(9 points)
Practice Exam #3 (Continued)
9. How many solutions does each equation have?
(a) −2(x − 4) = 8 − 2x
(a)
(b) 7x + 5 − 8x = 13
(b)
(c)
x 2x
x − 20
+
=
3
5
15
(c)
(6 points) 10. Answer the following questions by placing in the blank the appropriate Roman numeral for each equation
that satisfies the desired properties.
I.
III.
y = 2(x − 4) + 9
II.
y + 9 = −2(x − 4)
IV.
y = 9 − 2(4 − x)
4 + 12x
y =2−
4
(a) Write the numerals of the three equations whose graphs pass through the point (0, 1).
(a)
(b) Write the numerals of the two equations whose graphs have the same slope.
(b)
Page 4
Math 100A
Practice Exam #3 (Continued)
(9 points) 11. Consider the relation between the time spent walking, w, and biking, b, on a 40 mile trip if you walk
at 5 mph and bike at 10 mph.
(a) Write a constraint equation.
(a)
(b) Choose two solutions to the constraint equation and explain their meaning.
(b)
(c) Graph the equation and clearly mark your two solutions from part (b).
b
✻
5
✲
−10
−5
5
−5
−10
Page 5
w