Download Math 161 Review for Exam 1

Math 161 Review for Exam 1
1. Plot at least 5 points and sketch the graph.
x
(a) y  2
(b) y  3  x  1
(c) y  x  2
x 1
(e) y  ( x  2) 2  4 (f) y  2 x  3
(g) y  3
(d) y  x 3  2
(h) x  1   y  3  25
2
2
2. Find the x-intercept(s) and y-intercept(s) for each equation in problem 1.
3. For each equation in problem 1 tell whether it is symmetric with respect to the x-axis, the yaxis, or the origin.
4. Sketch the graph.
(a) 2 x  3 y  12
(b) x  5
(c) y  2 x  4
(d) 3x  7 y  0
5. Solve for x.
2
5
14

 2
(a)
x  3 x  4 x  x  12
(b) 2 x 2  11x  6
(c) 5  2 
(d) 23x  7  5x  2x  4  10
(e)
(g) 0.2x  0.7x  4  5
(j) 32 x  6  6 x  18
(h) x 2  6  5 x
(k) x 2  12  5 x
(i) x 2  13  6 x
(l) x 2  9
(n) x 2  6 x  0
(o) 2x  8  18
(q) x  2  x 2  54
(r) x 3  3x 2  4 x  12
(t) 2 x  12  11 x
(u) x 4  2 x 3  8 x  16
(m) 32x  7  4x  8  22x  6  9
(p)
2x  1  x  4  3
3
x 1
3x 1
5
  x  6   (f) xx  6  6  x
4 2
6
2
2
 x 
 x 
(s) 
  24  11

 x 1
 x 1
6. Use algebra to solve the following problems.
(a) The perimeter of a rectangle is 22 feet. The length is 5 feet more than the width. Find the
length and width.
(b) A family paid $41.40 including a 15% tip for dinner at a restaurant. What was the original
bill before the tip?
(c) A chemist wishes to make 300 milliliters of 45% acid solution by mixing a 10% acid solution
with a 60% acid solution. How much of each acid solution should be used?
(d) A news stand operator pays $360 rent and 28 cents for each newspaper sold. S/he sells the
newspapers for 60 cents each. How many newspapers does s/he need to sell in order to
break even? Sketch a graph showing income, expense, profit, loss, and break even point.
(e) The profit p in dollars of a paint manufacturer selling x gallons of paint is
p  0.1x 2  8x  120 . How many gallons of paint does the manufacturer need to sell
in order to break even? Sketch a graph of the profit.
(f) The height h in feet of a rocket at time t seconds after the fuel runs out is
h  16t 2  96t  112 . How long does it take the rocket to reach the ground? Graph.
Math 161 Answers to Review 1
1.(a)
1.(b)
1.(c)
1.(d)
1.(e)
1.(f)
1.(g)
1.(h)
4.(a)
4.(b)
4.(c)
4.(d)
Math 161 Answers to Review 1
page two
2.(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
y-intercept also (0, 0)
y-intercept (0. 2)
no y-intercept
y-intercept (0, -2)
y-intercept (0, 0)
y-intercept (0, -3)
y-intercept (0, 3)
y-intercepts 0,3  6  (0, -2) and (0, 8)
x-intercept (0, 0)
x-intercepts (-2, 0) and (4, 0)
x-intercept (2, 0)
x-intercept (2, 0)
x-intercepts (-4, 0) and (0, 0)
x-intercept (3/2, 0)
no x-intercept
x-intercepts (-3, 0) and (5, 0)


3.(a) symmetric with respect to the origin
(b) none of the given choices but it is symmetric with respect to the line x = 1
(c) none
(d) none of the given choices but it is symmetric with respect to the point (0, -2)
(e) none of the given choices but it is symmetric with respect to the line x = -2
(f) none of the given choices
(g) symmetric with respect to the y-axis
(h) none of the given choices
5.(a) no solution (b) 1/2 , - 6 (c) 2 (d) 16/9 (e) 46/15 (f) 1, 6 (g) 26/3 (h) 3, 2
(i) 3  2i (j) all real numbers (k) 5  23 i  2 (l) 3 (m) 4/3 (n) 0, - 6 (o) 8  3 2
(p) 4, 40 (q) 8,  1  29  2 (r) 2, -3 (s) -3/2, - 8/7 (t) 16, 9/4 (u) 2, 1  3 i
6.(a) Solve 2(5 + w + w) = 22 to get width = 3 feet and length = 5 + width = 8 feet.
(b) Solve x + 0.15x = 41.40 to get original bill = $36.
(c) Solve 0.6x + 0.1(300-x) = 0.45(300) to get
x = 210 mL of 60% acid and 300-x = 90 mL of 10% acid.
(d) Solve 0.6x = 0.28x + 360 to get x = 1125 newspapers.
(e) Solve  0.1x 2  8 x  120  0 to get x = 20 gallons or 60 gallons
(f) Solve t > 0 and  16t 2  96t  112  0 to get t = 7 seconds.
6.(d)
6.(e)
6.(f)