Download Math 1005 Exam 2 Review 1. Solve the following equations for x. (a

Math 1005
Exam 2 Review
1. Solve the following equations for x.
(a) −4x − 4 = −2(x + 7)
(b)
7x + 2
6x + 3
= 6−
6
2
(c)
4
=3
x+4
(d) |4x − 16| = 12
(e) |x − 2| = 2x − 7
2. The perimeter of a rectangle is 500 meters. If five times the width is 4 more than twice the length,
find the dimensions of the rectangle.
3. A box contains nickels, dimes, and quarters worth $12.60. The number of dimes is 2 less than
three times the number of nickels, and the number of quarters is 4 less than twice the number of
dimes. How many of each coin are there?
4. Two cars are driving in opposite directions (starting at the same point), one at 55 mph and the other
at 65 mph. How long will it take before the cars are 300 miles apart?
5. Solve the following inequalities for x. Write your answer in interval notation.
(a) −6 > −6x − 18
(b) 4x + 1 ≥ −11
(c) 4x − 6 ≤ − 16 x + 1
(d) 7 < 2x + 5 ≤ 17
(e) |2x − 11| ≤ 13
(f) |150 − 20x| > 10
6. For each of the following find and graph A ∩ B and A ∪ B
(a) A = (3, ∞) and B = (−∞, 6]
(b) A = [2, 6] and B = (1, 5)
7. Perform the indicated operation.
(a) (−5 + 3ı) − (−3 + 4ı)
(b) (−3 + 6ı) · (−4 + 3ı)
(c)
3ı
5 − 3ı
(d)
−5 + 3ı
3 + 4ı
8. Simplify
(a) ı53
√
−16
(b) √
−4
(c)
√
√
−98 − 3 −50 + ı7
9. Solve the following equations by any method.
(a) 9x2 − 5x − 1 = 0
(b) 5x2 − 7x = 6
(c) 3x2 + 16x = −5
(d) x2 + 8x + 12 = 0
(e) (x + 9)2 + 45 = 0
(f) (x + 6)2 = 72
10. Solve the following equations
√
(a) −5x + 14 = x
√
(b) x + 7 x − 18 = 0
(c) x4 − 8x2 + 8 = 0
11. For each equation, determine whether its graph is symmetric with respect to the x-axis, the y-axis,
and the origin.
(a) xy2 + 3 = 0
(b) y = x
12. Write the equation of a circle that has center (6, −5) and passes through the point (−4, −4).
13. Find the center and radius of a circle with equation x2 + y2 + 6x + 8y + 9 = 0. Graph the circle.
14. Calculate the distance between the points (−7, 4) and (−4, 8).
15. Find the midpoint of the line segment joining the points (−5, −8) and (3, 6)
16. If M = (1, 1) is the midpoint of a line joining points A and B where A = (4, 1), find B.
17. Write an equation for a line that passes through the point (−2, 7) and has a slope of 4. Write your
answer in slope-intercept form and graph the line.
18. Write an equation for the horizontal line that passes through the point (−3, −1)
19. Sketch the graph of x = −3.
20. Write an equation of a line that passes through the points (1, 2) and (4, 4). Write your answer in
standard form.
21. What is the y-intercept of a line that passes through the point (4, 0) that has a slope of 12 ?
22. Find the x and y intercepts of the line 5x − 2y = 2. Sketch the graph.
23. Consider the line y = −5x + 9.
(a) Find the equation of the line that is perpendicular to this line and passes through the point
(3, 6)
(b) Find the equation of the line that is parallel to this line and passes through the point (3, 6).
24. The average lifespan of American women is modeled by the linear equation y = 0.2t + 73, where
t = 0 corresponds to 1960. Explain the meaning of the slope of this equation.