Download Practice Exam, version 2

Math 251, Practice Exam 2, version 2, Fall 2015
1. Two cars start 150 miles apart, driving toward each other. One car is
driving 10 mph faster than the other car. If the cars pass each other in 3
hours, find the rate of each car.
2. Solve the following inequality. Express your answer 3 ways:
(a) as an inequality
(b) as a graph on the number line
(c) in interval notation
2 − 4x ≤ 5
3. Graph the line below by finding the x and y-intercepts and then connecting these points.
3x − 4y = 6
4. Graph each line and state its slope:
(a) x = -3
(b) y = 4
5. Consider the line y = -4x +5.
(a) What is its slope?
(b) What is the slope of any line perpendicular to this line?
(c) Find an equation for the line through (1, 2) that is perpendicular to
the given line.
6.
(a) Find the equation of the line through (−2, 3) and (−3, −1).
(b) Graph the line in part (a).
7. Graph.
4x − 2y < 6
8. Solve by elimination.
3x
x
+4y = −4
+8y =
2
1
9. Solve by substitution.
x + 2y = 4
3x + 6y = −8
10. We plan to mix some coffee worth $6 per pound with some coffee worth
$3 per pound to get 90 pounds of coffee worth $4 per pound. How many
pounds of each type of coffee should we use?
11. Sketch the system of inequalities on one graph.
y ≤ 2x − 4
3x − y < 1
12. Evaluate.
(a) −50
(b) −32
(c) (−4)−2
13. Simplify.
x 2 y −3
x 5 y2
−3
14. The Double Helix Nebula, a conglomeration of dust and gas stretching
across the center of the milky way galaxy, is about 25,000 light-years
from Earth. Of one light-year is about 6,000,000,000,000 miles, about how
many miles is the Double Helix Nebula from Earth? Calculate your answer by converting both numbers to scientific notation and then multiplying them. Give your answer in scientific notation.
15. Add.
3x3 − 4x + 5 + 8x3 − 4x2 + 5x − 2
16. Multiply.
( x + 3)3
2
17. Find an expression representing the area of the rectangle shown below.
x2 − 7
x2 + 4
18. Divide.
4x3 − 2x2 + 5x − 2
6x2
19. Factor completely.
x3 + 8x2 − 20x
20. Factor completely.
6x2 − x − 2
3