Pre-Test 1 (Chapters 1 – 2)
MATH 141
Section 1.1
1) Find the distance d(P1 , P2) between the points P1 = (5, -5) and P2 = (7, -1).
2) Find the midpoint of the line segment joining the points P1 = (8, 6) and P2 = (6, 2).
3) Graph the equation y = x2 - 1 by plotting points.
4) Graph the equation y = -2x2 + 9 using a graphing utility.
5) Use a graph utility to create a table that displays the points on the graph of
4x2 – 2y = 16 for x = -3, -2, -1, 0, 1, 2, and 3.
6) Graph the equation y = 5x2 – 13 using a graphing utility. Use a graphing utility to
approximate the intercepts rounded to two decimal places, if necessary.
7) List the intercepts of the graph.
y
f(x)=(-5/4)x^2-(5/2)x+15/4
9
8
7
6
5
4
3
2
1
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
-1
-2
-3
-4
-5
-6
-7
-8
-9
Section 1.2
8) Use a graphing utility to approximate the real solutions, if any of the equation
x3 – 6x + 3 = 0 rounded to two decimal places.
9) Solve the equation, 2(2x – 3) = 3(x + 4).
10) Solve the equation,
x2 x6

.
x5 x7
1
11) An inheritance of $590,000 is to be divided among Chris, Kelly and Jose in the
following manner: Kelly is to receive 4/5 of what Chris gets, while Jose gets 1/6 of
what Chris gets. How much does Kelly receive?
Section 1.3
12) Solve the equation x2 – 6x + 5 = 0 by factoring
13) Solve the equation (x + 5)2 = 16 by the Square Root Method.
14) Find the real solutions, if any, of the equation 2x2 + 3x - 9 = 0. Use the quadratic
equation.
15) A ball is thrown vertically upward from the top of a building 128 feet tall with an
initial velocity of 112 feet per second. The distance s (in feet) of the ball from the
ground after t seconds is s = 128 + 112t – 16t2. After how many seconds will the
all pass the top of the building on its way down?
Section 1.4
Write the expression in the standard form a + bi.
16) (6 + 7i) – (-4 + i)
17) (4 + 6i)(2 – 7i)
18)
5i
2i
19) Solve the equation x2 + x + 3 = 0 in the complex number system.
Section 1.5
20) Find the real solutions of the equation 14 x  21  x  2 .
21) Find the real solutions of the equation 2(x+1)2 +6(x+1) + 4 = 0.
22) Solve the equation | 2x + 8 | = 2.
23) Find the real solutions of the equation x3 + 2x2 – 9x – 18 = 0 by factoring.
Section 1.6
24) Two friends decide to meet in Chicago to attend a Cub’s baseball game. Rob
travels 216 miles in the same time that Carl travels 196 miles. Rob’s trip uses
more interstate highways and he can average 5 mph more than Carl. What is
Rob’s average speed?
25) BJ can overhaul a boat’s diesel inboard engine in 20 hours. His apprentice takes
2
60 hours to do the same job. How long would it take them working together
assuming no gain or lost in efficiency?
Section 1.7
26) Solve the inequality, 6x  5  7 x 1 .
27) Solve the inequality, 27  4x  1  7 .
28) Solve the inequality, | x  8 |  13 .
29) Solve the inequality, | 4k  2 |  3 .
Section 2.1
30) List the intercepts for the graph of the equation x2 + y – 49 = 0.
31) List the intercepts for the graph of the equation y 
x 2  36
.
6x4
32) List the intercepts of the below. Tell whether the graph is symmetric with respect to
the x-axis, y-axis, origin or none of these.
y
9
8
7
6
5
4
3
2
1
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
-1
-2
-3
-4
-5
-6
-7
-8
-9
33) List the intercepts and type(s) of symmetry, if any, for y 2   x  4 .
34) Graph the equation y = 1/x by plotting points.
Section 2.2
35) Graph the line containing the points P(-3, -2); and having slope m = -3/2.
36) Find an equation of the line in general form containing the points (5, 0) and (0. -6).
37) Find the slope and intercept of the line 3x + 7y = 21.
3
38) Find the general form of the equation of the line with slope m = 5/6 and containing
the point (0, 3).
39) Find the equation of the line perpendicular to the line y 
1
x  2 ; containing the
4
point (4, -2).
40) Find the equation of the line parallel to the line y = -3x – 4; containing the point
(3, 3).
Answer Key
1. 2 5
2. (7, 4)
3.
y
9
8
7
6
5
4
3
2
1
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
-1
-2
-3
-4
-5
-6
-7
-8
-9
4
4.
y
9
8
7
6
5
4
3
2
1
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
-1
-2
-3
-4
-5
-6
-7
-8
-9
5.
x
|
-3
-2
-1
0
1
2
3
y
6. (0, -13), (1.61, 0), (-1.61, 0)
-14
-12
-10
-8
-6
-4
-2
7. (-3, 0), (0, 3), (1, 0)
9. { 18 }
10. { 22/5 }
12. { 1, 5 }
13. { -9, -1 }
14. { 3/2, -3 }
15. 7 seconds
17. 50 – 16i
18. -1 + 2i
8. {2.15, 0.52, -2.67}
11. $240,000
16. 10 + 6i
1
11
1
11
i,  
i }
19. {  
2
2
2
2
20. { 5 }
21. { -3, -2 }
22. { -3, -5 }
24. 54 mph
26. ( -∞, -6 ] or x ≤ -6
25. 15 hours
23. { -3, 3, -2 }
5
28. ( -∞, -5 ) or ( 21, ∞ )
27. ( 2, 7 ]
29. [ -5/4, ¼ ]
x ≤ -5 or x > 21
30. ( -7, 0 ), ( 0, 49 ), ( 7, 0 )
31. ( -6, 0 ), ( 6, 0 )
32. Intercepts ( 0, 2) and ( 0, -2 )
Symmetric with respect to the x-axis, y-axis, and origin.
33. Intercepts ( 4, 0 ), ( 0, 2 ) and ( 0, -2 )
Symmetric with respect to the x-axis.
34.
y
9
8
7
6
5
4
3
2
1
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
-1
-2
-3
-4
-5
-6
-7
-8
-9
.
6
35.
y
9
8
7
6
5
4
3
2
1
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
-1
-2
-3
-4
-5
-6
-7
-8
-9
36. 6x – 5y = 30
37. slope = -3/7 and (0, 3 ) intercept
38. -5x + 6y = 18
39. y = -4x + 14
40. y = 3x + 12
7