Math 1111- Summer 2013
Name:
Score:
Test 1: Sections 1.1, 1.3, 1.5, 1.6, and 2.4
Directions: ONLY use PENCIL please. Work each of the problems out in the space provided, and show all of your work.
Leave all answers in reduced fraction form. Each problem is worth 5.6 points.
1. Solve the following equation. Section 1.1
2. Solve the following equation. Section 1.1
1
6 �𝑚 − � − 𝑚 = 5(7 − 𝑚)
3
1
𝑥+3
+
3
𝑥−3
=
2
(𝑥−3)(𝑥+3)
3. Find all real solutions of the following equation. Section 1.1
x3 = 27
4. Find all real solutions of the following equation. Section 1.3
3𝑥 2 + 7𝑥 + 4 = 0
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Leave all answers in reduced fraction form.
5. What is the discriminant of the following equation? Section 1.3
2𝑥 2 − 5𝑥 = −6
6. For problem #5, determine the number of real solutions of the equation. Please circle one of the three options
below. Section 1.3
2 real solutions
1 real solution
0 real solutions(2 imaginary solutions)
7. A rectangular bedroom is 5 feet longer than it is wide. Its area is 104 square feet. What is the width of the
room? Section 1.3
8. Find all real solutions of the following equation. Section 1.5
9. Find all real solutions of the following equation. Section 1.5
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𝑥 4 − 𝑥 3 − 6𝑥 2 = 0.
√4 − 6𝑥 = 2𝑥
Leave all answers in reduced fraction form.
10. Find all real solutions of the following equation. Section 1.5
𝑥 4 − 5𝑥 2 + 4 = 0.
11. Find ALL solutions, real and complex, of the following equation. Section 1.5
𝑥 4 − 16 = 0
12. Solve the following linear inequality. Express the solution using interval notation. Section 1.6
1 < 3𝑥 + 4 ≤ 16
Solution set using interval notation: _________________
13. Solve the nonlinear inequality. Express the solution using interval notation.
(x+2)(x – 1)(x – 3) < 0
Section 1.6
Solution set using interval notation: _________________
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Leave all answers in reduced fraction form.
14. Solve the nonlinear inequality. Express the solution using interval notation. Section 1.6
𝑥−5
>0
𝑥+3
Solution set using interval notation: _________________
15. Find an equation of the line that satisfies the given conditions. Section 2.4
Through (1, −6); parallel to the line x + 2y = 6.
Find the slope and y-intercept of the line, and draw its graph for problems 16 – 18. Section 2.4
3x – 4y = 12
16. The slope of 3x – 4y = 12 is ___________,
17. The y-intercept of 3x – 4y = 12 is _______________.
18. The graph of 3x – 4y = 12 is below.
Page 4 of 4
Leave all answers in reduced fraction form.