Download Exam 1.1 - Mrs. Matthews Class

ALGEBRA EXAM 1.1
____
1. Justify each step.
7 + 2(x – 3) + 5x =
a.
b.
c.
d.
e.
f.
(3 points)
7 + 2x – 6 + 5x
= 7 + 2x + (–6) + 5x
= 7 + (–6) + 2x + 5x
= 7 + (–6) + (2 + 5)x
= 1 + 7x
= 7x + 1
2. Completely classify:
(1 points)
3. Are the negative numbers closed under subtraction? Explain your answer.
(2 points)
4. A camera manufacturer spends $2,100 each day for overhead expenses plus $9 per camera for labor and
materials. The cameras sell for $14 each. How many cameras must the company sell in one day to equal
its daily costs?
(2 points)
5. Suppose you had d dollars in your bank account. You spent $22 but have at least $28 left. How much
money did you have initially? Write and solve an inequality that represents this situation. (1 point)
A.
;
C.
;
B.
;
D.
;
For questions 6-7 solve the equation for the given variable.
6. dx + fy = g; y
7.
(2 points)
(2 points)
; F.
8. Susie has designed an exercise program for herself. One part of the program requires her to walk between
25 and 30 miles each week. She plans to walk the same distance each day five days a week. Write an
inequality to show the range of miles that she should walk each day?
(2 points)
9. A student scored 83 and 91 on her first two quizzes. Write and solve a compound inequality to find the
possible values for a third quiz score that would give her an average between 85 and 90. (2 points)
For questions 10-11, identify the letter of the choice that best completes the statement or answers the question.
10. Which number is a solution of the inequality:
x(7 – x) > 8
(1 point)
A. -1
B. 8
C. 2
D. 0
11. Identify the graph of the inequality from the given description:
A.
C.
–5
–4
–3
–2
–1
0
1
2
3
4
5
–5
–4
–3
–2
–1
0
1
2
3
4
5
B.
x is negative.
(1 point)
–5
–4
–3
–2
–1
0
1
2
3
4
5
–5
–4
–3
–2
–1
0
1
2
3
4
5
D.
12. Write an inequality for the graph:
(4 points)
(A)
(B)
–14 –12 –10 –8 –6 –4 –2
(C)
0
2
4
–5 –4 –3 –2 –1
6
0
(D)
1
2
3
4
5
–14 –12 –10 –8 –6 –4 –2
Solve the inequality. Graph the solution.
13. 21a – 3(4a + 2) > 24
14. 12x – 3x + 11 ≥ 4x – (17 – 9x)
15. -6x – 1 + 4 > 5 OR 11 + x – 7 ≥ 2
3
2
16. 3| 3 – 2 (x – 2) + 5 | < 6
0
2
4
6
(2 points)
(2 points)
(3 points)
(3 points)
Solve the following equations.
17. 3p – 1 = 5(p – 1) – 2(7 – 2p)
18. ¼|x – ⅓| = 20x
(2 points)
(2 points)
19. The length of a rectangle is 5 centimeters less than twice its width. The perimeter of the rectangle is 26
cm. What are the dimensions of the rectangle?
(2 points)
20. Which of the following inequalities could be represented by the graph?
–2
I.
II.
III.
–1
0
1
2
3
4
5
6
7
(1 point)
8
-3y < -15 or y < 1
5 < 2a + 3 < 13
|x – 3| > 2
A.
I only
B.
I and II
C.
II and III
D.
I and III
21. The width of a rectangle is 33 centimeters. The perimeter is at least 776 centimeters. Write and solve an
inequality to find the length of the rectangle.
(2 points)
22. The student council wants to rent a ballroom for the junior prom. The ballroom’s rental rate is $1500 for
3h and $125 for each additional half hour. Suppose the student council raises $2125. What is the
maximum number of hours for which they can rent the ballroom?
(3 points)
23. The ideal width of a safety belt strap for a certain automobile is 5 cm. An actual width can vary by at
most 0.35 cm. Write and solve an absolute value inequality for the range of acceptable widths.(2 points)
24. Scarlet has to build a rectangular pen for her peacock, Paulie. Scarlet has P feet of fencing.
a. Scarlet decides that the width of Paulie’s pen will be half of the length of his pen. Write an
equation describing the relationship between P and the width of the pen, w.
(2 points)
b. Solve the equation for w.
(1 point)
ANSWERS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
25.
a.
Distributive
b.
Defn of subtraction
c.
Comm. Of add
d.
Distributive
e.
Addition
f.
Comm. Of Add
Q, R, Neither prime nor composite
No; the difference between 2 negatives is not always negative.
420 cameras
D
y = g – dx
f f
F = 9C + 32
5
5<x<6
81 < x < 96
C
D
a.
x ≥ -½
b.
x ≤ -6 OR x > 2
c.
-3 ≤ x ≤ 1
d.
x < -7
a > 10; GRAPH
3
x ≤ 7; GRAPH
x < -⅔ OR x ≥ 7; GRAPH
5 < x < 7; GRAPH
p=3
x= 1
243
W = 6, L = 7
D
l ≥ 355
5½ hours
4.65 ≤ x ≤ 5.35
(a)
P = 6w;
(b)
w=P
6