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ALGEBRA 2011 FIRST SEMESTER FINAL
Multiple Choice
Identify the choice that best answers the question. YOU M4Y WRITE ON THE TES1; BUT JvfAKE SURE YOU
CAREFULLY BUBBLE IN THE ANSWERS ON THE SCANTRON FORM.
Simplify the expression.
1. _54
a.
2.
20
125
C.
-625
d.
625
b.
64
c.
230
d.
2-30
c.
d.
_m216
c.
d.
[ r
(_1)5
(-2r3
a.
3.
b.
-
1
64
(m:~T
a.
b.
a.
b.
a.
1
16
b.
g26h20
25
16
c.
1
1
16
d.
-8
_
6. 6.612 ·6'
a.
182t .. 2
7. -{6r1
6
b.
8. 33.32 + 12 -7 4
a. 291
h.
a.
9.
1
_16
219
-6
d.
1
6
c.
437
d.
867
c.
d.
d.
-3
m n
m-13n-1
-9
a.
11.
1
6
(~r
a.
10.
c.
n
n -14
b.
m3n P~
c.
b.
5 +c
C.
{_h4)5
a.
_h9
12. (-5 - c)(-l)
a. -5 + c
2
5- c
d.
-5 - c
13. - 4X 3 • 2Y -2 . 5·Y 5 ·X
b.
c.
-18n + 81mn - 153np
-2n + 9m - 17p
d.
a.
14.
-8
d.
1
n( -6+27m-S1p)
a.
b.
c.
-2n + 9mn - 17np
-2n - 9mn + 17np
15. For every real number x, y, and z, the statement (x - y)z
a. always
b. sometimes
Name the property the equation illustrates.
16. 8.2 + (-8.2) = 0
a. Inverse Property of Addition
b. Addition Property of 0
c. Identity Property of Addition
d. Inverse Property of Multiplication
17. 7 +
a.
b.
c.
d.
(4 + 4) = (7 + 4) + 4
Inverse Property of Addition
Associative Property of Addition
Commutative Property of Multiplication
Commutative Property of Addition
3
=
xz - yz is __
c.
never
true.
18. 2(-~) = ( -%)2
a.
b.
c.
d.
Associative Property of Addition
Commutative Property of Multiplication
Inverse Property of Multiplication
Commutative Property of Addition
19. O+x=x
a. Identity Property of Addition
b. Multiplication Property of 0
c. Commutative Property of Addition
d. Inverse Property of Multiplication
1 x 1 = -2. I
Inverse Property of Multiplication
Multiplication Property of-1
Identity Property of Addition
Identity Property of Multiplication
20.
-2.
a.
b.
c.
d.
21.
1
8x - = 1
8
a. Identity Property of Division
b. Inverse Property of Addition
c. Inverse Property of Multiplication
d. Multiplication Property of -1
22.
Simplify the sum.
(4zP + 4u2 + 2) + (6u3
a.
b.
-
2u + 8)
10 - 2u + 4u2 + 10 u3
-2u3 - 2lP + 4u 10
c.
d.
4
-2u3 + 4u2
10u3 + 4u2
-
2u + 10
2u + 10
Simplify the product using FOIL.
23.
(4x
a.
b.
+ 3)(2x + 5)
2
+ I4x - 15
8x
8x·
2
14x - 15
-
C.
8x2 + 26x + 15
d.
8x2
c.
d.
2(5x
-
26x
+ 15
Factor the expression.
24.
20x}
a.
b.
25.
26.
27.
+ 22x - 12
2(5x
2(5x
2)(2'( + 3)
+ 2)(2x - 3)
3x3 + 3x2 + X + 1
a. x(3x2 + x + 1)
b. (x + 3)(3x2 - 1)
(lOx - 2)(4x + 3)
+ 4)(2x - 3)
c.
d.
3X2(X + 1)
c.
d.
(2x + 9y)2
c.
d.
(4m - 3n)2
(4m + 3n)2
c.
-9
(x
+ 1)(3x2 + 1)
4x2-81y2
+ 9)(2\": - 9)
a.
(2~
b.
(2"\C + 9y)(2x - 9y)
16m2 - 24mn + 9n2
a. (4m - 3n)(4m + 3n)
b. (16m - 3n)(m + 3n)
(2x-
9y)2
Solve the equation.
28.
3p - 1
a.
3
=
5(p - 1) - 2(7 - 2p)
b.
0
d. ~-10
5
.------~--.----.
-------
29.
Sp
7 - 18 = -43
-31
b.
-8~
c.
-so
d.
-3S
ll=-d+lS
11
b.
-4
c.
4
d.
6
a.
30.
a.
S
31. Which properties of equality justify steps c and f?
a.
23 = -11-
4x
b.
23=-1l+(-4x)
c.
23 + 11 = -11 + (-4x) + 11
d.
23+11 =-11+
e.
34
34
f.
-
-4
= -4x
-4x
---
-4
-8.S =x
g.
a.
b.
c.
d.
11 + (-4x)
Subtraction Property of Equality; Multiplication Property of Equality
Addition Property of Equality; Division Property of Equality
Addition Property of Equality; Subtraction Property of Equality
Multiplication Property of Equality; Division Property of Equality
Solve the inequality. Then graph your solution.
32. -.!. ~ 2
4
a. x ~-8
(
b.
I
-10
c.
•
-8
I
-6
I
-4
I
-2
I
0
.j
6
I
8
I
d.
I
I
I
--4
-2
I
0
2
.j
•
6
8
I
10
I
-iO -8
10
x~6
-10 -8 -6
x~8
)
---'l
-1
I
0
2
I
I
-6 -4
-
I
0
2
4
x~-8
I
-10
6
I
-6
•
-8
I
"
I
6
•
8
,
I
6
8
I
10
I
10
)
)
33.
E.>-6
4a.
x::;;-24
(
b.
c.
-28
-24
•
I
-20
I
-J6
I
I
-l~ -12
•
I
-S
I
-6
I
-32
I
I
-12
-S
-.f
I
0
)
-31
x2:-lO
d.
-10
I
-.f
-"
I
0
I
2
x 2: -24
)
X
(
34. Evaluate b - 2a - c for a = -7, b = 3, and c =-7.
a. 24
b. 3
c.
I
-28
•
-14
I
-20
I
-16
I
-12
I
0
I
2
10
4
•
I
6
I
12
10
d. -18
3
a.
-8
36. Evaluate
a. 4
b.
-3
I-x - 4'! for x = -2
b.
8
andy
c.
8
d.
4
c.
-4
d.
-8
= 3.
7
-.f
I
0
)
2: 10
Complete the equation, by supplying the missing exponent.
35.
I
-8
I
l~
I
16
I)
18
37.
a. Find the value of a.
b. Find the value of the marked angles.
(4a + 12)°
(3a
a.
not drawn to scale
22; 100°
+ 32)0
b.
19; 88°
c.
20; 92°
c.
0.805
c.
d.
7m-2=8m+4-m
8y + 9 = 8y - 3
c.
j =-25
d.
j=-15
d.
24; 108°
d.
8.05
Write the number in scientific notation.
38.
0.0805
a.
80.S x 100-3
b.
8.05 x 10
39. Which equation is an identity?
a.
11 - (2v + 3) = -2v - 8
b. Sw+ 8-w = 6w -2(w- 4)
40.
I~I +1
a.
b.
=-4
no solution
= 15 or -15
j
8
~--.-
..---
--------
..
-
..
X
_._--_
.._.
__
.....
__ .... _---
10-1
X
10-2
41. Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms.
2 -- l lx? - 8x + 6x2
a.
b.
42.
- 5x2 - 8x + 2~quadratic trinomial
5x2 - 8x - 2; quadratic trinomial
c.
d.
-6X2 -
6x2
-
8x - 2; cubic polynomial
8x + 2; cubic trinomial
The length of a rectangle is 5 centimeters less than twice its width. The perimeter of the rectangle is 26 em,
What are the dimensions of the rectangle?
a. length = 5 em; width = 5 em
c. length = 6 em; width = 7 em
b. length = 7 em; width = 6 em
d. length = 4 em; width = 9 em
Write the number in standard notation.
43.
9 x 104
a.
44.
c.
9,000
90,000
360
School guidelines require that there must be at least 2 chaperones for every 25 students going on a school trip.
How many chaperones must there be for 80 students?
a. 6 chaperones
c. 3 chaperones
b. 40 chaperones
d. 7 chaperones
Find the square.
45.
d.
(4x - 6y3)2
a.
b.
16x2
16x2
-
24xy3 + 36y"
48xy3 + 36y6
C.
d.
9
16x2 + 36y6
16x2 -- 4xy3 + 36y6
__
46. Write the perimeter of the figure.
3x + 2
6x
5x
not to scale
a.
__
47.
9x+ Tx
b.
llx+ 3x+ 2
c.
14x + 2
d.
14x
d.
18
The perimeter of the rectangle is 24 em. Find the value ofx.
3 em
D1HlTI
a.
3
b.
12
c.
8
3
10
_
-._-_._._._--------------_._--------.-_
..
----
48.
49.
The sum offour consecutive odd integers is -72. Write an equation to model this situation, and find the values
of the four integers.
a. n + (n - 2) + (n - 4) + (n - 6) = - 72;
n = - 21; 11 - 2 = - 23; n - 4 = - 25; 11 - 6 = - 27
b. n + n + 2 + n + 4 + n + 6 = - 72;
n = - 21; 11 + 2 = - 23; n + 4 = - 25; 11 + 6 = - 27
c. 11 - (n + 2) - (n + 4) - (n + 6) = - 72;
n = -20: 11 + 2 = -18; 11 + 4 = -16; n + 6 = -14
d. n + n + 2 + n + 4 + n + 6 = - 72;
11 = - 21; 11 + 2 = - 19; n + 4 = - 17; 11 + 6 = - 15
Ixl-7=6
a.
x = 13
b.
x
=
13 or x
= -13
c.
d.
x=-1
no solution
c.
d.
7p8 + lOp7 + 7p5 + 4pi
12pl6 + 21pl2 + 15p4
c.
6
Simplify the product.
50.
3p4(4p4 + 7p3 + 4p + 1)
l2ps + 3p7 + 4p5 + pi
b. 12p8 + 21p7 + 12p5 + 3p4
a.
Find the degree of the monomial.
5l.
7m6n5
a. 5
b.
11
d.
7
Complete.
52.
Z2
a.
b.
+ 9z - 90
=
(z - 6)(z + %£l )
-9
15
c.
90
d.
-15
11
~~
..---.--
..•
--------
-
-.
---------.---.-------~------.--.-.--------------------~~~~--------
Simplify the expression. Write the answer using scientific notation.
53.
(4 x I08r2
a.
54.
17
6.25 x 10-
h.
6.25
X
10-18
C.
0.0625
X
10-16
d.
-8
X
10-16
Simplify.
(2n2 + 4n + 4)(4n - 5)
a.
8n3 + 26n2
b.
8n3
+
-
6n2 -
36n - 20
411 - 20
d.
8n3 + 4n2 - 6n - 20
8n3 - 6n2 + 36n - 20
C.
x<--
C.
Solve the inequality.
55.
12x-3x+ll>4x-(17-9x)
a.
56.
x>-7
h.
x<7
14
11
d.
x>--
14
11
Determine whether the statement is sometimes, always or never true.
4
If ax + b - 4 = b and a o then x = -.
a
a. always
b. sometimes
c. never
*
Identify the graph of the inequality from the given description.
57. x is negative.
a.
( I i
-+
b.
(
I
~5
-3
I
-2
I
-I
0
0
-3
-2
I
-I
•
I
-+
0
C.
2
I
d.
-5
'I
12
-2
I
-1
•
-2
I
-1
0
0
I
-5
4
--4
I
-4
-3
0
I
2
I
4
I
)
I
4
I
)
Simplify the difference.
58. (-7x-5x4+5)-(-7x4-5-9x)
a. 2.\,4 + 2x + 8
b. -14x4 + lOx + 10
c.
d.
-14.\,4 - lOx + 10
2x4 + 2x + 10
c.
19
4
Solve the proportion.
59.
w + 14
4w + 6
a.
__
3
4
8
19
b.
15
28
d.
2
7
60. Find the area of the UN SHADED region. Both figures are squares. Write your answer in standard form.
x
x+5
+ lOx + 25
+ 8x + 25
a.
_2X2
c.
b.
X2
d.
13
lOx + 25
+ lOx + 25
X2
ID: D
ALGEBRA 2011 FIRST SE~IESTERFINAL
Answer Section
MUL TIPLE CHOICE
1. C
2. B
3. B
4. A
5. C
6. C
7. D
8. D
9. A
10. C
11. D
12. B
13. B
14. C
15. A
16. A
17. B
18. B
19. A
20. D
21. C
22. D
23. C
24. A
25. D
26. B
27. C
28. A
29. D
30. C
3l. B
32. D
33. C
34. A
35. C
36. A
37. C
38. D
1
ID: D
39. B
40. A
41. A
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
B
C
D
B
C
A
D
B
B
B
52.
53.
54.
55.
56.
57.
58.
B
B
B
B
A
A
D
59.
C
60.
C
2