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Complete Solutions to Practice Test -17-
1. What are the solutions to the quadratic equation ?036152 xx
A. 3, 6
B. 6, 6
C. 3, 12
D. 4, 9
E. -4, -9
Factor. You need two numbers that will multiply
to 36 and add to -15.
× = 36
1 36
2 18
3 12
4 9
6 6
+
37
2015
13
12
036152 xx
0)3)(12( xxNow use the zero factor property.
012 x12x
03 x3x
}12,3{x
Answer C
2. If for all x and y, , then
A.
B.
C.
D.
E. undefined
xy 2
xy 2xy 2yx 2
?b02 ybx
Solve for b.
02 ybxAdd b to
both sides.
bb byx 2
Answer A
3. For all
A.
B.
C.
D.
E.
,4x ?4
1682
x
xx
4x
4x
8x
8x
20x
Factor.
)4(
)4)(4(
4
1682
x
xx
x
xx
Cancel. )4( x
Answer B
4. What is the value of the expression when
A.
B.
C.
D.
E.
xxxx 8534 ?2x
4068
648
64
10756
6166
)2(8)2(5)2(3)2(4
Substitute and simplify.
161068
)4(1068
4068
Answer A
5. If then
A. 0 B. 4 C. 9 D. 25 E. no solution
9554,1 xx
?xRadical Equation
First isolate the radical.
9554 xSubtract 4 from
both sides. 44 555 xSquare both sides to
get rid of the radical. 22555 x
2555 xSubtract 5 from
both sides.
55 205 xDivide by 5.
4xAnswer B
6. For all
A.
B.
C.
D.
E.
?2500and0 49 yxyx
7283 yx
yxyx 222 510
105 23 yx
xyx 105 24
35 23 yx
Find the square root of x9.
9x xxxxxxxxx
Each pair of (xx) inside represents one x outside.
xxxxx
xx4Choice D is the only answer
that matches this result.
7. If the ratio of 4 to b is 5 to 7 then b = ?
A. 3
B.
C.
D. 16
E.
5
28
4
35
7
20
Write the proportion as two equal fractions.
7
54
b
Cross multiply. b5)7(4 b528
Divide by 5.
5
5
5
28 b
b5
28Answer B
8. Simplify
A.
B.
C.
D.
E.
3
2
5
b
a
5
8
b
a
6
15
b
a
8
128
b
a
2
53
b
a
3
2
3
5
b
a
When raising a power to a power multiply the exponents.
3
2
5
b
a 32
35
b
a
6
15
b
a
Answer B
9. Simplify
A.
B.
C. 6
D.
E.
?3
32
2
32
324
3
3226
3
324
5
352
Simplify the radicals.
3
32
2
)2(16
3
32
2
243
32
1
22
The common denominator is 3
3
32
1
22
3
3
3
3226
Answer B
10. Which equation best describes this graph?
A.
B.
C.
D.
E.
6
4
2
-2
-5
(-1, 4)322 xxy
322 xxy
322 xxy
362 xxy
432 xxy
The y-intercept of the graph is (0, 3).
This eliminates choices A and E.
The point (0, 3) works in B, C, and D.
10. Which equation best describes this graph?
A.
B.
C.
D.
E.
6
4
2
-2
-5
(-1, 4)322 xxy
322 xxy
322 xxy
362 xxy
432 xxy
Try the point (-1, 4) in B.
3)1(2)1(4 2 3214
04 Try the point (-1, 4) in D.
3)1(6)1(4 2 3614
84
This eliminates choice B.
This eliminates choice D.
10. Which equation best describes this graph?
A.
B.
C.
D.
E.
322 xxy
322 xxy
322 xxy
362 xxy
432 xxy
Try the point (-1, 4) in C.
3)1(2)1(4 2 3214
44
Answer C
11. For all B and C and A ≠ 0, if then A.
B.
C.
D.
E.
C
AB
C
BA
C
AB
A
BC
B
AC
CBAx ?x
Solve for x
CBAx BB
BCAx
Subtract B
Divide by A
A
BC
A
Ax
A
BCx
Answer D
5
23
3
24
12. Simplify
A.
B.
C.
D.
E.
5
18
3
32
3
2
15
229
3
25
8
25
8
50
5
18
3
32 5
)2(9
3
)2(16
Simplify the radicals
The common denominator
is 15
5
23
3
3
3
24
5
5
15
29
15
220
15
229
Answer D
13. If 25 is subtracted from the square of a certain number b the result is 11. Which of the following equations determines the correct value of b?
A.
B.
C.
D.
E. 11252 b
1125 2 b
1215 b
25112 b
11252 b
Since the result is 11 we can expect the equation to = 11. Eliminate choices A, B, and C.
The word “from” indicates that the equation will start with b2.
Answer E or B
14. For all x,
A.
B.
C.
D.
E.
?)1032()753( 22 xxxx
382 xx
322 xx
1782 xx
1785 2 xx
325 2 xx
Distribute the negative through the second parenthesis. Make sure you change all the signs.
Combine like terms.
2x x8 3
1032753 22 xxxx
Answer A
15. If the reciprocal of a certain number x is added to the result is 2. What is x?
A. 1
B. 2
C. 3
D. -2
E. -3
3
5
If x is the number then the reciprocal of x is…
x
1
23
51
x)3( x )3( x
Multiply by 3x to clear the denominators.
xx 653 xx 55
x3
Answer C
16. Find the value of when
A. 12
B. 24
C. 36
D. 48
E. 60
xxxx 23182 .2x
222321822 Substitute x = 2
46364 2664
1224
36
Answer C
17. Which equation best describes this graph?
A.
B.
C.
D.
E.
562 xxy
562 xxy
562 xxy
562 xxy
432 xxy
6
4
2
-2
-4
5
(0, 5)
(3, -4)
The point (0, 5) does not work in choices C, D, or E.
Try the point (3, -4) in choice B.
5)3(6)3()4( 2 51894
324 Verify choice A, try the point
(3, -4) .
5)3(6)3(4 2 51894
594 44
Answer A
18 In the standard rectangular coordinate plane find the distance between (-3, 4) and (2 , -8).
A. 12
B. 13
C. 25
D. 144
E. 169
Use the distance formula.
212
212 )()( yyxxd
22 )48()32( d
22 )12()5( d
14425d
169d 13
Answer B
19 For all x,
A.
B.
C.
D.
E.
?)53( 2 x
259 2 x
259 2 x
25159 2 xx
25159 2 xx
25309 2 xx
)53)(53()53( 2 xxx
29x x15 x15 25
25309 2 xx
Answer E
20. For all
A.
B.
C.
D.
E.
?)32(3)3(, 2 babbaba
aba 62
22 18ba
22 186 baba
baba 1862 2
2a
)32(3)3( 2 babba
296)3)(3( babbaba
222 96933 babbababa
ababa 662 2a
Answer E
21. For all ?35832,2 xxxxx
A.
B.
C.
D.
E.
2610
621
6516
65205
31
)2(35)2(83)2(2)2(
6516342
65)4(3)2(2
65124
6516
Answer C
22. If x = -2 and y = 5, what is the value of the expression 2x3 – 3xy ?
A. 14
B. 46
C. 54
D. -46
E. -54
2x3 – 3xy
2(-2)3 – 3(-2)(5)
2(-8) – 3(-10)
-16 – -30
-16+30 = 14
23. What are the solutions to the quadratic equation x2 – 2x = 48? A. -12, -4
B. -8, -6
C. 6, 8
D. -6, 8
E. -8, 6
Set the equation equal to zero.
x2 – 2x = 48
x2 – 2x – 48 = 0
Factor
(x + 6)(x – 8) = 0
Write a solution set.
x = {-6 , 8}
24. For all x ±3,
A.
B.
C.
D.
E.
3
4
x
x
3
4
x
x
3
4
x
x
3
4
x
x
9
127
x
?9
1272
2
x
xx
24. For all x ±3, ?9
1272
2
x
xx
9
1272
2
x
xx
Rational Expression
Factor
)3)(3(
)4)(3(
xx
xx
Cancel
)3(
)4(
x
x
This is a match for D
25. Which is the complete factorization of
5y3 – 125y
Factor out the common 5y
5y(y2 – 25)
Difference of squares
5y(y + 5)(y – 5)
?1255 3 yy )255( 2 yy
)25(5 2 yy
)5)(5(5 yyy
2)5(5 yy
2)5(5 yy
A.
B.
C.
D.
E.
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