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Same as the last one–
” r
..
,..
—–~· —
, … ……._ _

~ .,
-~
–.. – – –
.. – –
– –
, …… _ .. -tr _ : _ __ .__
……… if
/
“”11r
– — – ···· –1 ,— ………. . ……… ··-· …. ‘– . .. . . _ __ –
Q1. Solve the system.
x + 2y= -9
{ Sx + 10y = -45
0
0
0
b. (-9, 0)
c. (0, 0)
0
d. y
a. inconsistent (no solution)
=-
x
2
– 9, where xis any real number
Q2. The Family Fine Arts Center charges \$21 per adult and \$12 per senior citizen for its
performances. On a recent weekend evening when 486 people paid admission, the total receipts
were \$6894. How many who paid were senior citizens?
0
a. 208 senior citizens
0
b. 368 senior citizens
0
c. 118 senior citizens
0
d. 278 senior citizens
Q3. Solve the system using the inverse method.
x
+
2y + 3z = -2
x + y + z = -7
{ -x + y + 2z = -10
0
0
a. x = -19, y = -61, z = -35
0
c. x = 15, y = -49, z = 27
d. x = -2, y = -28, z = 20
0
b. x = -1, y = -3, z = -2
Q4. Solve the system using the inverse method.
2x + 6y= 2
{ 2x- y = -5
0
= 1, y = -2
0
a. x
b. x
0
c. x
= -1,
0
d. x
= 2, y = -1
= -2, y = 1
=2
y
QS. Verify that the values of the variables listed are solutions of the system of equations.
x – y + 3z = -7
3x
+ z=-4
{
x+3y+ z=-19
x = o, y = -s, z =-4
0
0
a. solution
b . not a solution
Q6. Find the inverse of the matrix.
[-~ ~ 1
0
a.
]..
4
0
b.
:
24
0
c.
l
_~ l
~4 -~
0
6
~41 ! 1
— 0
4
0
0
d.
1
6
1
5
4
24
Q7. Solve the system of equations.
x-y+2z=-1
2x+z=0
{
x+Sy+z=S
0
0
0
0
a . x = O, y = 1, z = O
b. x = 1, y =1, z = 1
c. x = 0, y = 1, z = -1
d. x = 0, y = 0, z = 1
QB. A retired couple has \$190,000 to invest to obtain annual income. They want some of it invested
in safe Certificates of Deposit yielding 7%. The rest they want to invest in AA bonds yielding 10%
per year. How much should they invest in each to realize exactly \$17,200 per year?
0
0
0
0
a.
b.
c.
d.
\$120,000 at
\$130,000 at
\$130,000 at
\$140,000 at
7% and \$70,000 at 10%
7% and \$60,000 at 10%
10% and \$60,000 at 7%
10% and \$50,000 at 7%
Q9. Write the partial fraction decomposition of the rational expression.
3×3 + 2×2
(x2 + 5)2
0
a.
3x + 2
x2+s
+
15x + 10
(x2 + 5)2
0
b.
3x + 2
x2+s
+
15x – 10
(x2 + 5)2
0
c.
3x + 2
x2+s
+
-lSx-10
(x2 + 5)2
0
d.
3x – 2
x2+s
+
-15x+10
(x2 + 5)2
Q10. Perform the indicated operations and simplify.
Let A=
[ 3 -4]
0
a.
[-1532
0
b.
[68 3
8 -2
0
c.
r-10 -19 12J
-15 31 -25
0
d.
[32
7
5 -23
‘B
-2 5
= rs1 -20 -38]
19 40]
31 -37
, and C
=
u ri
-9
-5
6
31]
-5
50]
-37
Q11. Use the elimination method to solve the system.
2x+10y= -72
{ 11x + 2y = 81
0
0
a. x = 11, y = -11
b. x = -2, y = 9
c. x = 9, y = -9
0
d. x
0
= -9,
y
=9
Q12. Find the inverse of the matrix.
[ 41
0
~]
a. No inverse
. Find AB
+ BC.
0
15
4
4
-15
b.
0
l
4
1
—15 15
c.
1
– 4- – 15
0
15
1
1
15
4
15
d.
15
1
15
4
1
15
15
Q13. Solve the system using the inverse method.
x + 2y + 3z = 2
x + y + z = -12
{
2x + 2y + z = 10
0
0
= -36, y = -38, z = -14
= -14, y = 88, z = -32
c. x = -60, y = 82, z = -34
d. x = 8, y = 24, z = 10
a. x
b.
0
0
x
Q14. An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in
highway driving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were
driven in the city?
0 a . 153 miles
0
b. 168 miles
0
0
c. 147 miles
d. 132 miles
Q15. Use the properties of determinants to find the value of the second determinant, given the
value of the first.
s t u
v w x
4 2 8
Given
0
a. -24
0
b. -3
c. 24
d. 3
0
0
>
=3, find the value of
32 – s 16 – t 64 – u
v
w
x
8
4
2
>.
Q16. Use the properties of determinants to find the value of the second determinant, given the
value of the first.
x
u
y z
vw
1 -1 3
0
0
0
0
a. -44
b. 44
c. 88
d. -88
UV W
= -44
-2 2 -6
xy z
=?
Q17. A movie theater charges \$8.00 for adults and \$5.00 for children. If there were 40 people
altogether and the theater collected \$272.00 at the end of the day, how many of them were adults?
0
0
0
0
Q18. Verify that the values of the variables listed, are solutions of the system of equations.
x +y = 0
{ x-y=-10
x 5, y 5
=
=
0
a. not a solution
0
b. solution
Q19. Perform the indicated operation, whenever possible.
r-! ~ 1 – r-~ ~ 1
0
0
a. [-2]
0
c.
0
d.
b.
[-~ -~ 1
r-~ ~ 1
[~ -~ 1
Q20. Jenny receives \$1270 per year from three different investments totaling \$20,000. One of the
investments pays 6°/o , the second one pays 8°/o, and the third one pays 5°/o. If the money invested
at 80/o is \$1500 less than the amount invested at 5010, how much money has Jenny invested in the
investment that pays 6°/o?
0 a. \$8500
0 b. \$4500
0 c. \$10,000
0 d. \$1500
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