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

a. 16 adults

b. 10 adults

0

0

c. 29 adults

d. 24 adults

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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