take home quizes al-jaber

8/17/2019 Take Home Quizes Al-jaber

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Math 103 Formula Sheet

Financial Management

Simple Interest: I nt rt = P Future Value for Simple

Interest:V F = P

Future Value forCompound Interest:

V (1 ) F = P +n

r nt Present Value forCompound Interest:

P = F V ( 1 + )r

n

Future Value forcontinuous compounding:

V e F = P r · t Effective Annual Yield: AY E = (

Future Value of anAnnuity(Pmt is the amount of eachdeposit):

V F = ( )r n

P mt [ ( 1 + ) 1 ]r nn t

−

Periodic deposits for anAnnuity(FV is the future value of

the annuity):

mt P = F

[ ( 1

Periodic MortgagePayments(B is the amount ofmortgage):

mt P = B ( )r

n

[ 1 ( 1 + ) ]− r nn t −

Probability and Counting Rules Permutation rule: P .n k =

n !( n k )!−

Combination rule: C .n k

( E ) ( E ) P = 1 − P ( E ) ( E ) P = 1 − P

( A or B ) ( A) ( B ) P = P + P ( A or B ) ( A) ( B ) ( A and B ) P = P + P − P

( A and B ) ( A)· P ( B ) P = P ( B giv en A) P =n u m b e r of o u t c o m e s within

n u m b e r of common o u t c o m e s f

Statistics Mean forindividualdata:

x =n

∑

x

Mean for grouped data:

x =n

· x∑

f m

StandardDeviation:

s =n 1−

∑

( x x)− 2

Z-score: z = s

x x−

= x mean

x= data values add all the values∑

= f = frequency = class or class midpoint xm s =


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Standard Normal Distribution Cumulative Probabilities (Percentiles)

T a b l e V a l u e s r e p r e s e n t a r e a t o t h e l e f t o f z

Z 0 . 0 0 0 . 0 1 0 .0 2 0 . 0 3 0 . 0 4 0 . 0 5 0 . 0 6 0 . 0 7 0 . 0 8

- 3 .0 0 0 . 0 0 1 3 0 . 0 0 1 3 0 .0 0 1 3 0 . 0 0 1 2 0 . 0 0 1 2 0 . 0 0 1 1 0 . 0 0 1 1 0 . 0 0 1 1 0 . 0 0 1 0

- 2 .9 0 0 . 0 0 1 9 0 . 0 0 1 8 0 .0 0 1 8 0 . 0 0 1 7 0 . 0 0 1 6 0 . 0 0 1 6 0 . 0 0 1 5 0 . 0 0 1 5 0 . 0 0 1 4

- 2 .8 0 0 . 0 0 2 6 0 . 0 0 2 5 0 .0 0 2 4 0 . 0 0 2 3 0 . 0 0 2 3 0 . 0 0 2 2 0 . 0 0 2 1 0 . 0 0 2 1 0 . 0 0 2 0

- 2 .7 0 0 . 0 0 3 5 0 . 0 0 3 4 0 .0 0 3 3 0 . 0 0 3 2 0 . 0 0 3 1 0 . 0 0 3 0 0 . 0 0 2 9 0 . 0 0 2 8 0 . 0 0 2 7

- 2 .6 0 0 . 0 0 4 7 0 . 0 0 4 5 0 .0 0 4 4 0 . 0 0 4 3 0 . 0 0 4 1 0 . 0 0 4 0 0 . 0 0 3 9 0 . 0 0 3 8 0 . 0 0 3 7

- 2 .5 0 0 . 0 0 6 2 0 . 0 0 6 0 0 .0 0 5 9 0 . 0 0 5 7 0 . 0 0 5 5 0 . 0 0 5 4 0 . 0 0 5 2 0 . 0 0 5 1 0 . 0 0 4 9

- 2 .4 0 0 . 0 0 8 2 0 . 0 0 8 0 0 .0 0 7 8 0 . 0 0 7 5 0 . 0 0 7 3 0 . 0 0 7 1 0 . 0 0 6 9 0 . 0 0 6 8 0 . 0 0 6 6

- 2 .3 0 0 . 0 1 0 7 0 . 0 1 0 4 0 .0 1 0 2 0 . 0 0 9 9 0 . 0 0 9 6 0 . 0 0 9 4 0 . 0 0 9 1 0 . 0 0 8 9 0 . 0 0 8 7

- 2 .2 0 0 . 0 1 3 9 0 . 0 1 3 6 0 .0 1 3 2 0 . 0 1 2 9 0 . 0 1 2 5 0 . 0 1 2 2 0 . 0 1 1 9 0 . 0 1 1 6 0 . 0 1 1 3

- 2 .1 0 0 . 0 1 7 9 0 . 0 1 7 4 0 .0 1 7 0 0 . 0 1 6 6 0 . 0 1 6 2 0 . 0 1 5 8 0 . 0 1 5 4 0 . 0 1 5 0 0 . 0 1 4 6

- 2 .0 0 0 . 0 2 2 8 0 . 0 2 2 2 0 .0 2 1 7 0 . 0 2 1 2 0 . 0 2 0 7 0 . 0 2 0 2 0 . 0 1 9 7 0 . 0 1 9 2 0 . 0 1 8 8

- 1 .9 0 0 . 0 2 8 7 0 . 0 2 8 1 0 .0 2 7 4 0 . 0 2 6 8 0 . 0 2 6 2 0 . 0 2 5 6 0 . 0 2 5 0 0 . 0 2 4 4 0 . 0 2 3 9

- 1 .8 0 0 . 0 3 5 9 0 . 0 3 5 1 0 .0 3 4 4 0 . 0 3 3 6 0 . 0 3 2 9 0 . 0 3 2 2 0 . 0 3 1 4 0 . 0 3 0 7 0 . 0 3 0 1

- 1 .7 0 0 . 0 4 4 6 0 . 0 4 3 6 0 .0 4 2 7 0 . 0 4 1 8 0 . 0 4 0 9 0 . 0 4 0 1 0 . 0 3 9 2 0 . 0 3 8 4 0 . 0 3 7 5

- 1 .6 0 0 . 0 5 4 8 0 . 0 5 3 7 0 .0 5 2 6 0 . 0 5 1 6 0 . 0 5 0 5 0 . 0 4 9 5 0 . 0 4 8 5 0 . 0 4 7 5 0 . 0 4 6 5

- 1 .5 0 0 . 0 6 6 8 0 . 0 6 5 5 0 .0 6 4 3 0 . 0 6 3 0 0 . 0 6 1 8 0 . 0 6 0 6 0 . 0 5 9 4 0 . 0 5 8 2 0 . 0 5 7 1

- 1 .4 0 0 . 0 8 0 8 0 . 0 7 9 3 0 .0 7 7 8 0 . 0 7 6 4 0 . 0 7 4 9 0 . 0 7 3 5 0 . 0 7 2 1 0 . 0 7 0 8 0 . 0 6 9 4

- 1 .3 0 0 . 0 9 6 8 0 . 0 9 5 1 0 .0 9 3 4 0 . 0 9 1 8 0 . 0 9 0 1 0 . 0 8 8 5 0 . 0 8 6 9 0 . 0 8 5 3 0 . 0 8 3 8

- 1 .2 0 0 . 1 1 5 1 0 . 1 1 3 1 0 .1 1 1 2 0 . 1 0 9 3 0 . 1 0 7 5 0 . 1 0 5 6 0 . 1 0 3 8 0 . 1 0 2 0 0 . 1 0 0 3

- 1 .1 0 0 . 1 3 5 7 0 . 1 3 3 5 0 .1 3 1 4 0 . 1 2 9 2 0 . 1 2 7 1 0 . 1 2 5 1 0 . 1 2 3 0 0 . 1 2 1 0 0 . 1 1 9 0

- 1 .0 0 0 . 1 5 8 7 0 . 1 5 6 2 0 .1 5 3 9 0 . 1 5 1 5 0 . 1 4 9 2 0 . 1 4 6 9 0 . 1 4 4 6 0 . 1 4 2 3 0 . 1 4 0 1

- 0 .9 0 0 . 1 8 4 1 0 . 1 8 1 4 0 .1 7 8 8 0 . 1 7 6 2 0 . 1 7 3 6 0 . 1 7 1 1 0 . 1 6 8 5 0 . 1 6 6 0 0 . 1 6 3 5 - 0 .8 0 0 . 2 1 1 9 0 . 2 0 9 0 0 .2 0 6 1 0 . 2 0 3 3 0 . 2 0 0 5 0 . 1 9 7 7 0 . 1 9 4 9 0 . 1 9 2 2 0 . 1 8 9 4

- 0 .7 0 0 . 2 4 2 0 0 . 2 3 8 9 0 .2 3 5 8 0 . 2 3 2 7 0 . 2 2 9 6 0 . 2 2 6 6 0 . 2 2 3 6 0 . 2 2 0 6 0 . 2 1 7 7

- 0 .6 0 0 . 2 7 4 3 0 . 2 7 0 9 0 .2 6 7 6 0 . 2 6 4 3 0 . 2 6 1 1 0 . 2 5 7 8 0 . 2 5 4 6 0 . 2 5 1 4 0 . 2 4 8 3

- 0 .5 0 0 . 3 0 8 5 0 . 3 0 5 0 0 .3 0 1 5 0 . 2 9 8 1 0 . 2 9 4 6 0 . 2 9 1 2 0 . 2 8 7 7 0 . 2 8 4 3 0 . 2 8 1 0

- 0 .4 0 0 . 3 4 4 6 0 . 3 4 0 9 0 .3 3 7 2 0 . 3 3 3 6 0 . 3 3 0 0 0 . 3 2 6 4 0 . 3 2 2 8 0 . 3 1 9 2 0 . 3 1 5 6

- 0 .3 0 0 . 3 8 2 1 0 . 3 7 8 3 0 .3 7 4 5 0 . 3 7 0 7 0 . 3 6 6 9 0 . 3 6 3 2 0 . 3 5 9 4 0 . 3 5 5 7 0 . 3 5 2 0

- 0 .2 0 0 . 4 2 0 7 0 . 4 1 6 8 0 .4 1 2 9 0 . 4 0 9 0 0 . 4 0 5 2 0 . 4 0 1 3 0 . 3 9 7 4 0 . 3 9 3 6 0 . 3 8 9 7

- 0 .1 0 0 . 4 6 0 2 0 . 4 5 6 2 0 .4 5 2 2 0 . 4 4 8 3 0 . 4 4 4 3 0 . 4 4 0 4 0 . 4 3 6 4 0 . 4 3 2 5 0 . 4 2 8 6

- 0 .0 0 0 . 5 0 0 0 0 . 4 9 6 0 0 .4 9 2 0 0 . 4 8 8 0 0 . 4 8 4 0 0 . 4 8 0 1 0 . 4 7 6 1 0 . 4 7 2 1 0 . 4 6 8 1


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For values of z less than -3.09 use 0.0010

Standard Normal Distribution Cumulative Probabilities (Percentiles)T a b l e V a l u e s r e p r e s e n t a r e a t o t h e l e f t o f z

Z 0 . 0 0 0 .0 1 0 . 0 2 0 .0 3 0 . 0 4 0 .0 5 0 . 0 6 0 .0 7 0 . 0 8 0 .0 9

0 . 0 0 0 . 5 0 0 0 0 . 5 0 4 0 0 . 5 0 8 0 0 . 5 1 2 0 0 . 5 1 6 0 0 . 5 1 9 9 0 . 5 2 3 9 0 . 5 2 7 9 0 . 5 3 1 9 0 . 5 3 5 9

0 . 1 0 0 . 5 3 9 8 0 . 5 4 3 8 0 . 5 4 7 8 0 . 5 5 1 7 0 . 5 5 5 7 0 . 5 5 9 6 0 . 5 6 3 6 0 . 5 6 7 5 0 . 5 7 1 4 0 . 5 7 5 3

0 . 2 0 0 . 5 7 9 3 0 . 5 8 3 2 0 . 5 8 7 1 0 . 5 9 1 0 0 . 5 9 4 8 0 . 5 9 8 7 0 . 6 0 2 6 0 . 6 0 6 4 0 . 6 1 0 3 0 . 6 1 4 1

0 . 3 0 0 . 6 1 7 9 0 . 6 2 1 7 0 . 6 2 5 5 0 . 6 2 9 3 0 . 6 3 3 1 0 . 6 3 6 8 0 . 6 4 0 6 0 . 6 4 4 3 0 . 6 4 8 0 0 . 6 5 1 7

0 . 4 0 0 . 6 5 5 4 0 . 6 5 9 1 0 . 6 6 2 8 0 . 6 6 6 4 0 . 6 7 0 0 0 . 6 7 3 6 0 . 6 7 7 2 0 . 6 8 0 8 0 . 6 8 4 4 0 . 6 8 7 9

0 . 5 0 0 . 6 9 1 5 0 . 6 9 5 0 0 . 6 9 8 5 0 . 7 0 1 9 0 . 7 0 5 4 0 . 7 0 8 8 0 . 7 1 2 3 0 . 7 1 5 7 0 . 7 1 9 0 0 . 7 2 2 4

0 . 6 0 0 . 7 2 5 7 0 . 7 2 9 1 0 . 7 3 2 4 0 . 7 3 5 7 0 . 7 3 8 9 0 . 7 4 2 2 0 . 7 4 5 4 0 . 7 4 8 6 0 . 7 5 1 7 0 . 7 5 4 9

0 . 7 0 0 . 7 5 8 0 0 . 7 6 1 1 0 . 7 6 4 2 0 . 7 6 7 3 0 . 7 7 0 4 0 . 7 7 3 4 0 . 7 7 6 4 0 . 7 7 9 4 0 . 7 8 2 3 0 . 7 8 5 2

0 . 8 0 0 . 7 8 8 1 0 . 7 9 1 0 0 . 7 9 3 9 0 . 7 9 6 7 0 . 7 9 9 5 0 . 8 0 2 3 0 . 8 0 5 1 0 . 8 0 7 8 0 . 8 1 0 6 0 . 8 1 3 3

0 . 9 0 0 . 8 1 5 9 0 . 8 1 8 6 0 . 8 2 1 2 0 . 8 2 3 8 0 . 8 2 6 4 0 . 8 2 8 9 0 . 8 3 1 5 0 . 8 3 4 0 0 . 8 3 6 5 0 . 8 3 8 91 . 0 0 0 . 8 4 1 3 0 . 8 4 3 8 0 . 8 4 6 1 0 . 8 4 8 5 0 . 8 5 0 8 0 . 8 5 3 1 0 . 8 5 5 4 0 . 8 5 7 7 0 . 8 5 9 9 0 . 8 6 2 1

1 . 1 0 0 . 8 6 4 3 0 . 8 6 6 5 0 . 8 6 8 6 0 . 8 7 0 8 0 . 8 7 2 9 0 . 8 7 4 9 0 . 8 7 7 0 0 . 8 7 9 0 0 . 8 8 1 0 0 . 8 8 3 0

1 . 2 0 0 . 8 8 4 9 0 . 8 8 6 9 0 . 8 8 8 8 0 . 8 9 0 7 0 . 8 9 2 5 0 . 8 9 4 4 0 . 8 9 6 2 0 . 8 9 8 0 0 . 8 9 9 7 0 . 9 0 1 5

1 . 3 0 0 . 9 0 3 2 0 . 9 0 4 9 0 . 9 0 6 6 0 . 9 0 8 2 0 . 9 0 9 9 0 . 9 1 1 5 0 . 9 1 3 1 0 . 9 1 4 7 0 . 9 1 6 2 0 . 9 1 7 7

1 . 4 0 0 . 9 1 9 2 0 . 9 2 0 7 0 . 9 2 2 2 0 . 9 2 3 6 0 . 9 2 5 1 0 . 9 2 6 5 0 . 9 2 7 9 0 . 9 2 9 2 0 . 9 3 0 6 0 . 9 3 1 9

1 . 5 0 0 . 9 3 3 2 0 . 9 3 4 5 0 . 9 3 5 7 0 . 9 3 7 0 0 . 9 3 8 2 0 . 9 3 9 4 0 . 9 4 0 6 0 . 9 4 1 8 0 . 9 4 2 9 0 . 9 4 4 1

1 . 6 0 0 . 9 4 5 2 0 . 9 4 6 3 0 . 9 4 7 4 0 . 9 4 8 4 0 . 9 4 9 5 0 . 9 5 0 5 0 . 9 5 1 5 0 . 9 5 2 5 0 . 9 5 3 5 0 . 9 5 4 5

1 . 7 0 0 . 9 5 5 4 0 . 9 5 6 4 0 . 9 5 7 3 0 . 9 5 8 2 0 . 9 5 9 1 0 . 9 5 9 9 0 . 9 6 0 8 0 . 9 6 1 6 0 . 9 6 2 5 0 . 9 6 3 3

1 . 8 0 0 . 9 6 4 1 0 . 9 6 4 9 0 . 9 6 5 6 0 . 9 6 6 4 0 . 9 6 7 1 0 . 9 6 7 8 0 . 9 6 8 6 0 . 9 6 9 3 0 . 9 6 9 9 0 . 9 7 0 6

1 . 9 0 0 . 9 7 1 3 0 . 9 7 1 9 0 . 9 7 2 6 0 . 9 7 3 2 0 . 9 7 3 8 0 . 9 7 4 4 0 . 9 7 5 0 0 . 9 7 5 6 0 . 9 7 6 1 0 . 9 7 6 72 . 0 0 0 . 9 7 7 2 0 . 9 7 7 8 0 . 9 7 8 3 0 . 9 7 8 8 0 . 9 7 9 3 0 . 9 7 9 8 0 . 9 8 0 3 0 . 9 8 0 8 0 . 9 8 1 2 0 . 9 8 1 7

2 . 1 0 0 . 9 8 2 1 0 . 9 8 2 6 0 . 9 8 3 0 0 . 9 8 3 4 0 . 9 8 3 8 0 . 9 8 4 2 0 . 9 8 4 6 0 . 9 8 5 0 0 . 9 8 5 4 0 . 9 8 5 7

2 . 2 0 0 . 9 8 6 1 0 . 9 8 6 4 0 . 9 8 6 8 0 . 9 8 7 1 0 . 9 8 7 5 0 . 9 8 7 8 0 . 9 8 8 1 0 . 9 8 8 4 0 . 9 8 8 7 0 . 9 8 9 0

2 . 3 0 0 . 9 8 9 3 0 . 9 8 9 6 0 . 9 8 9 8 0 . 9 9 0 1 0 . 9 9 0 4 0 . 9 9 0 6 0 . 9 9 0 9 0 . 9 9 1 1 0 . 9 9 1 3 0 . 9 9 1 6

2 . 4 0 0 . 9 9 1 8 0 . 9 9 2 0 0 . 9 9 2 2 0 . 9 9 2 5 0 . 9 9 2 7 0 . 9 9 2 9 0 . 9 9 3 1 0 . 9 9 3 2 0 . 9 9 3 4 0 . 9 9 3 6

2 . 5 0 0 . 9 9 3 8 0 . 9 9 4 0 0 . 9 9 4 1 0 . 9 9 4 3 0 . 9 9 4 5 0 . 9 9 4 6 0 . 9 9 4 8 0 . 9 9 4 9 0 . 9 9 5 1 0 . 9 9 5 2

2 . 6 0 0 . 9 9 5 3 0 . 9 9 5 5 0 . 9 9 5 6 0 . 9 9 5 7 0 . 9 9 5 9 0 . 9 9 6 0 0 . 9 9 6 1 0 . 9 9 6 2 0 . 9 9 6 3 0 . 9 9 6 4

2 . 7 0 0 . 9 9 6 5 0 . 9 9 6 6 0 . 9 9 6 7 0 . 9 9 6 8 0 . 9 9 6 9 0 . 9 9 7 0 0 . 9 9 7 1 0 . 9 9 7 2 0 . 9 9 7 3 0 . 9 9 7 4

2 . 8 0 0 . 9 9 7 4 0 . 9 9 7 5 0 . 9 9 7 6 0 . 9 9 7 7 0 . 9 9 7 7 0 . 9 9 7 8 0 . 9 9 7 9 0 . 9 9 7 9 0 . 9 9 8 0 0 . 9 9 8 1

2 . 9 0 0 . 9 9 8 1 0 . 9 9 8 2 0 . 9 9 8 2 0 . 9 9 8 3 0 . 9 9 8 4 0 . 9 9 8 4 0 . 9 9 8 5 0 . 9 9 8 5 0 . 9 9 8 6 0 . 9 9 8 6

3 . 0 0 0 . 9 9 8 7 0 . 9 9 8 7 0 . 9 9 8 7 0 . 9 9 8 8 0 . 9 9 8 8 0 . 9 9 8 9 0 . 9 9 8 9 0 . 9 9 8 9 0 . 9 9 9 0 0 . 9 9 9 0


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For values of z more than 3.09 use 0.9990


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Math 103 : Quiz One Name:_____ _____ ____ _____ _Location: Al JaberI nstruc tor : Alfr edo Bonilla

1. Fin d the va lue : ( ) ( 6 )− 2 − 3 + 1 3

+ 3 − 8 3

2. Fin d the va lue : [ (5 ) ( 4 )]8 − 3 − 2 − 7 − 5 − 2

3 . P e r f o r m t he i n d i c a te d o p e r a t io n s, r e d u c e t o l o we st t e r m s, a nd w r i t e t h e a n swe r a s a m i x e dnumber if po ssible: 7 )÷2( 2

1 − 331

61

4 . P e r f o r m th e i n d ic a t e d o pe r a t i o ns a n d si mp l i f y th e a n sw er i f p o ssib l e : 6 √4 8 + 3 √27 − 5√75

5 . Us e t he d is tr ib uti ve p ro pe rt y t o s im pl if y: ( )√6 √2 −√6

6 . P e r f o r m th e i n d ic a t e d o pe r a t i o n a n d r e d u ce i f p o ssib l e :a. )5

12 − (− 2

15

b. ÷( ) – 25

14

−

7

10

7 . P e r f o r m th e i n d i c at e d o p e r at i o n s a n d r ed u c e t o l o we st t e r ms:

÷2517

453 − 5

1 − 21

8. Perform the indicated operation by first expressing both numbers in Scientific notation. Write

the answer in scientific notation:

9 . F i r st u se t h e p r op e r t i es o f e x p o n e n t s t o si mp l i f y e a c h e x pr e ssi o n a n d t he n e v a l u a te i f possible.

a. ∙336 3−


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b. − 50

c.2 9

2 7

10. a. Find the prime factorization of 48 and 180.

b. Use the prime factorization to find the greatest common divisor (also called greatestcommon factor) of 48 and 180.

c. Use the prime factorization to find the least common multiple of 48 and 180.


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Math 103: Quiz Two Name:____________________Location: Al Jaber

Instructor: Alfredo Bonilla

1 . E va lu at e f o r x xy4 2 − 3 − y 2 , y x =− 2 =− 3

2 . S i mp l i f y t h e a l g e b ra i c e x p r e ssio n : [ 3 ( 2 x ) 4 x )]6 − 2 − 5 − ( − 7

3 . T h e su m o f t w o n u m b er s i s t h i r t y . U si n g z t o r e p r e se n t th e sm a l l e r n u mb e r ( a n d n o o t h e rvariables), translate "the sum of twice the larger number and negative ten" into an algebraicexpression and simplify.

4 . S ol ve : x 7 36 − 1 =− 8

5 . S o lv e th e pr o p or t io n :10

x 3− = 52

6 . S o lv e f o r r : S = P + P r t

7 . T h e b u s f a r e in a c i t y i s $ 1 .5 0 . P e o p le w h o u se t h e b u s h av e t h e o p ti o n t o p u r c ha se a m o n t hl ydiscount pass for $30. With the discount pass the bus costs $0.25. How many times mustsomebody use the pass in a month so that the cost without the discount pass is the same asthe cost with the discount pass? (For full credit you must solve an appropriate equation andwrite your answer with the correct units.)

8 . T h e c o st o f a n e w c a r c a n b e e st i ma t e d b y t h e f o r m u la w h e r e x is.4 x 50 x , 00C =− 2 2 + 9 + 8 5the number of years after 1990.

a . U se t h e f or m u l a to e st i ma t e t h e c o st o f a ne w c a r i n 2 0 0 5 .

b. If the actual cost of a new car in 2005 was $21,750, does the formula underestimate oroverestimate the actual price? By how much?


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9 . I f t h e a v e r ag e sa l a r y f o r a f ir st y e a r d o ct o r w a s $ 2 9 50 i n 1 9 2 6 a n d t ha t a v e r a ge sa l a r yincreased $470 every year, in what year was the average salary for a first year doctor$27,390? (For full credit you must solve an appropriate proportion and write your answer

with the correct units.)

10. In a wildlife preserve 45 elk are captured, tagged, and then released. Later 132 elk arecaptured and 11 are found to have tags. Estimate the number of elk in the preserve. (For fullcredit you must solve an appropriate proportion and write your answer with the correctunits.)

1 1 . S o l v e : ( 2 x ) (3 x 4) x 75 − 5 − 2 − 1 = 6 − 1


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Math 103: Quiz Three Name:____________________Location: Al JaberInstructor: Alfredo Bonilla

1 . M ul ti pl y: 7 x )(2 x )( − 2 + 3

2 . M ul ti pl y: x (4 x x 0 x )5 4 4 − 2 3 − 1 2

3 . G i v e n t h e f u n c t io n , f i n d t h e f o l l o wi n g :( x) f = 2 x2 − 5

a. ( ) f − 2

b. (0) f

c. ( 1) f

4 . W h i c h of t h e f o ll o w i ng g r a p h s a re g r a p h s of f u n c t io n s:

5 . F ac to r: x 1 x2 + 4 − 2

6 . S ol ve : x x4 2 + 3 − 2 = 0

7 . S o l v e t h e i ne q u a l it y a n d g r a p h th e so l ut i o n : x 67 + x < 4 + 1


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8 . I n a c o u r se t h at h a s f o u r e q u al l y w e ig h t e d t est s a st u d e nt m a k e s g r a de s o f 9 6 , 8 0 , a n d 9 7 onthe first three tests. If the student needs to have an average of at least a 90 on the four tests to

get an A, what must the student get on the fourth test in order to get an A for the course? (Forfull credit you must solve an appropriate inequality and state the answer correctly.)

9 . U s e g r a ph p ap e r t o gr a p h y =− 31 + 1


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Math 103: Quiz Four Name:____________________

Location: Al JaberInstructor: Alfredo Bonilla

1 . T w o y o g u r ts a n d t h r e e sa l a d s c o nt a i n 9 3 0 c a lo r i e s. F o u r y o gu r t s a n d t w o sa l ad s c o n t a i n 9 4 0calories. Find the number of calories contained in the yogurt and the number of caloriescontained in the salad.

2 . S o l v e t he sy st e m o f e qu a t i o ns u si n g t h e a dd i t i on m e t h o d :4x – 5y = 223x + 2y = 5

3 . S o l v e t he sy st e m o f e qu a t i o ns u si n g t h e sub st i t ut i o n m e th o d :3x – y = 5x + 3y = –5

4 . F i n d t h e sl o p e o f t h e l i n e c o n t a in i n g t h e p o i n t s a n d, )(− 1 2 2, )( − 4

5 . A c o m p a n y t h at m a k e s c o f f e e m a ch i n e s b e l ie v e s t h a t i ts p r o f i t i n d o l la r s, P , c a n b e m o d e l ed by the formula , where t is the number of coffee makers(t ) .4 x 00 x 5, 0 0 P =− 0 2 + 8 − 2 0 produced and sold. What is the maximum profit that the company can expect?

6 . G i v e n t h e q u a d r a ti c f u n c t io n x y = x 2 + 4 + 3a. Determine whether the parabola opens upwards or downwards.

b. Find the vertex.c. Find the x-intercepts.d. Find the y-intercept.e. Graph the function on graph paper

7 . A n sw e r t h e f o ll o wi n g:a. Write logarithmic form.1

27 = 3 3−

b. Write in exponential form.1 00, 005 = log 10 0


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8 . T h e n u m b er o f p e o p l e l iv i n g i n E u ro p e c a n b e m o d el e d u si ng t h e f u n c t io n. The function represents the number of people living in Europe in millions( x) 4 0∙2 f = 5 0 . 0 1 3 x and x is the number of years after 2000.a. According to this model what will the population in Europe be in the year 2018?

b. Does the model over estimate or under estimate the actual population in Europe in the year2018 if the actual population turns out to be 695 million? By how much?

Graph the following on graph paper:

9. x y = log 2

10. x = − 2

11 . ( x) f = 3 x 2−


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M a t h 1 0 3 : Q u i z F i v e N a m e : __ _ _ _ _ _ __ _ _ _ _ _ _ __ _ _ _Location: Al JaberInstructor: Alfredo Bonilla

1 . A p r i n c i pa l o f $ 2 1 0 0 i s b o r r o w ed o v e r 9 m o n t h s. T h e f u tu r e v a l u e i s $ 2 2 1 0. D e t e r m in e t h eloan’s simple interest rate to the nearest tenth of a percent.

2 . A sa l e sma n r e c e i v es a l a r g e C h r ist m a s b o nu s f o r m e e t in g t h e c o m pa n y ’ s g o a ls:a . H o w m u c h o f th e C h r i stm a s b o n u s m ust b e p u t a sid e n o w i n o r d er t o h a v e $ 1 0 ,0 0 0 i n 7

years if the interest is compounded quarterly at 4.5%?

b. If the salesman puts aside $7000 at 4.2% compounded continuously, how much moneywill he have in 10 years?

3 . A n sw e r a l l t h r e e q u e st io n s:

a . 4 2 is 1 2% o f w h at n um b er ?

b. 90.2 is what percent of 220?

c . A c a r d e a l e r’ s sa l e s w e n t f r o m 1 2 , 3 00 c a r s i n 2 0 0 6 t o 9, 8 0 0 c a r s so ld i n 2 0 0 9 . Wh a t i s t h e percent decrease in the car dealer’s sales to the nearest tenth of a percent?

4 . A w o r k e r d e c i de s t o p u t a si d e $ 6 5 0 e a ch m o n t h i n a r e t i r em e n t a c c o un t t h a t p a y s 5 . 5 %compounded monthly.

a. How much will he have accumulated after 35 years?

b. Find the interest.

5 . T h e p r i c e of a h o m e i s $ 2 5 0 ,0 0 0 . T h e b a nk r e q u i r e s a 1 0% d o w n p a y me n t f o r a 2 0 y e a rmortgage at 3.9%.


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a. Find the monthly payment.

b. Find the total cost of the interest.

M a t h 1 0 3 : Q u i z S i x N a m e : __ _ _ _ _ _ __ _ _ _ _ _ _ __ _ _ _Location: Al JaberInstructor: Alfredo Bonilla

1 . T h e se t o f 8 e q ua l l y l ik e l y o u t co m e s f o r f l ip p i n g a f a i r co i n t h r e e ti m e s a r e

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

HHT means a head (H) on the first toss, a head (H) on the second toss, and a tail (T) on thethird toss. Find the probability of flipping the following when the coin is flipped three times:

a . E x a ct l y t w o t a il s .

b. At least one head.

2 . I f t h e p r o b a b il i t y o f w i n n in g $ 1 0 , 0 0 0 i n a l o t te r y i s , w h a t i s t h e p r o b a b i li t y o f n o t15 0 , 0 0 0

winning $10,000 in the lottery?

For questions 3, 4, 5, 6, and 7 amateur athletes were classified according to nutrition and injury

rate. The results are in the chart.

Injury RateLow Average High

Poor 2 7 14 Nutrition Good 16 5 6

3. If one athlete is randomly selected, what is the probability that the athlete has a high injuryrate?

4. If one athlete is randomly selected, what is the probability that the athlete has good nutritionand an average injury rate?

5. If one athlete is randomly selected, what is the probability that the athlete has a low oraverage injury rate?


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6. If one athlete is randomly selected, what is the probability that the athlete that has goodnutrition or an average injury rate?

7. If one athlete is randomly selected, what is the probability that the athlete has good nutritiongiven that the athlete has a low injury rate?

8 . H o w m a n y r esu l t s a r e th e r e f o r f i r st , se c o n d , an d t h i r d , in a r a c e o f e i g h t spr i n t e rs?

9 . H o w m a n y wa y s c a n a c o m mi t t e e o f 3 te a c h e r s a n d 4 stu d e n t s b e f or m e d f r o m a g r ou p o f 8teachers and 16 students?

10. How many possible license plates are there that have three letters followed by five digits?

For 11, 12, 13, 14, and 15, consider a jar that contains the following. Each token has an equal probability of being chosen and the four problems are unrelated.

four green tokens numbered 1, 2, 3, and 4three red tokens numbered 1, 2,and 3three orange tokens numbered 1, 2, and 3

11. One token is drawn from the jar. What is the probability of drawing a number 2 token or anumber 3 token?

12. One token is drawn from the jar. What is the probability of drawing a number 2 token or atoken that is orange?

13. Two tokens are drawn in succession. What is the probability of drawing two number 3tokens?

14. A token is drawn, replaced, and then a second token is drawn. What is the probability ofdrawing two green tokens?

15. If one token is drawn, what is the probability of drawing a number 2 token given that thetoken is green?


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UMUCMath 103

Final Exam – Practice

● You have two and a half hours to complete this exam.● The examination has 20 questions.● This is a closed book, closed notes examination.● You may use a calculator on the examination.● A formula sheet and a statistical table are available from your instructor should you not have

your copy with you.

1. S olv e:

2 . A 3 0 - y e a r - ol d w o r k e r p l a n s t o r e t i r e a t a g e 6 5 . H e b e l i e ve s t h a t $ 5 0 0 , 0 00 i s n e e d e d t o r e t i r ecomfortably. How much should be deposited now at 3.5% compounded monthly to meet the$500,000 retirement goal?

3 . A m u f fi n r e c ip e c a ll s f o r 3 / 4 c u ps su g a r f o r 3 d o z en m u f fi n s. H o w m u ch s u g ar w i ll y o uuse to make 8 dozen?

4 . W e i g h ts o f t h e P a c i f ic y e l l o wf i n t u n a f o l l o w a n o r m a l d i st r ib u t i o n w i t h m e a n 6 8 p o u n d sand standard deviation 12 pounds.a. What percent of the tuna have a weight of more than 89 pounds?

b. What percent of the tuna have a weight of between 53 and 74 pounds?

5. Th e fu nction C( x) = .76 x + 171.4 models the cholesterol level of a person, as a function of hisage x, in years.a ) Compute C(2 0)

b) Interpret the answer.

6 ) G iv en t he e qu at io n o f a l in ea ) F in d t he x -in te rc ep t.

b) Find the y-intercept.c ) Fin d the slop e.d ) Graph th e line .


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7 ) A c a r c a n b e r e n t e d f r o m C o n t in e n t a l R e n t a l f o r $ 8 0 p e r w e e k p l u s 2 5 c e n t s f o r e a c h m i l edriven. How many miles can you travel if you can spend at most $400 for the week?

8 ) Y o u a r e t a k i n g a m u l t ip l e c h o i c e t e st t h a t h a s 5 q u e st io n s. E a c h o f t h e q u e st io n s h a s t h r e eanswer choices, with one correct answer per question. If you select one of these threechoices for each question and leave nothing blank, in how many ways can you answer thequestions?

9 ) A f a r m e r w a n t s t o f i n d o u t a b o u t t h e r e l a t io n sh i p b e t w e e n t h e a m o u n t o f r a i n i n M a r c hand crop yield in June.

March Rainfall in inches x 3 7 2 6 5

Crop yield in bushels peracre y 5 12 4 1

06

a ) S et u p a s ca tt er d ia g ra m f o r t he d at a. b) Does there appear to be a positive linear correlation, negative linear correlation, or

no linear correlation?

10 ) S olv e:

1 1 ) A b a se b a l l f r a n c h i se i s o w n e d b y th r e e pe o p l e . T h e f i r st o w n s 5 / 1 2 o f th e f r an c h i se . T h eseconds owns 1/3. What fraction of the franchise is owned by the third person?

1 2) G iv en t he f un ct io na ) Fin d the ve rtex.

b) Find the x-intercepts.c ) Fin d the y-intercept.d ) G ra ph th e f un ct io n

1 3 ) A c la ss is c o ll e c t i ng d a ta o n e y e co l o r a n d ge n d e r . T h e y o r g a n i ze t h e d a t a t h e y c o l l ec t e d

into the table below. Numbers in the table represent the number of students from the classthat belong to each of the categories.

Brown Blue GreenMale 22 18 10Female 18 20 12

Find the probability that a randomly selected student from this classa ) D oe s n ot h av e b ro wn e ye s.


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b) Has brown eyes or blue eyes.c ) I s f em al e o r h as g re en e ye s.d ) I s m al e, g iv en t he s tu d en t h as b lu e e y es .e ) I s f em al e a nd h as g re en e ye s.

1 4 ) T h e p o p u l a ti o n P o f b a ss i n a l a k e i s p r e d i ct e d b y t h e f u n c t i on w h e r e tis time in months since the lake was initially stocked. Evaluate P(12) and explain whatthis means.

1 5 ) A t ag e 2 5 y o u de c i d e t o pu t asi d e $ 8 0 e a c h mo n t h i n t o a r e ti r e m e nt a n nu i t y t h a t p a y s2.5% compounded monthly.a ) H ow m uc h w il l y ou h av e s av e d a f te r 4 0 y ea r s?

b) Find the interest.

1 6 ) T h e p r i c e o f a h o m e i s $ 1 8 0 , 0 00 . T h e b a n k r e q u i r es a 2 0 % d o w n p a y m e n t f o r a 1 5- y e a r

mortgage at 4%.a ) F in d t he m on th ly p ay me nt . b) Find the total interest paid.

1 7 ) T w o M c D o n al d ' s Q u a r t e r P o u n d e r s a n d t h r e e B u r g e r K i n g W h o p p e rs w i t h c h e e se c o n t a in520 milligrams of cholesterol. Three Quarter Pounders and one Whopper with cheesecontain 353 milligrams of cholesterol. Determine the cholesterol content in each item.

1 8 ) T h e r e a r e 22 c a rs i n t h e p a r k i n g l o t . R o b e r t w a n t s t o fi n d so m e st a t ist i c a l d a t a c o n c e r ni n gthese cars and finds out how old these cars are. The results can be read from thefollowing frequency polygon.


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a ) F in d t he m od al c ar a ge b) Find the median car age

c ) F in d t he m ea n a ge o f t he c ar sd ) F i nd t h e s t an d a rd d e vi a ti o n o f t h e a g e s o f t h e c a r s

1 9 ) T h e na m e s o f 1 0 m e n an d 7 w o m e n a r e e nt e r e d i n a sw ee p st a k e s d r a w i n g. T wo n a me s a r e d r a w n

at random in succession. What is the probability thata ) t h e f i rs t n a m e i s a m a n ’s a n d t h e s e co n d i s a w o ma n ’s ? b) both names are women’s?

2 0 ) T h e f u n ct i on c a n b e u s e d t o m o d el t h e n u mb e r o f c e ll p h o nesubscribers in the Unites States from 2000 through 2007, where f(x) represents thenumber of cell phone subscribers in millions, x years after 2000. Evaluate and interpretf(4).

21 ) S olv e:

2 2 ) I f $ 10 , 5 0 0 i s b o r r o w e d a n d $ 1 2 , 0 0 0 m u st b e pa i d b a c k a f t e r t h r e e y e a r s, w h a t i s t h esimple interest rate?

2 3 ) A te l e p h o ne m a nu f a c t u re r b e li e v e s t h a t t h e p r o f i t i n d ol l a r s, P , th e c om p a n y m a k e s i srelated to the number of telephones produced and sold, x, by the function

. According to the function, what is the maximum profit that the manufacturer can expect?

2 4 ) F r om a c la s s o f 2 0 s tu de n ts :a ) H o w m a ny w a y s a r e t h er e t o s e le c t 5 s t ud e n ts t o w o rk o n acommittee?

b) How many ways are there to select a president, vice president, andtreasurer?

2 5 ) C o n si d er t h e l i f e ti m e o f 8 t e l e v isi o n se t s: 7 , 9 , 5 , 7 , 8 , 7 , 1 2 , 1 0a ) Fin d the mode

b) Find the medianc ) Fin d the meand ) F in d t he s ta nd ar d d ev ia ti on


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Answers to Math 103

Practice Final Exams

1. x=5/2

2. $147,140.97

3. 2 cups sugar

4. 0.0401 or 4.01% ; 0.5859 or 58.59%

5. 186.6; at age 20, cholesterol level is186.6

6. (2,0); (0,-4); m=2; graph

7. 1280 miles

8. ways

9. scatter plot, positive linear correlation

10.

11. 1/4

12. (-1,-4); (-3,0) & (1, 0); (0,-3); graph

14. 743.54; population of bass in lake after 12months is ~ 744

15. $65,873.50; $27,473.50

16. $1,065.15; $47,727

17. 77 mg chol in quarter pounder & 122 mg cholin whopper

18. mode = 3 ; med = 3 ; mean = 2.68 ; st. dev. =1.2

19. 35/136 ~ 0.26; 21/136 ~ 0.154

20. 180.17; 180.17 million cell phone subscribersin 2004

21.

22. r = 4.76%

23. $2,380,000

24. ;

25. 7 years ; 7.5 years ; 8.125 years ; 2.17 years


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13. 3/5; 39/50; 3/5; 9/19; 3/25

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