Math 1325
Practice Test 1
Test over Lines, Functional Notation, Domain of Functions, Cost-Revenue-Profit, SupplyDemand, Compound Interest, Effective Annual Yield, Future Value of Annuity, Sinking Fund, &
Amortization
5

#1 Find the slope of the line that passes through  ,6  and  3,4 .
2

#2 Find the equation of a line with a slope of 3 that passes through the point (-1,3).
#3 Find the equation of a line passing through (2,0) that is parallel to 2x + 3y = 6.
#4 Given f ( x)  x 2  4 , evaluate:
#5 Given g ( x) 
a) f(2)
b) f(a + h)
x 1
, state the domain of g(x).
x  x  12
2
#6 Ameritech Corp. produces gaskets and has a monthly fixed cost of $48,000. Each gasket cost
$8 to produce and sells for $14. How much profit will Ameritech earn if it makes and sells
10,000 gaskets?
#7 Shadowfax Industries produces ink cartridges. The company has a monthly fixed cost of
$12,000. Each ink cartridge it produces cost $5 to make. It sells each cartridge for $15. How
many cartridges must Shadowfax produce to break even?
#8 The demand equation for the Schmidt-3000 fax machine is 3x + p – 1,500 = 0, where x is the
quantity demanded per week and p is the unit price in dollars. The supply equation is 2x – 3p +
1,200 = 0, where x is the quantity the supplier will make available in the market when the unit
price is p dollars. Find the equilibrium quantity and the equilibrium price for the fax machines.
#9 If $2,500 is invested into an account paying 7% annual interest, compounded semiannually,
how much is the investment worth in ten years?
#10 Find the effective rate of annual interest corresponding to a nominal rate of 8% compounded
monthly.
#11 If Rinaldo puts $600 a quarter into a retirement account that pays 12% annual interest,
compounded quarterly, how much will be available for retirement in 9 years?
#12 Carson has decided to open an account for the purpose of buying a computer that will cost
$30,000. If the account earns 10% interest per year, compounded quarterly, how much will each
equal quarterly installment have to be in order to purchase the computer in two years?
#13 The Smith’s have borrowed $96,000. The loan is to be amortized with monthly payments
for 25 years at an annual interest rate of 9% compounded monthly. Find the monthly payment
and the total amount of interest paid.
#14 Mystery question. Good luck.
SOLUTIONS
5

#1 Find the slope of the line that passes through  ,6  and  3,4 .
2

y 2  y1 4   6
46
10
2
20



 10    
6 5  11
x 2  x1  3  5 2
11
11
 
2 2
2
20
m
11
m
#2 Find the equation of a line with a slope of 3 that passes through the point (-1,3).
y  y1  m( x  x1 )
y  3  3( x  1)
y  3  3( x  1)
y  3  3x  3
y  3x  6
#3 Find the equation of a line passing through (2,0) that is parallel to 2x + 3y = 6.
2x  3y  6
3 y  2 x  6
2
6
y  x
3
3
2
y  x2
3
2
3
y  y1  m( x  x1 )
m
2
y  0   ( x  2)
3
2
4
y  x
3
3
Put this equation in slope-intercept form in order to
find the slope because the slope of the line you want
will be equal to the parallel line: 2x + 3y = 6.
#4 Given f ( x)  x 2  4 , evaluate:
a) f(2)
f ( 2)  ( 2) 2  4
f ( 2)  4  4
f ( 2)  8
b) f(a + h)
f (a  h)  a  h   4
2
f (a  h)  a  h a  h   4
f (a  h)  a 2  ah  ah  h 2  4
f (a  h)  a 2  2ah  h 2  4
#5 Given g ( x) 
x 1
, state the domain of g(x).
x  x  12
2
x 2  x  12  0
( x  4)( x  3)  0
x  4  0, x  3  0
x  4, x  3
 x  4, 3
The domain of this function will be restricted by
x-values that make the denominator equal to zero
because an expression with zero as the divisor is
undefined.
Domain :  ,4   4,3  3, 
#6 Ameritech Corporation produces gaskets and has a monthly fixed cost of $48,000. Each
gasket cost $8 to produce and sells for $14. How much profit will Ameritech earn if it makes and
sells 10,000 gaskets?
C ( x)  8 x  48,000
R( x)  14 x
P( x)  R( x)  C ( x)
P( x)  14 x  8 x  48,000 
P( x)  14 x  8 x  48,000
P( x)  6 x  48,000
P(10,000)  6(10,000)  48,000
P(10,000)  $12,000
#7 Shadowfax Industries produces ink cartridges. The company has a monthly fixed cost of
$12,000. Each ink cartridge it produces cost $5 to make. It sells each cartridge for $15. How
many cartridges must Shadowfax produce to break even?
C ( x)  5 x  12,000
R ( x)  15 x
The break-even point will exist where
revenue equals cost.
Break even : R ( x)  C ( x)
15 x  5 x  12,000
10 x  12,000
x  1,200 cartridges
#8 The demand equation for the Schmidt-3000 fax machine is 3x + p – 1,500 = 0, where x is the
quantity demanded per week and p is the unit price in dollars. The supply equation is 2x – 3p +
1,200 = 0, where x is the quantity the supplier will make available in the market when the unit
price is p dollars. Find the equilibrium quantity and the equilibrium price for the fax machines.
3 x  p  1,500
p  1,500  3 x
To solve the system of equations, solve
one equation for one variable (p).
2 x  3(1,500  3 x)  1,200  0
2 x  4,500  9 x  1,200  0
2 x  9 x  4,500  1,200  0
11x  3,300  0
11x  3,300
x  300
p  1,500  3(300)
p  600
300 units priced at $600
Substituting this result into the second
equation, allows the solution for the other
variable (x).
The equilibrium quantity is 300 fax
machines. To find the equilibrium price,
substitute 300 in for x in the first equation.
#9 If $2,500 is invested into an account paying 7% annual interest, compounded semiannually,
how much is the investment worth in ten years?
r

A  P 1  
 m
mt
 .07 
A  2,5001 

2 

A  $4,974.47
210
A stands for the amount earned
at the end of the investment
(future value). P stands for
amount invested. m stands for
the number of compounding
periods in one year. t stands for
the time in years. r stands for
the interest rate as a decimal.
#10 Find the effective rate of annual interest corresponding to a nominal rate of 8% compounded
monthly.
m
r

reff  1    1
reff stands for the effective rate
 m
of annual interest. m stands for
12
 .08 
reff  1 
 1
 12 
reff  .083
the number of compounding
periods in one year. r stands for
the nominal interest rate as a
decimal.
reff  8.3%
#11 If Rinaldo puts $600 a quarter into a retirement account that pays 12% annual interest,
compounded quarterly, how much will be available for retirement in 9 years?

 1 
A  P



r

m
r
m
mt

 1




  .12  49 
  1
 1 
4 



A  600


.12


4


 1.0336  1
A  600

.03


A  $37,965.57
A stands for the amount earned at the
end of the annuity investment (future
value). P stands for amount invested
each annuity period. m stands for the
number of compounding periods in
one year. t stands for the time in
years. r stands for the interest rate as a
decimal.
#12 Carson has decided to open an account for the purpose of buying a computer that will cost
$30,000. If the account earns 10% interest per year, compounded quarterly, how much will each
equal quarterly installment have to be in order to purchase the computer in two years?


R  S

 1 
 

r

m

mt

r
  1
m



.1


4


R  30,000
  .1  42 
 1    1 
4

 
R stands for payments. S stands
for the sum of all the payments
into the sinking fund plus
interest earned. m stands for the
number of compounding
periods in one year. t stands for
the time in years. r stands for
the interest rate as a decimal.
 .025 
R  30,000 

8
 1.025  1
R  $3,434.02
#13 The Smith’s have borrowed $96,000. The loan is to be amortized with monthly payments
for 25 years at an annual interest rate of 9% compounded monthly. Find the monthly payment
and the total amount of interest paid.


r


m


RP
 mt
 
r 
1  1   
  m  


.09


12


R  96,000
  .09  1225 
1  1 


  12 

R stands for payments. P stands
for amount borrowed. m stands
for the number of compounding
periods in one year. t stands for
the time in years. r stands for the
interest rate as a decimal.


.0075
R  96,000
300 
1  1.0075 
R  $805.63 monthly payment
I  $805.63  300 $96,000
I  $241,689  $96,000
I  $145,689
The interest paid will equal the sum of the payments
minus the amount borrowed. The sum of the
payments equals the monthly payments times the
number of months.