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Name: Directions: Please show all work and be as neat as possible.
7 points 1. Find the slope-intercept form of the equation of the line that passes through the points ( 3 , − 5 ) and ( 10 , 16 ).
y = 3 x − 14
6 points 2. a) Is this the graph of a function? No
b)^ Is this the graph of a function? Yes
6 points 3. Evaluate the following exactly without using your calculator.
a)
27
= 259 b) log 4 641 = − 3
6 points 4. The graph of f (x) = 3 x^2 − 30 x + 93 is a parabola. Find the vertex of this parabola.
Vertex: ( 5 , 18 )
8 points 5. Find all solutions x for the following equations.
a) x^2 − 10 x + 21 = 0 b) 2 x^2 − x − 21 = 0
x = 3 x = − 3 or x = 7 or x = (^72)
6 points 6. Find the interest rate on a loan of $7, 300 that charges $3, 285 of simple interest after 6 years.
Interest Rate: 7 .5%
7 points 7. How much should be invested now at 3.2% simple interest if $5, 500 is needed in 5 years?
Initial Investment: $4741. 38
6 points 8. What is the balance of an account after 15 years if $20, 000 is invested at a 2.5% interest rate compounded quarterly?
Final Balance: $29, 065. 89
7 points 9. Find the present value of an investment whose final amount is $52, 126 after 6 years at 6.75% interest com- pounded semiannually.
Present Value: $35, 000. 01
6 points 10.Find the term of a loan of $10, 000 at 17% interest compounded monthly that will have an amount due of $32, 597.
Term: 7 years
Formulas
(You may tear this page off)
Lines:
m = y 2 − y 1 x 2 − x 1
y = mx + b y − y 1 = m(x − x 1 )
Quadratics:
f (x) = ax^2 + bx + c
b 2 a , c −
b^2 4 a
Simple Interest:
I = Prt
A = P( 1 + rt)
Compound Interest:
A = P
r m
)mt
P = A
r m
)−mt
APY =
r m
)m − 1
Annuities:
FV = PMT
1 + (^) mr
)mt − 1 r m
PMT = FV
r ( m 1 + (^) mr
)mt − 1
t =
log
( FV
PMT
r m +^1
m log
1 + (^) mr
PV = PMT
1 + (^) mr
)−mt r m
PMT = PV
r m 1 −
1 + (^) mr
)−mt
