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Exam I MAT 112 Summer 2009 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 = x+ 6 points 2. a) Is this the graph of afunction? b) Is this the graph of afunction?
6 points 3. Evaluate the following exactly without using your calculator. a) (^12527 )−^2 /^3 = b) log 4 641 =
6 points 4. The graph of f (x) = 3 x^2 − 30 x + 93 is a parabola. Find the vertex of this parabola.
Vertex: 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 = x = or x = or x =
6 points Exam I6. Find the interest rate on a loan of $7^ , 300 that charges $3MAT 112, 285 of simple interest after 6 years.^ Summer 2009
Interest Rate: 7 points 7. How much should be invested now at 3.2% simple interest if $5, 500 is needed in 5 years?
Initial Investment: 6 points 8. What is the balance of an account after 15 years if $20quarterly? , 000 is invested at a 2.5% interest rate compounded
Final Balance: 7 points 9. Find the present value of an investment whose final amount is $52pounded semiannually. , 126 after 6 years at 6.75% interest com-
Present Value: 6 points 10.Find the term of a loan of $10$32, 597. , 000 at 17% interest compounded monthly that will have an amount due of
Term:
Exam I MAT 112 Summer 2009
(You may tear this page off)^ Formulas
Lines: m = y x^22 −−^ yx^11 y = mx + b y − y 1 = m(x − x 1 )
Quadratics: f (x) = ax^2 + bx + c^ ( − 2 ba , c − b 4 a^2 )
Simple Interest: I = Prt A = P( 1 + rt)
Compound Interest: A = P^ ( 1 + (^) mr^ )mt P = A^ ( 1 + (^) mr^ )−mt APY =^ ( 1 + (^) mr^ )m − 1 Annuities: FV = PMT
( 1 + (^) mr )mt (^) − 1 m^ r^ PMT^ =^ FV^ (^1 +^ mrm^ r^ )mt^ −^1 t = log m^ log(^ PMTFV ( 1 m+r^ + (^) mr^1 )) PV = PMT 1 −^
( 1 + (^) mr )−mt mr^ PMT^ =^ PV^1 −^ (^1 +m^ r^ mr^ )−mt
