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KOC¸ UNIVERSITY
MATH 101 - FINITE MATHEMATICS
Midterm I October 22, 2007
Duration of Exam: 90 minutes
INSTRUCTIONS: No calculators may be used on the test. No books, no notes, no questions and no talking allowed. You must always explain your answers and show your work to receive full credit. Use the back of these pages if necessary. Print (use CAPITAL LETTERS) and sign your name, and indicate your section below.
Surname, Name: —————————————————
Signature: ————————————————————
Section (Check One):
Section 1: S. K¨u¸c¨uk¸cifci (Tue-Thu 11:00) —– Section 2: S. K¨u¸c¨uk¸cifci (Tue-Thu 14:00) —– Section 3: M. Sarıdereli (Mon-Wed 14:00) —– Section 4: M. Sarıdereli (Tue-Thu 11:00) —– Section 5: E. S¸. Yazıcı (Tue-Thu 15:30) —–
PROBLEM POINTS SCORE
TOTAL 100
- Let L be the line passing through the points P 1 (2, 1) and P 2 , where P 2 is the intersection
point of the two lines y = −x + 1 and y = − 2 x − 1.
(a) (5 points) Find the slope of the line L.
(b) (5 points) Write an equation of the line L in standard form.
(c) (5 points) Find the y-intercept of the line L.
(d) (5 points) What is the intersection point of the graphs of the inverses of the two linear
functions f (x) = −x + 1 and g(x) = − 2 x − 1?
- (i) (4 points) Find the domain of the function f (x) =
log(x + 2) √ 4 − x
(ii) (6 points) Sketch the graph of the function f (x) = log 10(x + 3). Indicate at least three
points on the graph.
(iii) (15 points) Find the value of x in the following equations.
(a) 3^2 −^3 x^ = 9^5 x−^6
(b) x^2 ex^ − 5 xex^ = 0
(c) log(x + 6) − log(x − 3) = 1
(e) log 49 1 /7 = x
(f) log 25 x = 1/ 2
- (a) (5 points) Show the identity
sin(2x) 1 + cos(2x)
= tan(x).
(b) (8 points) Find c if a = 1, b =
2, and A = π/6, where a, b, and c are the sides across
the corners A, B, and C, respectively, in the triangle ABC.
(c) (7 points) Sketch the graph of f (x) = cos(x − π 2 ) − 1. Indicate at least four intercepts
on the graph.
