Directions: Fill in the following in the appropriate spaces on the answer sheet and darken the corresponding

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1 MATH 55 FINAL -FORM A Fall 0 Directions: Fill in the following in the appropriate spaces on the answer sheet and darken the corresponding ovals:. Last name, first and middle initials.. Student Z Number. (LEFT-justify in the ID field.). Section: A= A= A= A4=4 A5=5 A6=6 B= B= B= B4=4 B5=5 B6=6 C= C= C= 4. Your signature on the back. 5. No Scratch paper outside of the Exam is permitted. 6. Only a basic non-text capable, non-graphing calculator is permitted. 7. Graphing calculators, cell phones and pdas shall be stowed out of sight. IF VISIBLE YOU WILL BE DEEMED TO BE CHEATING AND WILL RECEIVE A ZERO SCORE FOR THE EXAM!!! 8. Check that your exam contains exactly 50 problems. Each problem is worth 5 points. ************** [A] Simplify x / x /4 x /8 x /8 x /4 x /4 [A] Simplify x 5xy y. x+y x y x+y x+y x y

2 [A] Factor the expression x / (x+) x 5/ +6x /. x 5/ (x+) x / (x+) x / (x+) 6x / (x+) [4A] Simplify [5A] If f(t) = t, then f (t) = t t+ t t+ [6A] If f(x) = x +x then f(+h) f() h = h h+4 h [7A] If f(x) = x+4 and g(x) = x, find the product (fg)(x) and the composition (f g)(x). (fg)(x) = 6x +x 4 and (f g)(x) = 6x+7 (fg)(x) = 6x +5x 4 and (f g)(x) = 6x+7 (fg)(x) = 6x 5x 4 and (f g)(x) = 6x 7 (fg)(x) = 6x x 0 and (f g)(x) = 6x+

3 [8A] Let f(x) = g(x+) for some function g(x). To obtain the graph of f(x) we can: shift the graph of g(x) left units then reflect around the x-axis. shift the graph of g(x) left units then reflect around the y-axis. shift the graph of g(x) right units then reflect around the x-axis. shift the graph of g(x) right units then reflect around the y-axis. [9A] What is the domain of the function f(x) = x+ x? (,] (,) [, ) (, ) (e) (,) (, ) [0A] A wire with length is bent into the shape of a circle. What is the area A of the circle? 4π 4/π /π /π (e) None of these [A] The population of a small town obeys the exponential law. If the population increased from 5,000 to 0,000 from 008 to 00, what will the population be in 04? 40,000 0,000 60,000 80,000 [A] Find the vertex of the parabola y = x +4x+. (,) (, ) (,) (, ) [A] The graph of x y 6x = 0 is: a circle a line a parabola an ellipse but not a circle (e) a hyperbola

4 [4A] The graph of x +y 6x = 0 is: a circle a line a parabola an ellipse but not a circle (e) a hyperbola [5A] Where does the curve 9x +4y = 6 cross the y-axis? Never (0, ) and (0,) (,0) and (,0) (e) (0, ) and (0,) (,0) and (,0) [6A] Evaluate log 5. 0 e Undefined [7A] Evaluate log e Undefined [8A] Evaluate e 0. 0 e Undefined [9A] Which is the largest? ln(e ) log e (e) [0A] WhichONEofthefollowingisalwaystrueforageneral logarithmfunctiong(x) = log b (x), b > 0,b? The function is increasing The graph crosses the y-axis at y = The function is decreasing (e) The graph crosses the x-axis at x = The x-axis is an asymptote 4

5 [A] WhichONEofthefollowingisalwaystrueforageneral exponentialfunctionf(x) = b x, b > 0,b? The function is increasing The graph crosses the y-axis at y = The function is decreasing (e) The graph crosses the x-axis at x = The y-axis is an asymptote [A] Simplify lna for a > 0. lna lna ln a [A] Simplify ex e x e / e x e x e x [4A] Convert polar coordinates of (, π ) to rectangular coordinates: (,0) (,0) (0,) (0, ) [5A] Convert rectangular coordinates of (, ) to polar coordinates: The only possible polar coordinate is (, π 4 ) The only possible polar coordinate is (, π 4 ) Possible polar coordinates are (, π 4 ) and (, π 4 ) Possible polar coordinates are (, π 4 ) and (, π 4 ) 5

6 [6A] Which of the following is the polar graph of r =? (e) [7A] Which of the following is the polar graph of θ = 5π 4? (e) [8A] Two angles of a triangle are π 6 and π 5. What is the third angle? π 0 π 6 7π 0 7π 0 [9A] Suppose that ABC is a right triangle with C = π. If AC = and AB = 5, then: cosb = 5 & sinb = 4 5 & tanb = 4 cosb = 4 5 & sinb = 5 & tanb = 4 cosb = 4 5 & sinb = 5 & tanb = 4 are true. cosb = 5 & sinb = 4 5 & tanb = 4 6

7 [0A] Evaluate cos π. 0 ( [A] Evaluate: cos π 4 ) [A] Evaluate tan( π ) [A] What is the amplitude of f(x) = 7sin(4x )? [4A] What is the period of f(x) = 4sin(7x )? π π 7 π π [5A] What is the phase shift of f(x) = 7sin(x 4)? 4 9π 7 π 7

8 [6A] If sinα = with π < α < π and cosβ = 5 with π < β < π: Find the exact value of cos(α+β): [7A] Simplify sinx sinx. sinx cosx tanx [8A] Solve cos θ 6cosθ+9 = 0. Either θ = cos ( ) or θ = cos () θ = cos ( )+kπ θ = cos ()+kπ No solution 8

9 [9A] Which is the graph of y = sinx? π/ - π/ π/ - π/ π - π π - π (e) π - π [40A] Solve sin θ cos θ =. θ = ± π 8 +kπ θ = ±π 4 +kπ θ = ± π 4 +kπ θ = ± π 8 +kπ 9

10 [4A] Simplify and evaluate sin ( ) π cos ( ) π cos 7 ( ) π sin ( ) π. 7 [ [4A] Simplify cos (cos π 9 ]) (e) π 9 7π 9 π 9 [ [4A] Simplify cos (cos π 9 7π 9 ]) π 9 7π 9 π 9 7π 9 [44A] A triangle has sides of length a,b,c opposite angles A,B,C respectively. If a = 5, b = and c = 6, then cosb = cosb = There is such a triangle but cos(b) is not as above. (e) No such triangle is possible. cosb = [45A] A triangle has sides of length a,b,c opposite angles A,B,C respectively. If sina = 6, sin(b) = 0 and a = 0, then b = 6 b = 8. b = b = 40 0

11 [46A] Find the area of the sector of radius 0 in. and central angle 9. [A = θr when the angle is in radians.] 5π in 0π in 90π in 8π in [47A] A triangle has sides of length a,b,c opposite angles A,B,C respectively. If b = 7, a = 8, and B = sin ( ), then 8 A = sin ( 7 ) only A = π sin ( 7 ) only Either A = sin ( 7 ) or A = π sin ( 7 ) There is such a triangle but A is not as above (e) No such triangle is possible [48A] A triangle has sides of length a,b,c opposite angles A,B,C respectively. If b = 7, a = 5, and B = sin ( ), then 5 A = sin ( 7 ) only A = π sin ( 7 ) only Either A = sin ( 7 ) or A = π sin ( 7 ) There is such a triangle but A is not as above (e) No such triangle is possible

12 [49A] Simplify ( ) cscx sinx sinx cos x sin x cos x sin x [50A] Simplify tan β secβ + tan β secβ cos β sin β