1. Algebra II (H) FINAL EXAM REVIEW CHAPTERS 6, 7, 8, 9, 10, 12

2. Chapter 6 1. If f(x) = 5x and g(x) = -2x +1, solve for f(g(-3)) – g(f(-3)).

3. Chapter 6 2. Given that f(x) = ⅓ x 2 + 1, solve for the value of f -1 (x) and prove the inverse is a function. The inverse relation, is not a function as it fails the test.

4. Chapter 6 Simplify fully each equation

5. Chapter 6 Simplify each expression fully. Do not leave negative exponents or non-simplified radicals.

6. Chapter 6 Solve each equation and verify your solution. When this problem is solved, the resulting answer is 121/4. When this answer is checked, a false statement occurs. The solution is .

7. Chapter 7 -10 -6 -2 0 2 6 10 14 22 18 14 10 6 2 -4

8. Chapter 7 Suppose you invest $1600 at an annual interest rate of 4.6% compounded monthly. How much will you have in the account after 4 years? P = $1600; r = 0.046, n = 12, t = 4

9. Chapter 7 Write the equation in exponential form and solve for the value of x. 2 x = 512 2 x = 2 9 x = 9 4 -3 = x 1 / 64 = x

10. Chapter 7 Write the equation in logarithmic form and solve for x. log 5 390625 = x x = 8 log 6 x = 4 x = 1296

11. Chapter 7 Evaluate the logarithm. log 0.01

12. Chapter 7 Solve each equation and check your solutions.

13. Chapter 7

14. log 8 z-4 = log 6.3 (z – 4)log 8 = log 6.3 z log 8 – 4 log 8 = log 6.3 z log 8 = log 6.3 + 4 log 8 z = (log 6.3 + 4 log 8)/log 8 z = 4.8851 3e 2x = -4 +5 = 1 e 2x = 1 / 3 ln e 2x = ln (0.3333) 2x ln e = ln (0.3333) x = ln (0.3333) / 2 = - 0.5493

15. Chapter 8

19. Describe the vertical asymptote(s) and hole(s) for the graph of asymptote: x = 5 and hole: x = 1 Find the horizontal asymptote of the graph of no horizontal asymptote If degree of a(x) > b(x) then 0 horizontal asymptotes If degree of a(x) < b(x) then horizontal asymptote is y = 0 If degree of a(x) = b(x) then horizontal asymptote is y = lead coefficient of a(x)/lead coefficient of b(x)

20. Chapter 8 What is the graph of the rational function? Note the vertical asymptote at x = -1 and the horizontal asymptote at y = 2 / 1 = 2.

21. Chapter 8 Solve the equation. Check the solution.

22. Chapter 8 Suppose x varies directly as y, and x varies inversely as z. Find z when x = 8 and y = -6 if z = 26 when x = 8 and y = 13.

23. Chapter 9 For each given equation, determine the type of conic section it is and all of its characteristics. x 2 - 3y 2 + 2x - 24y - 41 = 0 (x 2 + 2x + 1 2 ) – 3(y 2 + 8y + 4 2 ) = 41 + 1 – 48 (x + 1) 2 – 3(y + 4) 2 = - 6 -6 -6 -6 (y + 4) 2 – (x + 1) 2 = 1 2 6 This shape is a hyperbola. vertical The values of the key variables are as follows: h = -1, k = -4, a 2 = 2, b 2 = 6, c 2 = 8. Center (-1, -4) vertices (-1, Foci (-1,

24. Chapter 9 Write the equation of the given circle in standard form. The center is ( -8, -5) and the radius is √6. (x – h) 2 + (y – k) 2 = r 2 h = -8, k = -5, r = √6. (x +8) 2 + (y +5) 2 = 6

25. Chapter 9 Identify the type of conic section represented in each equation 12y 2 – 6y + 5x – 20 = 0 x 2 – 4 = y 2 + 2y – 6 5x 2 – 2y 2 + 6 = 0 parabola hyperbola

26. Chapter 10 Find the thirteenth term of an arithmetic sequence if the first term is 3 and the common difference is 3.

27. Chapter 10 Find the sum of the first 17 terms of the arithmetic sequence 10, 14, 18, 22, 26...

28. Chapter 10 Find the ninth term of the geometric sequence if a 1 = 7 and r = 2.

29. Chapter 10 Find the sum of the first 25 terms of the series.

30. Chapter 10 Find the sum of the sequence -4, -1, - ¼, … This is an infinite geometric sequence with r = 1 / 4

31. Chapter 10 Find the sum of the first 25 terms of the series and write in summation notation.

32. Chapter 10 Write a recursive formula for the sequence. 2, 7, 12, 17, 22, … 1, 3, 11, 123, 15131, …

33. Chapter 12 Solve for all unknown parts of the triangle. Round your answers for side lengths to the nearest tenth and to the nearest degree for angles.  A = 35 o a = _____________  B = __________ b = _____________  C = 90 o c = 22 A B C a b c

34. Chapter 12  = -240 o coterminal #1 ____________ coterminal #2 _________ reference angle _________ 360 + (-240) = 120 -360 + (-240) = - 600 Reference angle 180 - 120 = 60 In Q II

35. Chapter 12 Convert the given angle to radians/degree measure base on what is given. Express radian measures in fraction form.  = 7 / 12  R  = 3 / 4  R  = 1 / 5  R  = 300 o  = 225 o  = 120 o

36. Chapter 12 Find the amplitude, period, and any translations that are present from the equation. f(x) = 3sin( 2  -  / 2 ) + 1 Amplitude = 3 Period =  Horizontal shift =  / 4 Vertical shift = 1 up

37. Chapter 12 Determine the arc length of an arc that is  / 3 radians and a radius of 5 cm.

38. Chapter 12 Determine the value for each of the remaining functions when tan  = - 1 in Quadrant 2.