Advanced Algebra - Tamalpais Union High School District



Honors Advanced Algebra Name:_______________________________

Fall Final Exam Review 2014

Date______________________ Per._______

Do all of the following on separate paper. Use graph paper for graphs. Try to do it with no notes. It should all be done with no calculators unless it says C (which means Calc is OK.)

Linear Representations and Solving Equations and Inequalities

1. Find the slope for the following:

a) through the points [pic] and [pic]

b) through the points (7,2) and (7,3)

c) through the points (5,2) and (9,2)

2. Write the equation of the line in slope/intercept form for:

a) a vertical line through (6,1)

b) a horizontal line through (6,1)

c) the line containing the points (5,7) and (-3,11)

d) the line parallel to the line [pic] containing the point (-3,11)

e) the line perpendicular to [pic] containing the point (4,9)

3. Solve each literal equation for the indicated value.

a) [pic] for r b) [pic] for [pic]

4. Solve for x: [pic]

Solve each absolute value equation.

5. [pic] 6. [pic] 7. [pic]

Numbers, Functions, Relations, and Transformations

8. Let [pic] and [pic]. Simplify all answers.

a) [pic] b) [pic] c)[pic] d.) [pic]

9. Write the function for the graph of [pic] translated 3 units to the right and 5 units down.

10. Write the function for the graph of [pic] translated 6 units down and reflected over the

x-axis.

11. Find the inverse of each function: a) [pic] b) [pic]

12. For each of the following graph the function, state the domain and range.

|[pic] |h) [pic]is shown, |

|[pic] | |

|[pic] | |

|[pic] | |

|[pic] | |

|[pic] | |

|[pic][pic] | |

| | |

| |i. What is f(1)? For what values of x is f(x) >0? |

| |ii. graph:[pic] |

13. The graph of f(x) is shown.

a. Describe in words the transformation given by

g(x) = 1 – 3f(x – 2).

b. Graph g(x)

14. Find the inverse of matrix A = [pic]by hand

15. Piecewise Functions

|a) Given the following graph state the function. |c) Given the function, draw the graph. |

| |[pic] |

| |d) Given the function, draw the graph. |

| | |

| |[pic] |

| | |

| | |

| | |

|b) | |

| | |

| | |

| | |

| | |

16. Use [pic] and [pic]

a. Write the equation for [pic] b. Graph [pic]

Systems of Equations and Inequalities:

17. Graph each set on one set of axes a) [pic] b) [pic]

c) [pic] d. [pic]

18. Solve the system using substitution. [pic]

19. Solve the system using elimination. [pic]

20. Graph the system of inequalities: [pic] 21. Write the equation for the graph below:

22. C. Solve the system. [pic]

Polynomial Functions

Sketch a graph of the quadratic function with the given vertex and through the given point. Then write the equation in vertex form.

23. Vertex (0, 0); point (-3, 3) 24. Vertex (1, 5); point (2, 1)

Rewrite each equation in vertex form. (Use the method of completing the square.) Sketch a graph and identify the vertex and approximate zeros.

25. [pic] 26. [pic] 27. [pic]

Graph each quadratic function. Identify the axis of symmetry, the vertex, the x-intercept(s), the y-intercept, and the domain and range of each function.

28. [pic] 29. [pic] 30. [pic]

Simplify each expression.

31. [pic] 32. [pic]

33. a) [pic] b) [pic] c) [pic]

Factor each expression completely.

34. [pic] 35. [pic] 36. [pic]

37. [pic] 38. [pic] 39. [pic]

Solve each quadratic equation.

40. [pic] 41. [pic] 42. [pic]

Write each polynomial function in general form. Then classify it by degree and by number of terms. Describe its end behavior.

43. [pic] 44. [pic] 45. [pic]

Write a polynomial function, P(x), in general form for each set of zeros and given information.

46. [pic] , y intercept 12 47. [pic] , P(2)=100 48. [pic], a = 1

Divide.

49. [pic] 50. [pic] 51. [pic]

For each equation, state the number of complex roots, and list the possible rational roots.

52. [pic] 53. [pic]

Find all roots.

54. [pic] 55. [pic]

56. One x-intercept of the graph of the cubic function [pic] is -9. What are the other zeros?

Use synthetic division and the Remainder Theorem (both methods) to find [pic].

57. [pic] 58. [pic]

59. C Roscoe hit a ball straight up at a speed of 110 ft/s. His bat hit the ball at a height of 3 ft. above the ground. After how many seconds did the ball hit the ground?

-2-1012343896563313460. C Find a polynomial function that models the data.

Exponential, Power, Inverse and Logarithmic Functions

C The half life of a certain element is 16 hours. How much will be left of a 12 mg sample after 10 hours?

C A medication is eliminated from the bloodstream at a rate of 18% per hour. How much of a 100mg dose remains in the bloodstream after 4 hours?

C A bacteria population is doubling every 20 minutes. If the initial count is 4,560, how many will there be after 2 hours?

C Find the final amount of a $1000 investment after 9 years at 8% interest compounded annually. What is the final amount of the same investment compounded quarterly? What if it is compounded continuously?

C Sam has a choice between an investment that pays 6% annual interest compounded monthly and an investment that pays 5.9% interest compounded daily. Which investment will earn Sam more money over the same period of time?

a. Write [pic]in logarithmic form. b. Write [pic] in exponential form.

Simplify each expression: a. [pic] b. [pic] c. [pic]

Find the inverse of [pic]

Solve each equation for x. State the exact answer and an approximation for the (C) ones rounded to the nearest hundredth.

[pic](C)

[pic]

[pic]

[pic]

[pic]

[pic]

If [pic], find [pic]for sea water if its pH is 8.5 (C)

[pic]

[pic]

[pic]

[pic](C )

Write each expression as a single logarithm, then simplify!

[pic]

[pic]

Write each expression as a sum or difference of logarithms, then simplify!

[pic]

[pic]

[pic]

Evaluate. No Calculators!

[pic]

[pic]

[pic]

[pic]

#88-91 Solve for x. State the exact answer and an approximation (C) rounded to the nearest hundredth.

[pic]

[pic](C)

[pic]

[pic]

C Ted just bought a new car for $25,500. Suppose the value of the car decreases by 15% each year.

What will be the value of the car after 5 years?

After how many years will the car be worth less than $5000?

Solve each equation

[pic] b.) [pic] c.) [pic]

C Linear Programming: Suppose you work for a small company that makes high-quality CD players. They wish to optimize the numbers of the two models that produce, “Home Happy” and “Car Carrier”. The assembly line can produce no more than 10 Home Happy models per day. No more than 32 CD players, total, can be produced per day. They must provide at least 200 labor hours for their employees: each Home Happy player takes 20 labor hours to make and each Car Carrier takes 10 hours to make. The company earns a profit of $40 on each Home Happy and $30 on each Car Carrier. How many of each model should they produce to maximize profit?

Define the variables, write the constraints, graph the feasible region, find the vertices, write an objective function, and find the best solution.

This review sheet is due on the day of the final! Don’t forget it!

The final exam is 2 hours- you will not get extra time. The content covers Ch 4-7 plus topics from Algebra 1 (like lines, quadratics, factoring, solving systems of equations, etc.) There is a calculator section that is 10 free response (some problems have multiple parts), and a non-calculator section that is 20 multiple choice. You may not use notes and no formulas will be provided. It is worth 20% of your overall grade. Work hard!!

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Domain:

Range:

Function:

Domain:

Range:

Domain:

Range:

Remember? That means Calc is OK

(3, 1)

(1.5, -1)

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