Advanced Algebra



Advanced Algebra

Final Exam Practice Problems

Final Exam week will take place Thursday, June 6th through Tuesday, June 9th. During this week you will be expected to display a cumulative understanding of the concepts and skills discussed in class during the entire year. The following is a list of skills that you will be tested on in the Advanced Algebra Final Exam from second semester. Please see the semester 1 exam review packet for practice from first semester.

LIST SKILLS!!!!!

Your final exam will consist of a variety of questions such as multiple choice, short-answer, and constructed response. This review packet was created to help you prepare for the exam and given to you several weeks in advance to help prevent becoming too overwhelmed with the work in reviewing for finals week. Over the next few weeks, continue to study and work through the practice problems and we will discuss the solutions as we move closer to the exam. Remember the exam will be worth 10% of your overall grade in class. If you have additional questions there will be final exam review sessions prior to the actual exam. Good Luck and Happy Learning!

The following are model problems to complete in preparing for the Advanced Algebra Final exam.

1. Simplify each radical expression:

a. [pic] b. [pic] c. [pic]

d. [pic] e. [pic] f. [pic]

g. [pic] h. [pic] i. [pic]

2. For each quadratic equation, find the roots, y-intercept and vertex then graph it:

a. [pic] b. [pic]

c. [pic] d. [pic]

3. Solve each equation:

a. [pic] b. [pic] c. [pic]

d. [pic] e. [pic] f. [pic]

4. Simplify.

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

e. [pic] f. [pic] g. [pic] h. [pic]

5. Simplify.

a. [pic] b. [pic] c. [pic]

d. [pic] e. [pic] f. [pic]

g. [pic] h. [pic] i. [pic]

6. Solve each equation (use the quadratic formula if necessary):

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

e. [pic] f. [pic] g. [pic] h. [pic]

7. If the system of equations y = 2x – 5 and -3y = kx – 2 has no solutions, what is the value of k?

8. If a rectangle measures 54 meters by 72 meters, what is the length, in meters, of the diagonal of the rectangle?

9. Given the quadratic equation f(x) = x² – 4x – 5

a. Sketch the graph and clearly identify the roots on the graph

b. Find the coordinates of the vertex. Is it minimum or maximum?

c. Solve the equation by factoring

d. Find an equation of the axis of symmetry

e. Use the quadratic formula to solve the equation.

10. The planning committee for the upcoming school play “Miss-terious” at LMSA asked the mathematics classes to give them some estimates about income that could be expected at different ticket price levels. The class did some market research to see what students would be willing to pay for tickets. They reported back the following model: I = -75p2 + 600p, where I stands for income and p for ticket price, both in dollars.

a. Find the predicted income if ticket prices are set at $3.

b. Write equations that can be used to help answer each of the following questions. Then solve those equations, check your solutions, and explain how you found the solutions.

i. What ticket price will give income of $1,125?

ii. What ticket price will give income of $900?

iii. What ticket price will give income of $970?

c. Find the price that will give maximum income,then find the maximum income.

11. On its first day of business, the Great Mideastern Ice Cream Store sold two sizes of ice-cream cones, one scoop for $1.00 and two scoops for $1.50. They sold 820 scoops of ice cream in cones for a total revenue of $690. At the end of the day, the manger wondered how many one-scoop and how many two-scoop cones they had sold, but no one had kept track. Represent the number of one-scoop cones sold by s and the number tow-scoop cones by t.

a. Write an equation relating s, t, and the number of scoops sold. (Note: equation will represent number of scoops sold, not number of ice creams!)

b. Write and equation relating s, t, and the total revenue from selling ice cream cones.

c. Assuming that the store sold 50 one scoop cones and 213 two-scoop cones, what was the total revenue?

d. Write an equation that expresses the number of one scoop cones ‘s’ as a function of the two-scoop cones ‘t’ and the total revenue ‘r’.

12. If one leg of a right triangle is 8 inches long, and the other leg is 12 inches long, how many inches long is the triangle's hypotenuse?

13. In [pic]ABC, if [pic]A and [pic]B are acute angles, and sin A = [pic], what is the value of cos A ?

14. In right triangle [pic]ABC to the right, what is the sine of [pic]A ?

15. Lengths for the triangle below are given in feet. 16. In the figure below, [pic]B is a right angle and the measure of

What is the value of x ? [pic]A is 30°. If [pic]is 10 units long, then how many units long is [pic]?

17. In right triangle ABC,  tan A = 2.08.  18. Find the area of the isosceles triangle STU.

Find m(A to the nearest degree.

19. For each equation below identify the family of functions this equation belongs to.

a. y = [pic] b. y = 3x(2.5 – ½ x) c. y = 2x³ - 10 d. y = [pic] e. y = 2(½ x(

f. y = [pic]

20. For each of the following graphs, identify the family of functions to which it belongs.

21. Determine if x is a function of y for the following relations. If it is, then find its domain and range.

|a. | |b. | |c. |

x |-3 |-1 |1 |3 |5 | |x |9 |4 |1 |0 |1 |4 |9 | |x |-2 |-1 |0 |1 |2 |3 | |Y |27 |-1 |1 |27 |125 | |y |-3 |-2 |-1 |0 |1 |2 |3 | |y |2 |1 |0 |-1 |-2 |-3 | |22. Graph each piecewise function:

a. b. c.

23. Evaluate the following compositions of functions.

If f(x)=x+6 and g(x)=x2:

a) (f○g)(a2) b) (g○g)(a+b) c) (f○f)(-6) d) (g○f)(-16) e) g(-5)

24. Factor the following expressions.

a) [pic] b) [pic] c) [pic] d) [pic] e)[pic] f)[pic]

25. Simplify the following expressions:

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

e) [pic] f.) [pic] g) [pic] h)[pic]

26.  Find the missing sides without using a calculator. Leave your answer in simplest radical form.

27. Evaluate each expression.

a) log17(300) b) log3(300) c) [pic] d) [pic] e) ln(e(x + 1)) f) eln(56) g) ln(e5c)

28. Condense each expression, and write it as a single logarithm. Then simplify, if possible.

a) log5(2x) – log5(4) b) 2 log7(2) + log7(45) c) log3(108) + log3(y) – log3(27y)

d) 5loga(z) + loga(y) – 3loga(z)

29. Solve each equation.

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

f) [pic] g) [pic] h) [pic]

i) [pic]

-----------------------

Final Exam Review Opportunities will be:

• Wednesday, May 30, 2012

• Wednesday June 5, 2012

[pic]

[pic]

[pic]

30°

60°

30°

60°

[pic]

[pic]

30°

[pic]

[pic]

60°

45°

[pic]

[pic]

[pic]

45°

45°

45°

[pic]

[pic]

45°

[pic]

[pic]

[pic]

45°

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download