Pre AP Algebra 2 – Fall 2017 Final Exam Review This is a partial review. There may be other topics that we have studied that are not on this review. They are fair game for the exam. Study all quizzes, tests, homework and notes for the semester. 1. Use the vertical line test to determine whether or not each graph is the graph of a relation or a function. Write relation or function for your answer. ____________ ____________ ____________ 2. Are the following relations or functions. Write relation or function for your answer. { (0, 1), (1, 2), (2, 3), (3, 4) } _______

{ (1, 1), (1, 2), (2, 3), (2, 4) } _______

3. For each scenario, determine which event is Independent and which event is Dependent. Explain your reasoning.

o The height of a burning candle over a period of hours.

o The size of a balloon after a number of breaths have been blown into it

4. The graph to the right is of the function ℎ 𝑥 . Fill in the blanks with the appropriate interval notation regarding the domain and range of ℎ(𝑥) and 𝑓(𝑥).

ℎ(𝑥) 𝑓 𝑥 = ℎ(𝑥 + 5)

domain

range

5. The graph to the right is of the function 𝑔 𝑥 . Fill in the blanks with the appropriate interval notation regarding the domain and range of 𝑔(𝑥) and 𝑝(𝑥).

𝑔(𝑥) 𝑝 𝑥 = 𝑔 𝑥 − 3

domain

range

6. Describe the transformations (from the parent function) in each equation below.

i. y = -(x)2 + 3 ii. y = (x – 1) + 2 iii. y = -(x + 3) - 6 iv. y = (x – 3)2 + 2 7. Write the formula for:

i. slope-intercept form of a line______________________

ii. point-slope form of a line ________________________

8. Write equations of a line in point-slope form which satisfy the requirements below. i. passes through (3, 11) & (-6, 5) ii. passes through ( -6, 3) and slope = −.

/

9. Graph the following linear equations and inequalities.

𝑦 = −43𝑥 − 1 𝑦 − 3 = 2(𝑥 − 4) 3𝑥 − 4𝑦 ≤ 12 𝑦 >

34𝑥 + 3

10. Solve the systems of equations and inequalities by manually graphing. Check your answer using a calculator.

𝑥 + 𝑦 = 6 3𝑥 − 4𝑦 = 4

5𝑥 − 𝑦 = 3 𝑦 = 5𝑥 − 3

𝑦 > 𝑥 − 2

𝑦 + 3 ≤ −12 (𝑥 + 8)

11. Solve by substitution. 𝑛 = 3𝑚 + 7 4𝑚 + 9𝑛 = 1 12. Solve by elimination. 4𝑝 + 5𝑞 = 7 3𝑝 − 2𝑞 = 34 13. Convert the following system to a matrix equation. 3𝑥 − 2𝑦 = 18 5𝑥 + 𝑦 = 17 14. Solve the system of equations by the method of your choice. Confirm your answer using the calculator. 𝑥 − 2𝑦 + 3𝑧 = 3 2𝑥 + 𝑦 + 5𝑧 = 8 3𝑥 − 𝑦 − 3𝑧 = −22 15. Perform the following matrix operations if possible. If it is not possible to perform the operation, explain why it is not possible.

i. 1 3 0 2 7 52 4 3 6 2 3 26 7 5 7 3 4

é ù é ù é ùê ú ê ú ê ú+ - - -ê ú ê ú ê úê ú ê ú ê ú-ë û ë û ë û

ii. 1 3 0 22 4 3 66 7 5 7

é ù é ùê ú ê ú-ê ú ê úê ú ê ú-ë û ë û

iii. 1 3

0 2 32 4

6 5 76 7

é ù-é ùê ú

ê úê ú -ë ûê úë û

iv. 1 3

0 2 32 4

6 5 76 7

é ù-é ùê ú - ê úê ú -ë ûê úë û

16. Using the Distributive Method of Multiplication (FOIL), expand the following: (5𝑥 − 2)(2𝑥 + 3) 17. Use the grid provided to graph the inequality 𝑦 > .

>𝑥 + 3. Which of the following points are solutions?

a. (−4,1) b. (−4,4) c. (1,3) d. (3,4) 18. Solve the following inequality: −9𝑟 > 20 + 𝑟 19. Solve the following inequality: 3𝑧 − 39 > 13 + 2𝑧 20. Use the number line below to graph the solution to the inequality 5x - 4 > 3x – 6 5𝑥 − 4 > 3𝑥 − 6 21. Alex and Fred decide to pool their money together to purchase a birthday gift for their mother. Alex has $4 more than Fred. Altogether they have $12. How much money does Alex have? 22. Mr. Smith wants to mix pens costing $0.35 each with pencils costing $0.15 each. The mixture will cost $6.45. If the number of pencils is 3 more than the number of pens, how many of each type should be in the package? 23. Nick’s rectangular garden has a length of (4x – 1) and a width of (x + 3). Write a standard form equation that describes the area, A, of Nick’s garden in terms of x?

23. Factor the following: i. 2𝑥> + 3𝑥 + 1 ii. 18𝑥> − 3𝑥 iii. 8𝑥> − 13𝑥 + 9 iv. 𝑥> + 7𝑥 − 8 24. The equation that describes the path of a rocket after it is shot into the air is ℎ = 30𝑡 − 5𝑡>. The height, h, of the rocket is a function of t, the time, in seconds, since the rocket left the ground. What is the height in feet after the rocket has been in the air 5 seconds? 25. Write a quadratic equation that describes the graph of the parabola shown below. Find the roots of the function using the quadratic formula.

26. Write a quadratic equation that describes the shift in the vertex of the parabola 𝑦 = 3𝑥> − 4 is translated 5 units up? 27. What are the x-intercepts of the graph of the equation (3𝑥 − 2)(𝑥 + 7)? 28. What are the x-intercepts of the graph of the equation 𝑥> − 2𝑥 = 15? 29. The area of a warehouse with a rectangular floor is 2436 square yards. The perimeter of the warehouse floor is 200 yards. Find length, l, and the width, w, of the warehouse floor? 30. The area of a rectangular flag is 14 square feet. The length of the flag is 5 feet longer than the width. What are the dimensions of the flag? 31. Barbara is considering switching cell phone plans so she can send more text massages. Her current cell phone company chargers her $60 a month for unlimited calls plus $0.15 per text message. Text-a-Lot charges a flat fee of $75 per month for unlimited calling and texting. a. Write a system of equations to represent this situation. b. For what number of text messages will the two plans charge the same amount. c. For what number of text messages will Barbara’s current plan charge her less than the Text-a-Lot plan? d. For what number of text messages a month should Barbara switch to the Text-a-lot plan?

32. In a baseball game, an outfielder throws the ball to home plate. The height of the throw (in meters) is modeled by the function ℎ 𝑡 = −4.9𝑡> + 19.6𝑡 + 1.3, with time measured in seconds. a. What is a reasonable domain and range for the situation? b. From what height was the ball thrown? c. What is the maximum height of the ball? d. For approximately how many seconds was the ball in the air? 33. Solve each equation below using the quadratic formula. For each problem, state the discriminant of the quadratic formula and the solution(s) to the equation. What type of solutions (rational, irrational, or complex) does each equation below have? a) 2𝑥> + 12𝑥 − 10 = 0 b) 𝑥> − 4𝑥 + 29 = 0 c) 4𝑥> − 35𝑥 − 9 = 0 34. Sketch a graph of each of the following functions.

𝑦 = − 𝑥 − 2 + 3 𝑦 = 2𝑥 + 1 − 4 𝑦 = −2 𝑥 + 2 − 4 35. The senior class wants to sell candy to raise money for a senior trip. They can buy the candy for their fundraiser from Sweet Tooth or from Chocolate Frenzy. Sweet Tooth will sell them the candy for an initial payment of $60 and $1 for each box. Chocolate Frenzy will sell them the candy for an initial payment of $40 and $2 for each box. When does each company offer the better deal and why? 36. The measure of the largest angle of a triangle is equal to twice the sum of the measures of the other two angles. The sum of the measures of the smallest and largest angles is three times the measure of the remaining angle. Find the measures of the three angles. 37. Mr. Smith wants to mix pens costing $0.35 each with pencils costing $0.15 each. The mixture will cost $6.45. If the number of pencils is 3 more than the number of pens, how many of each type should be in the package? 38. Solve the following absolute value equations. Check your answers in a calculator. i. 3𝑥 + 14 = 7 ii. 2𝑥 − 5 = 3𝑥 − 5

39. Stephanie throws her paper plane into the air. The equation that represents the plane’s flight is −0.1𝑡> + 2𝑡 + 5 = ℎ, where h is in feet and t is time in seconds. Answer the following questions using the equation given. Round your answers to 3 decimal places. i. At what 2 times is the plane 12 feet above the floor? ii. When does the plane hit the ground? iii. How high does the plane go? iv. How long after Stephanie throws the paper airplane does it reach its maximum height? 40.