Name: _____________________________Final Exam Study Guide

Algebra 1A 2013*We will be completing this study guide in parts. If you know how to complete all problems on this Study Guide, you will do very well on the Final Exam.*If you choose to skip a night of studying and practice, you probably will not do as well as you would like!

Part One: Classifying Numbers, Measures of Central Tendency and Algebraic Properties

Due: Wednesday, 5/221. Describe each number as completely as possible using all terms that apply. Choose from: irrrational, rational, integer, whole, and natural.

a) -5

b) 0.25

c) pi

d) 0

e) 109

f) 2⇃

2. Algebraic Properties: Please write the CAPITAL LETTER of the property represented by each statement.A. Associative Property B. Commutative Property C. Distributive PropertyD. Identity Property of Addition E. Identity Property of MultiplicationF. Inverse Property of Addition G. Inverse Property of Multiplication

a. 8(1) = 8 ______ b. 8 + (7 + 9) = 8 + (9 + 7) ______

c. 8 + (-8) = 0 ______ d. 8(1/8) = 1 ______

e. 8(7 - 9) = 8(7) - 8(9) ______ f. 8 + 0 = 8 ______

g. 8 + (7 + 9) = (8 + 7) + 9 ______

3. Measures of Central Tendency: Please find the mean, median, mode and range of the following data set:56, 65, 102, 56, 57, 62

a) mean

b) median

c) mode

d) range

e) Are there any outliers in the data set? Explain your answer using complete

sentences and algebraic terms.

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4. Measures of Central Tendency Word Problem: Choose either Problem #1 or Problem #2 to complete. (Note: you will also have CHOICE on the Final Exam.)

Problem #1: Billy Bob scored the following on his first four math tests: 83, 87, 92, and 89. What is the minimum score Billy Bob needs on his fifth test in order to have a mean of 90? Write and solve an equation to solve this problem. Do you think Billy Bob can achieve this goal? Explain.

Problem #2: In her first four years of professional softball, Lena Leroy hit 40, 42, 50, and 25 home runs. What is the minimum number of homeruns Lena will need in her fifth year in order to have a mean of 45 homeruns per year? Write and solve an equation to solve this problem. Do you think Lena can achieve this goal? Explain.

Part Two: Expressions and Equations

due Thursday, 5/235. Simplifying: Please simplify each expression completely. BOX your final answers.

a) -9(-x + 7)

b) -4(h - 2) + 6(2h + 6)

c) x + y + 1 + x + 2 + y + 1

d) (2r - 7)4

6. Using complete sentences and algebraic terms, please explain how expressions and equations are alike and how they are different. (Give at least one similarity and one difference.)

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7. Using complete sentences and algebraic terms, please explain how an equation can have a solution of ALL REAL NUMBERS.

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8. Solve the following equations. Show ALL of your work and BOX your final answers.

a) -8 + x = 3

b) 5b = -20

c) 9 h = - 45 10

d) -6(y + 1) - 2y = 4(-2y + 1) -10

e) -7(2h - 1) = 21

9. WITHOUT ACTUALLY SOLVING, please explain how you would solve the equation: -5x + 6 = 36. Use complete sentences and algebraic terms. Please be sure to JUSTIFY each step.

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Part Three: Inequalities and Absolute ValueDue: Friday, 5/24

10. Solve each inequality or absolute value equation/inequality and GRAPH the solution on a number line. BOX YOUR FINAL ANSWERS.

a) h - 5 < - 12

b) -3x < 15

c) 1/5t > - 10

d) -10 < 2x + 3 < 8

e) 5y < - 10 OR y + 8 > 1

f) l2p + 1l = 21

g) l4f - 9l < 3

h) le + 14l > 5

11. Absolute Value Word Problem: Choose Problem #1 OR Problem #2. (Note: you will also have choice on the final exam.)

Problem #1: Abby is building an inground pool and wants the length of the pool to be three feet more than twice the width. He wants the area of the pool to be at least 110 square feet. DRAW A DIAGRAM, THEN WRITE AND SOLVE AN INEQUALITY TO FIND THE MINIMUM WIDTH AND LENGTH OF ABBY’S POOL.

Problem #2: Bria is making a circular pendant and she wants the circumference of the pendant to be no more than 12 inches. Using 3.14 for pi, find the maximum RADIUS of Bria’s pendant. DRAW A DIAGRAM, THEN WRITE AND SOLVE AN INEQUALITY to solve this problem.

Name: ________________________________Final Exam Study Guide: Algebra 1A 2013

Part Four: Word Problems (DRT, Simple and Compound Interest, Exponential Decay, Percent Change)

Due: Tuesday, 5/28

12. DRT: Choose and CIRCLE ONE of the following DRT problems to complete. (Note: on the Final Exam , you will also have a choice.)

Problem #1: Nodiyah left for the day, but she forgot her cell phone. She is riding in a car that is driving an average of 45 mph. Chris, seeing her cell phone, hops on his motorcycle an hour later to bring her the cell phone. If he is driving at an average of 55 mph, after how many hours will he catch up to Nodiyah?

Problem #2: Megan and Tyler are both at school, preparing to leave for summer vacation. Megan leaves at 3 pm, traveling north at a speed of 60 mph, to her cabin in Maine. Tyler leaves at 4 pm, traveling south at a speed of 50 mph, to his beach house in Florida. At what time will Megan and Tyler be 600 miles apart?

a) What type of DRT problem is this? _____________________

b) What is the general equation for this type of problem? _______________________

c) Fill in the DRT chart.

r t D

d) Write and solve an equation.

e) ANSWER the question.

13. Simple Interest: Taariq borrows $350 from his parents, who charge him 5% simple annual interest.

a) What is the total amount of INTEREST Taariq will owe his parents after three years?

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b) What is the total amount of money Taariq will owe his parents after three years?

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14. Exponential Word Problems: Choose Problem #1 OR Problem #2. (Note: you will also have CHOICE on the Final Exam.) Problem #1: Amira deposits $4,590 into a savings account with a 2.8% annual interest rate. Her savings account is compounded quarterly. Assuming Amira makes no deposits or withdrawals, how much money will be in Amira account after 5 years? (Use the compound interest formula to solve this problem. B = p(1 + r)t. Round to the nearest cent, if necessary.)

Problem #2: Judah is examining a compound with a half-life of 13 days. There are 590 grams of the compound to start. How many grams will be present after 39 days? (Use the exponential growth formula, y = abx. Remember, with half-life, the growth factor is always ½.)

15. Percent Change: Please answer each question related to percent change.

a) What is the formula used to find percent change?

b) A sweater originally priced at $88 is reduced to $34 at the beginning of spring. What is the percent decrease? Round to the nearest hundredth.

c) When WLPCS first began, there were 179 students. Now, there are 600 students. What is the percent increase? Round to the nearest hundredth.

Part Five: Relations, Functions, Slope and Linear EquationsDue: Wednesday, 5/29

16. Comparing: In complete sentences, please define relation and function and describe the relationship between the two.

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17. Function? Are the following relations functions? Explain your answer using complete sentences and algebraic terms.

a)

x y

-2 2

1 0

-2 3

-1 4 ______________________________________________________________________

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18. Function Notation: Given f(x) = -x2 - 8, find f(-1).

19. Slope: Find the slope of the line between the two points. Write your answers as reduced fraction, if possible.

a) (-3, 8) and (-1, 2)

b) (4, -6) and (12, -6)

c) (9, -2) and (9, 1)

20. Graphing Linear Equations: Please graph the linear equations on the coordinate planes provided. NAME YOUR LINES.

y = 2/5x - 1 y = -5 3x - y = -9 x = 1 y - 2 = ¼(x + 3)

21. Writing Equations: Write an equation in the requested form using the given information.

a) Write the equation for the line in slope-intercept form that passes through (2, -1) and

(4, -5).

b) Write an equation for the line in slope-intercept form that passes through (-8, 1) and is parallel to the line: y = -1/4x + 2.

c) Write an equation for the line in slope-intercept form that passes through (2,-3) and is perpendicular to the line: x – 2y = -9.

d) Write the equation of the line in STANDARD form whose equation in slope-intercept form is y = 1/4x - 2.

Part Six: Pythagorean Theorem, Trigonometry and Multiple ChoiceDue: Thursday, 5/30

22. Pythagorean Theorem: Use the PT and/or its converse to answer each question.

a) Write the Pythagorean Theorem.

b) Three sides of a triangle are 25 feet, 65 feet and 60 feet. Is this a right triangle? Show your work.

c) Jack leans a ladder 8 feet from the base of the beanstalk in order to climb it. The ladder is 16 feet long. How high on the beanstalk will the ladder reach? Draw a diagram and use the PT to solve. Round to the nearest tenth, if necessary.

23. Trigonometry: Using the diagram, please find the following. Write a, b, and c as reduced ratios.

a) sin A b) cos A c) tan A

24. Trigonometry Word Problem: Choose Problem #1 OR Problem #2. (Note: you will also have CHOICE on the Final Exam.) Problem #1: Allegra is looking up at Ay, who is standing on top of a building that is 58 feet tall. If the angle of elevation is 45 degrees, how far is Allegra from the base of the building?Draw a picture and write a trigonometric ratio to solve. Round to the nearest hundredth. Problem #2: Alex Crute is at the top of a cliff with a zipline that travels down his line of sight to Benjamin Wood, who is on the ground. If the zipline is 500 feet long, and the angle of depression is 78 degrees, how far is Benjamin from the base of the cliff? Draw a picture and write a trigonometric ratio to solve. Round to the nearest hundredth.

25. Multiple Choice: Write the CAPITAL LETTER of the correct answer in the blank provided.

_____ In the equation, 4x - 2 = 2x + 3, what is the first step?

A. Dividing each side by 4 B. Using the distributive property

C. Subtracting 2x from each side D. Crying

_____ What is the justification for the step below?

5y - 2 = 12 5y = 14

E. Addition Property of Equality F. Subtraction Property of Equality

G. Distributive Property H. Division Property of Equality

_____ What does the constant decrease portion of the graph represent?

A. the ball has been thrown and is traveling toward the ground

B. the ball is very briefly hitting the ground for the second time

C. the ball is hitting the ground very briefly

D. the ball has reached the maximum height of the first bounce

_____ How do you determine Greatest Possible Error?

E. (new - original)/original F. a2 + b2 = c2

G. one half of the measuring unit H. use the distributive property