Teaneck High School Algebra II Summer Assignment

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Pamela Hall
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1 Teaneck High School Algebra II Summer Assignment

2 Dear Parents and Students: This summer assignment must be completed prior to entering Algebra II in September of school year. The packet includes two major components: a review of essential math skills needed for this course and a project. It is recommended that you complete the skills component first as the exercises are designed to make sure you understand the concepts needed to complete the project. If you need assistance or further practice with any of these skills, we strongly recommend that you to use the following links as the resources: Below are the POLICIES of the summer packet The summer assignment is due the first day of class. On the first day of class, teachers will collect summer assignments. Any student who does not have the assignment will be given one by the teacher. Late projects will lose 10 points each day. Summer assignments will be graded as a quiz. This quiz grade will consist of 20% completion and 80% accuracy. Completion is defined as having all work shown in the space provided to receive full credit, and a parent/guardian signature. Any student who registers as a new attendee of Teaneck High School after August 15 th will have an extra week to complete the summer assignment. Summer assignment packets will be available on the district web site and available in the THS guidance office. HAVE A GREAT SUMMER!!!

3 ALGEBRA II SUMMER PROJECT STAY FIT IN MATH AND LIFE!! What will you do this summer? Go on vacation? Sleep until noon? Just hang out? No matter what you choose, there is little doubt it will be better than having to go to school! Let s face it it s easy to get lazy over the summer months, physically and academically. This project is intended to not only sharpen your math skills, but also challenge you to get or stay physically fit! Let s get started. First, complete the included skills packets to make sure you understand the concepts needed to complete the project. Once you ve done that, complete these steps: 1. Choose any physical activity you like to do (run, swim laps, jump rope you name it!). 2. Dedicate ONE WEEK to doing this activity every day. Your goal is to push yourself each day to do a little bit more than the day before! 3. Make an x/y chart to record your data from each day (how many miles you ran, how many jumping jacks you did, etc.). 4. Make sure to identify your independent and dependent variables and label your chart accordingly. 5. Graph your data on a coordinate plane. 6. Create a line of best fit for the data you collected. 7. Sketch your line of best fit on your coordinate plane. Once you ve completed your project, answer the following questions: If you continued doing your activity for a month, how many times would you do your activity on the 30 th day, based on your line of best fit? Is this prediction reasonable? Explain why or why not. Explain what you learned from this project. Did you increase your stamina? Are you more fit? Are you more dedicated to the activity of your choice? Did it help discipline you to perform the activity you chose? How did your math skills improve? **Projects will be displayed in the classroom, so quality effort is required**

4 PART 1: SKILLS PACKET Section 1: Evaluating Expressions EXAMPLE SOLUTION Evaluate 8ab 3 c for a = -5, b = 2, and c = -1. 8(-5)(-2) 3 (-1) = 8(-5)(-8)(-1) = 320 EXAMPLE Given V = πr 2 h, if V = 3140 in 3 and r = 10 in, find h. SOLUTION 3140 = 3.14(10) 2 h 3140 = 3.14(100)h 3140 = 314h h = 10 in Your turn! Evaluate each expression. 1. 8c+ab a when a = 4, b = 5, c = (a d + b) c if a = -1, b = 4, c = - 0.5, d = A = (b 1+ b 2)h 2 if A = 60 cm 2, b 1 = 20 cm, 3. b 2 = 10 cm, find h. 4. y = 2x 2 + w If y = 11w and w = 5, find x F = 9 C + 32 If F = 72, find C. 5. 5

5 SECTION 2: Solving Equations and Inequalities (10 points) EXAMPLE: SOLUTION: CHECK: Solve: 6d + 9 = 45 6d = 36 6(6) + 9 = 45 d = = = 45 EXAMPLE: SOLUTION: CHECK: Solve: -x + 6 > 7x + 4 -x + 6 > 7x + 4-7x -7x - 8x + 6 > x > -2 x < - ¼ *** *** Remember to switch the inequality symbol when dividing or multiplying both sides by a negative number!!! EXAMPLE: SOLUTION: CHECK: 2x + 3 < 5 or 4x 7 > 9 2x + 3 < 5 or 4x 7 > 9 2x < 2 4x > 16 x < 1 x > 4 Final Solution: x < 1 or x > 4 EXAMPLE: SOLUTION: CHECK: -18 < 2x + 10 < 6-18 < 2x + 10 < < 2x < < x < -2 Final Solution: -14<x<-2 Your turn! Solve show all steps to receive full credit. (2 points each) 1. 12x + 36 = 8x 48 Check: 1. Final Solution:

6 2. 6x 12 > - 18 Check: 2. Final Solution: 3. 5y + 8 < 4y 3 Check: 3. Final Solution: 4. 11x 9 > 13 or -4x 4 < 8 Check: 4. Final Solution: y Check: 5. Final Solution:

7 SECTION 3: WRITING EQUATIONS (10 points) EXAMPLES: Write an equation of a line with a slope of -3 and a y-intercept of 2 SOLUTION: Plug in the slope for m and the y-intercept for b in the equation y = mx + b Answer: y = -3x + 2 Write an equation of the line passing through the points (3, -8) and (8, 2). Use the formula m = y 2 y1 to find x 2 x 1 the slope: m = 2 ( 8) = 10 = Then, use either point and the slope to find the y-intercept. y = mx + b given m = 2 and (8, 2) 2 = 2(8) + b 2 = 16 + b -14 = b Answer: y = 2x 14 Your turn! Find an equation of the line passing through the given pair of points. Show all steps for full credit. ( 2points each) 1. Slope of 3 and a y-intercept of Equation 2. (-2, 5) and (-6, 8) 2. Equation

8 3. Slope -1 and point (2, -4) 3. Equation 4. (-2, -1) and (3, 4) 4. Equation 5. (1, 5) and (4, 2) 5. Equation

9 Section 4: Graphing Equations. (10 points) Example 1: Graph the equations using a table of values: -2x+y = -1 Solution: Choose values for x and substitute into the original equations to find y; choose x= -2, -1, 0, 1, 2 (any values can be chosen): X Y Example 2: Graph the equation using slope and y-intercept: y = 2x + 1 Solution: Identify the slope as the number in front of x. So, m= 2 and the y-intercept is the value added 1 to the x term, so b= 1. Plot 1 on the y-axis and then use the slope to go up 2 spaces and right 1 space.

10 Example 3: Graph the absolute value equation: Y = I x + 1 I 2 Solution: Make a table of values by plugging in x values and creating a t-chart of points. Choose x= -1 as the middle point. (-1 = zero value of x = vertex value of x): X Y Your turn! (2 points each) 1. Graph: y = -x + 4 x y

11 2. Graph y = 1 2 x 2 x y 3. Graph Y = I x + 3 I 2 x y

12 4. Graph y = x 2 + 3x 4 x y 5. Graph X = 4 x y

13 SECTION 5: Systems of Linear Equations (10 points) EXAMPLE: SOLUTION: 2(3x y = 13) 6x 2y = 26 Solve the system by linear combination: 2x + 2y = -10 2x + 2y = -10 3x y = 13 4x = 16 2x + 2y = -10 x = 4 2(4) + 2y = y = -10 2y = -18 y = -9 Final Answer: (4, -9) Solve the system by substitution: 2x y = 9 Solve the 2 nd equation for x. x + 3y = -6 x = -6 3y Substitute for x in 1 st equation 2(-6 3y) y = y y = y = 9-7y = 21 y = -3 Now substitute for y in either equation x + 3(-3) = -6 x 9 = -6 x = 3 Final Answer: (3, -3) Your turn! Show your work for full credit. (2 points each) 1. Solve by substitution: x + y = 4 1. Final Solution: x y = 8 2. Solve by linear combinations: 2x + 3y = Final Solution: 3x + 2y = 25

14 3. Solve using any method: 3x y = 4 3. Final Solution: x + 5y = Solve using any method: 2y = 3x Final Solution: x = 3y Solve using any method: y = 1 x Final Solution: y = -2x 1

AMS 10 SUMMER ASSIGNMENT

AMS 10 SUMMER ASSIGNMENT Dear Student, Welcome to AMS 10! In preparation for the fall, all students entering AMS 10 must complete this summer assignment. To be successful in mathematics, you must be willing