AMS 10 SUMMER ASSIGNMENT

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1 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 to devote time to practice. It is important that you have an understanding of the concepts that will be applied in this work before you start the next school year. The packet is to be completed by the first day of class. It will be collected and graded based upon completion and correctness. You MUST show all work in order to receive credit! The grade on this assignment will be your first quiz grade in AMS 10. Work on this packet throughout the summer. It will provide you with many of the skills that you are expected to have when entering AMS 10. Please complete this summer assignment and have a parent or guardian sign the packet once they have reviewed it. There are two parts to the assignment: 1) A skills packet 2) The Olympic Project. To help you with this assignment, you can get help and find examples on the following websites:

2 Skills Packet Scoring Rubric: This portion of your summer assignment makes up 50% of your grade. The project makes up the other 50%. Points Criteria Points Earned 10 points ( 2 points for each question) Section 1: Evaluating /10 10 points ( 2 points for each question) Section 2: Solve /10 10 points ( 2 points for each question) Section 3: Writing Equations /10 10 points ( 2 points for each question) Section 4: Graphing Lines /10 10 points (2 points for each question) Section 5: Solving Systems /10 50 Points Total / 50 PARENT SIGNATURE PART 1: SKILLS PACKET

3 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. 8c+ab when a = 4, b = 5, c = - - a (a d + b) c if a = -1, b = 4, c = - 0.5, d = (b 1+ b2)h 3. A = 2 if A = 60 cm 2, b1 = 2 0 cm, 3. b 2 = 10 cm, find h. 4. y = 2x 2 + w If y = 11w and w = 5, find x F = C + 32 If F = 72, find C SECTION 2: Solving Equations and Inequalities (10 points) EXAMPLE: SOLUTION: CHECK:

4 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: 2. 6x 12 > - 18 Check:

5 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: SECTION 3: WRITING EQUATIONS (10 points) EXAMPLES: Write an equation of a line with a slope SOLUTION: Plug in the slope for m and the

6 of -3 and a y-intercept of 2 y-intercept for b in the equation y = mx + b Answer: y = -3x + 2 y 2 y1 Write an equation of the line passing through Use the formula m = to find x 2 x1 2 ( 8) 8 3 the points (3, -8) and (8, 2). the slope: m = = = 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) 3 1. Slope of and a y-intercept of Equation 2. (-2, 5) and (-6, 8) 2. Equation 3. Slope -1 and point (2, -4)

7 3. Equation 4. (-2, -1) and (3, 4) 4. Equation 5. (1, 5) and (4, 2) 5. Equation 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):

8 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. 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):

9 X Y Your turn! (2 points each) 1. Graph: y = -x + 4 x y 1 2. Graph y = x 2 2

10 x y 3. Graph Y = I x + 3 I 2 x y 4. Graph y = x 2 + 3x 4

11 x y 5. Graph X = 4 x y

12 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 = Solve using any method: 3x y = 4 3. Final Solution:

13 x + 5y = Solve using any method: 2y = 3x Final Solution: x = 3y Solve using any method: y = x Final Solution: 2 y = -2x 1 Summer Packet Project Faster! Stronger! Olympic Times

14 Introduction The first Olympic Games featured only one game a foot race. The 2020 Olympics in Tokyo will include thousands of competitors in over 300 events. In this project, you will explore how linear functions can help to predict the timed Olympic events. The Task In your new job as a sports writer for Teaneck newspaper you have been assigned to cover the Tokyo Summer Olympics. They are sending you to Tokyo for the summer of But before you can go, you must generate local interests for the Olympics. Your plan is to write an article comparing men s or women s times over the years in a timed Olympic event. Your article must generate interest, excitement and anticipation for the Olympics. Thus, your plan is to generate a linear equation for the fastest times of the past, and use this equation to predict what the winning time for the next Olympics would be! Your article needs to contain the following information: 1. A brief history of the event including the names of participants that were well-known or in some way unique, and anything unusual that may have happened over the years; 2. The winning times for men or women in a timed event, such as a swimming or a running event; 3. Graphs of the winning times over the years for the event; 4. A prediction for what the winning time for the Tokyo Olympic would be. The Process To successfully complete this project, you will need to complete the following items. 1. Find data about timed Olympic events. For help, try these Web sites Decide on a timed Olympic event in which you are interested. 3. Make a table of the years and winning times for men or women in the event. 4. Research the history of the event to find any famous or unique people who have won the event over the years. 5. Draw a line of best fit for the scatter plot of the data, where x represents the years and y represents the winning times. 6. Come up with a linear equation for the line of best fit to predict Tokyo s winning time. 7. Be creative. Make it exciting! Add some additional data, information, or even pictures to your newspaper article.

Teaneck High School Algebra II Summer Assignment

Teaneck High School Algebra II Summer Assignment Dear Parents and Students: This summer assignment must be completed prior to entering Algebra II in September of 2016-2017 school year. The packet includes