ALGEBRA II/TRIG HONORS SUMMER ASSIGNMENT

Transcription

1 ALGEBRA II/TRIG HONORS SUMMER ASSIGNMENT Welcome to Algebra II/Trig Honors! In preparation for the fall, all students entering Algebra II/Trig Honors must complete this summer assignment. To be successful in mathematics, you must be willing to devote time and energy to practice these skills. Work on this packet throughout the summer. There are two parts to this assignment: 1) A skills packet and 2) The Olympic Project. Below are the POLICIES of the summer assignment: 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 (40% Part 1: Skills Packet and 40% Part 2: Project). 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. 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

3 Section 1: Evaluating Expressions PART 1: SKILLS PACKET 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 1 1. when a = 4, b = 5, c = a 2 2. (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)

4 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: 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)

6 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 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)

8 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.

9 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

10 1 2. Graph y = x 2 2 x y 3. Graph Y = I x + 3 I 2 x y

11 4. Graph y = x 2 + 3x 4 x y 5. Graph X = 4 x y SECTION 5: Systems of Linear Equations (10 points)

12 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: x + 5y = -4

13 4. 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

14 Introduction Faster! Stronger! Olympic Times The first Olympic Games featured only one game a foot race. The 2016 Olympics in Rio 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 Rio Summer Olympics. They are sending you to Rio 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 Rio 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 Rio s winning time. 7. Be creative. Make it exciting! Add some additional data, information, or even pictures to your newspaper article.