Sierra Verde STEM Academy Honors Algebra 1-2 Summer Packet

Transcription

1 Name: Due: August 14, 2015 Sierra Verde STEM Academy Honors Algebra 1-2 Summer Packet This packet contains topics that you are expected to know prior to entering Algebra 1-2. You have learned these skills over the past few years. These examples focus on both mathematical skills and problem solving. This packet should be completed independently. Upon your completion, your parent/guardian needs to sign the packet. As in your Algebra class next year some sections will require the use of a calculator, while in other sections a calculator is prohibited. In the directions, it will say if you are not allowed to use a calculator. If you are having a difficult time adding, subtracting, and multiplying numbers, I suggest you study this over the summer. For example, flashcards can be used to help you with basic facts. Also, you can do a Google search for more practice problems. Please show your work in the packet. You will be assessed on this material at the beginning of the school year. There are links to instructional videos from Khan Academy to help you remember some topics. This packet will also guide you through setting up the necessary online tools that we will be using in the seventh grade. Remind 101 Remind is a free, safe, and simple messaging tool that helps teachers share important updates and reminders with students & parents. Subscribe by text, or using the Remind app. Teachers will never see your phone number, nor will you see theirs. Visit remind.com to learn more. To receive messages via text, to You can opt-out of messages at anytime by replying, To receive messages via , send an to 6netz@mail.remind.com. To unsubscribe, reply with 'unsubscribe' in the subject line. - I am asking that you set up an account on Khan Academy and add me as a coach. If you need help with some of the skills please watch the suggested Khan Academy videos. Please sign up at khanacademy.org (or log in with their existing accounts) Visit khanacademy.org/coaches There, in the "Add a coach" field, enter the class code CP89AE Please see Khan Academy Time log on the last page of this packet. If you have any questions please me at Sallie.Netz-Mowrer@dvusd.org. I am very excited to see all of you in August. Have a relaxing and exciting summer break! See you soon. Sincerely, Sallie Netz-Mowrer Parent/Guardian Signature: Date:

2 Question Standard # 8th Grade AZCCRS Functions - Students need to define, evaluate and compare functions and to use functions to evaluate relationships between quantities. Given the linear function f1 in the table below and the linear function f2 represented by the equation y = -3.2x +6, which of the functions has a greater rate of change? 1 8.F.2 x y Given the linear function f1 from question 1, what is x for y = F.1 Given the linear function f1 represented by the equation y = -5, the linear function f2represented by the equation y = -5 + x, and the linear function f3 represented by the equation y = 3x - 9, which of the functions has a lowest rate of change? 3 8.F.2

3 Which of the following equations represent linear functions? How do you know? y = 3xy F.3 y = 2(3-2x) y = x(x + 1) y = x 2 Given the linear function f(x) in the table below, what are the initial value and the rate of change of the function? 5 8.F.4 x f(x) Determine if f(x), g(x), h(x) and i(x) are functions. Explain how you know. 6 8.F.1

4 Given the four functions in the table below, the only linear function between f1, f2, f3 and f4 is: 7 8.F.3 x f1 f2 f3 f In the figure below, the function displayed is linear and decreasing on the interval. 8 8.F.5

5 Question Standard 8th Grade AZCCRS Number System Know that there are numbers that # are not rational and approximate them by rational numbers. Represent the following rational number, a in fraction form: 9 8.NS.1 Represent the following rational number, b in fraction form: 10 8.NS.1 Represent the following rational number, c in fraction form: 11 8.NS.1 Determine of the numbers m and n are rational or irrational NS.1 The number reasoning. is between what two integers? Explain your 13 8.NS.2

6 Which of the following numbers are greater than 12 and less than 13? 14 8.NS.2 Compare the numbers x and y below 15 8.NS.2 Compare the numbers a and b below 16 8.NS.2

7 Question Standard # 8th Grade AZCCRS Expressions and Equations - Students need to work with radicals and integer exponents, understand the relations between proportional relationships, lines and linear equations and analyze and solve linear equations EE EE.2 What are the solutions of the equation x 2 = 81 An insect is 20mm long. If you put such insects in a line, how long is a line made with 10 million of them? Express the result in kilometers EE.3 The average growth rate of human hair is equal to m/day. At this rate, a hair grows 8mm in days EE = 21 8.EE.4

8 Two vehicles travel with constant speeds. Vehicle A speed is given in the graph below, while vehicle B speed is given by the equation v B = 61.2 t, where v B is measured in miles/hour and t is measured in hours EE.5 The faster of the two vehicles is because What is the equation of the line m shown in the coordinate plane below? Explain how you determined the equation of the line EE.6

9 The equation 2x x = 4x - x + 25 has solutions. Explain EE.7a Solve the following linear equation: 25 8.EE.7b Solve the following system of linear equations: 26 8.EE.8b y = 3x y - x = 1

10 Question Standard # 8th Grade AZCCRS Statistics and Probability - Students use sampling to draw inferences, draw informal comparative inferences about two populations and investigate chance processes and develop, use, and evaluate probability models. The scatter plot in the figure below shows the GPA of the students of a class versus their commute time. Which of the following statements is true? Justify your choice SP.1 a) The relationship between GPA and commute time is moderate positive linear. b) The relationship between GPA and commute time is moderate negative linear. c) The scatter plot does not have any outliers. d) There is no relation between GPA and commute time.

11 28 8.SP.2 All students of a school were asked what their preferred sport is and the results were recorded below. Which of the statements below are correct? Justify your answer. Favorite Sport by Gender Gender Baseball Football Basketball Totals Boys Girls Totals a) A higher percentage of boys than girls prefer baseball, while a higher percentage of girls than boys prefer basketball and football. b) A higher percentage of boys than girls prefer basketball and football, while a higher percentage of girls than boys prefer baseball. c) A higher percentage of boys than girls prefer football, while a higher percentage of girls than boys prefer baseball and basketball. d) A higher percentage of boys than girls prefer baseball and football, while a higher percentage of girls than boys prefer basketball. The graph below shows the diameters of a number of white oak trees versus their ages SP.3 The growth factor of white oak trees is approximately years per inch.

12 Assuming a linear growth rate in problem #3, what is the diameter of a 130 year old white oak tree? 30 8.SP.4 A study investigates the relationship between learning piano and the mathematics level of fifth grade students, by testing them with a mathematics quiz and recording the results in the table below SP.4 Student Studies Piano Mathematics Quiz Grade Yes No Yes No No Yes Yes No No Yes Yes No No No Yes No No No Yes No A C B D B A A C A D A A B C A D C B A B Of the fifth grade students tested who study piano, % received an A grade, and of the fifth grade students tested who do not study piano, % received C or D grades.

13 Question Standard # 8th Grade Common Core Geometry 8.G: Seventh grade students are expected to be able to understand congruence and similarity, understand and apply the Pythagorean Theorem, and solve real-world and mathematical problems involving volumes of spheres, cones and cylinders. If a and b are parallel lines, what is the value of angle α in the figure below? Explain how you determine your answer G.5 In triangle ΔABC, point F is the point of intersection of the bisector of angle ABC and the altitude AD of the triangle. The measure of BCA is 48, and the measure of BAC is 78. What is the measure of AFE? 33 8.G G.5 What is the supplement of a 56 angle?

14 The distance between the vertices A and G of the polygon ABCDEFGHI in the coordinate plane below is meters G.8 The rectangle solid in the figure below has the length equal to 3cm, the width equal to 4cm and the height equal to 5cm. Which of the following is the closest to the length of the diagonal CE? 36 8.G.7

15 The diagonal AC of rhombus ABCD is 24cm. If the area of the rhombus is 120cm 2, side AB measures cm G.7 A glass has a conical shape, and its dimensions are given below. What is the volume of glass necessary to manufacture the glass? 38 8.G.9 A cylinder C1 and a cone C2 have the same base: a circle of radius r. What is the ratio between the height of the cone and the height of the cylinder if the volumes of the two geometrical shapes are equal? 39 8.G.9

16 Minutes Khan Academy Log Please make sure by the beginning of the school year you have 100% of the 7 th and 8 th grade material on Khan mastered. For those of you wanting to get a jump start on the material for this coming school year you can work on the Algebra I material on Khan. Please spend 30 a week working on keeping you math skills sharp. Log your time here. Date Concept Level Mastered, Level 2 Level 1, Practiced, or Needs Practice Parent Signature