Review for EOC. Arithmetic Sequences, Geometric Sequences, & Scatterplots

Transcription

1 Review for EOC Arithmetic Sequences, Geometric Sequences, & Scatterplots

2 Over Lesson 3 4 What is the constant of variation for the equation of the line that passes through (2, 3) and (8, 12)? A. B. C. D.

3 Over Lesson 3 4 Which graph represents y = 2x? A. B. C. D.

4 Over Lesson 3 4 Suppose y varies directly with x. If y = 32 when x = 8, find x when y = 64. A. 6 B. 8 C. 24 D. 16

5 Over Lesson 3 4 Which direct variation equation includes the point ( 9, 15)? A. B. C. D.

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7 Identify Arithmetic Sequences A. Determine whether 15, 13, 11, 9,... is an arithmetic sequence. Explain. Answer: This is an arithmetic sequence because the difference between terms is constant.

8 Identify Arithmetic Sequences B. Determine whether is an arithmetic sequence. Explain. Answer: This is not an arithmetic sequence because the difference between terms is not constant.

9 A. Determine whether 2, 4, 8, 10, 12, is an arithmetic sequence. A. cannot be determined B. This is not an arithmetic sequence because the difference between terms is not constant. C. This is an arithmetic sequence because the difference between terms is constant.

10 B. Determine whether is an arithmetic sequence. A. cannot be determined B. This is not an arithmetic sequence because the difference between terms is not constant. C. This is an arithmetic sequence because the difference between terms is constant.

11 Find the Next Term Find the next three terms of the arithmetic sequence 8, 11, 14, 17,. Find the common difference by subtracting successive terms. The common difference is 3.

12 Find the Next Term Subtract 3 from the last term of the sequence to get the next term in the sequence. Continue subtracting 3 until the next three terms are found. Answer: The next three terms are 20, 23, and 26.

13 Find the next three terms of the arithmetic sequence 58, 63, 68, 73,. A. 78, 83, 88 B. 76, 79, 82 C. 73, 78, 83 D. 83, 88, 93

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15 Find the nth Term A. Write an equation for the nth term of the arithmetic sequence 1, 10, 19, 28,. Step 1 Find the common difference. In this sequence, the first term, a 1, is 1. Find the common difference. The common difference is 9.

16 Find the nth Term Step 2 Write an equation. a n = a 1 + (n 1)d Formula for the nth term a n = 1 + (n 1)(9) a 1 = 1, d = 9 a n = 1 + 9n 9 Distributive Property a n = 9n 8 Simplify.

17 Find the nth Term Check For n = 1, 9(1) 8 = 1. For n = 2, 9(2) 8 = 10. For n = 3, 9(3) 8 = 19, and so on. Answer: a n = 9n 8

18 Find the nth Term B. Find the 12th term in the sequence. Replace n with 12 in the equation written in part A. a n = 9n 8 Formula for the nth term a 12 = 9(12) 8 Replace n with 12. a 12 = 100 Simplify. Answer: a 12 = 100

19 Arithmetic Sequences as Functions NEWSPAPERS The arithmetic sequence 12, 23, 34, 45,... represents the total number of ounces that a bag weighs after each additional newspaper is added. A. Write a function to represent this sequence The common difference is 11.

20 Arithmetic Sequences as Functions a n = a 1 + (n 1)d Formula for the nth term = 12 + (n 1)11 a 1 = 12 and d = 11 = n 11 Distributive Property = 11n + 1 Simplify. Answer: The function is a n = 11n + 1.

21 Identify Geometric Sequences A. Determine whether the sequence is arithmetic, geometric, or neither. Explain. 0, 8, 16, 24, 32, = = = = 8 Answer: The common difference is 8. So, the sequence is arithmetic.

22 Identify Geometric Sequences B. Determine whether the sequence is arithmetic, geometric, or neither. Explain. 64, 48, 36, 27, = = = 4 48 Answer: The common ratio is geometric. 3, so the sequence is 4

23 A. Determine whether the sequence is arithmetic, geometric, or neither. 1, 7, 49, 343,... A. arithmetic B. geometric C. neither

24 B. Determine whether the sequence is arithmetic, geometric, or neither. 1, 2, 4, 14, 54,... A. arithmetic B. geometric C. neither

25 Find Terms of Geometric Sequences A. Find the next three terms in the geometric sequence. 1, 8, 64, 512,... Step 1 Find the common ratio = 8 8 = = 8 64 The common ratio is 8.

26 Find Terms of Geometric Sequences Step 2 Multiply each term by the common ratio to find the next three terms , ,144 ( 8) ( 8) ( 8) Answer: The next 3 terms in the sequence are 4096; 32,768; and 262,144.

27 Find Terms of Geometric Sequences B. Find the next three terms in the geometric sequence. 40, 20, 10, 5,... Step 1 Find the common ratio = = = 1 2 The common ratio is 1. 2

28 Find Terms of Geometric Sequences Step 2 Multiply each term by the common ratio to find the next three terms Answer: The next 3 terms in the sequence are 5, 2 5 4, and 5 8.

29 A. Find the next three terms in the geometric sequence. 1, 5, 25, 125,... A. 250, 500, 1000 B. 150, 175, 200 C. 250, 500, 1000 D. 625, 3125, 15,625

30 B. Find the next three terms in the geometric sequence. 800, 200, 50, 25,... 2 A. 15, 10, 5 B. 25, 25, C. 12, 3, 3 4 D. 0, 25, 50

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32 Find the nth Term of a Geometric Sequence A. Write an equation for the nth term of the geometric sequence 1, 2, 4, 8,.... The first term of the sequence is 1. So, a 1 = 1. Now find the common ratio = = = 2 a n = a 1 r n 1 Formula for the nth term a n = 1( 2) n 1 a 1 = 1 and r = 2 Answer: a n = 1( 2) n 1 The common ratio is 2.

33 Find the nth Term of a Geometric Sequence B. Find the 12 th term of the sequence. 1, 2, 4, 8,.... a n = a 1 r n 1 Formula for the nth term a 12 = 1( 2) 12 1 For the nth term, n = 12. = 1( 2) 11 Simplify. = 1( 2048) ( 2) 11 = 2048 = 2048 Multiply. Answer: The 12 th term of the sequence is 2048.

34 A. Write an equation for the nth term of the geometric sequence 3, 12, 48, 192,... A. B. C. D.

35 B. Find the 7th term of this sequence using the equation a n = 3( 4) n 1. A. 768 B C. 12,288 D. 49,152

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37 Evaluate a Correlation TECHNOLOGY The graph shows the average number of students per computer in Maria s school. Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation. Sample Answer: The graph shows a negative correlation. Each year, more computers are in Maria s school, making the students-per-computer rate smaller.

38 The graph shows the number of mailorder prescriptions. Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe it. A. Positive correlation; with each year, the number of mail-order prescriptions has increased. B. Negative correlation; with each year, the number of mail-order prescriptions has decreased. C. no correlation D. cannot be determined

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40 Write a Line of Fit POPULATION The table shows the world population growing at a rapid rate. Identify the independent and dependent variables. Make a scatter plot and determine what relationship, if any, exists in the data.

41 Write a Line of Fit Step 1 Make a scatter plot. The independent variable is the year, and the dependent variable is the population (in millions). As the years increase, the population increases. There is a positive correlation between the two variables.

42 Write a Line of Fit Step 2 Draw a line of fit. No one line will pass through all of the data points. Draw a line that passes close to the points. A line of fit is shown.

43 Write a Line of Fit Step 3 Write the slope-intercept form of an equation for the line of fit. The line of fit shown passes through the points (1850, 1000) and (2004, 6400). Find the slope. Slope formula Let (x 1, y 1 ) = (1850, 1000) and (x 2, y 2 ) = (2004, 6400). Simplify.

44 Write a Line of Fit Use m = and either the point-slope form or the slope-intercept form to write the equation of the line of fit. y y 1 = m(x x 1 ) y 1000 = (x 1850) y x 64,870 y 35.1x 63,870 Answer: The equation of the line is y = 35.1x 63,870.

45 The table shows the number of bachelor s degrees received since Draw a scatter plot and determine what relationship exists, if any, in the data. A. There is a positive correlation between the two variables. B. There is a negative correlation between the two variables. C. There is no correlation between the two variables. D. cannot be determined