Algebra 2 Spring Review for Chapters 8 and 9 Name: ______
Write the first four terms of the sequence.
1. an = 2n – 4
2.
3.
4.
Describe the pattern, write the next term, and write a rule for the nth term of the sequence.
5. –15, –24, –33, –42,...
6. 4.8, 5, 5.2, 5.4,...
7. 1, –6, 36, –216, ...
Find the sum.
8.
9.
10.
11. You enjoy reading in your free time and keep every book you have ever read. When you were five, you read 2 books and every year after you tripled the number of books you read. How many books did you have in your bookcase when you were 11 years old?
12. Write a rule for the nth term of the sequence. Then find . –6, –4, –2, 0, ...
Find the sum of the infinite geometric series, if it exists.
13.
14.
Write a recursive rule for the sequence.
15. 2, 6, 10, 14, 18, . . .
16. –36, 144, –576, 2304, –9216, . . .
Write an explicit rule for the sequence.
17.
18. In a right triangle, q is an acute angle and . Evaluate the other five trigonometric functions ofq.
19. In a right triangle, q is an acute angle and . Evaluate the other five trigonometric functions ofq.
20. Solve .
21. Solve .
22. Draw an angle that measures 260° in standard position.
23. Draw an angle that measures 700° in standard position.
24. Draw an angle that measures –340° in standard position.
25. Convert 35° to radians.
26. Convert to degrees.
27. Find the reference angle for .
28. Identify the amplitude of . Then graph the function and describe the graph of g as a transformation of the graph of .
29. Identify the amplitude of . Then graph the function and describe the graph of g as a transformation of the graph of .
Algebra 2 Spring Review for Chapters 8 and 9
Answer Section
1. ANS:
–2, 0, 2, 4, 6, 8
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 8.1
NAT: HSF-IF.A.3 KEY: terms of a sequence | sequence | writing terms of sequences
NOT: Example 1
2. ANS:
1, –2, 4, –8, 16, –32
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 8.1
NAT: HSF-IF.A.3 KEY: terms of a sequence | sequence | writing terms of sequences
NOT: Example 1
3. ANS:
, , , , ,
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 8.1
NAT: HSF-IF.A.3 KEY: terms of a sequence | sequence | writing terms of sequences
NOT: Example 1
4. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 8.5
NAT: HSF-IF.A.3 | HSF-BF.A.1a | HSF-BF.A.2
KEY: recursive rule | evaluating recursive rules for sequences | writing terms of sequences
NOT: Example 1
5. ANS:
arithmetic, ,
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 8.1
NAT: HSF-IF.A.3 KEY: terms of a sequence | sequence | writing rules for sequences
NOT: Example 2
6. ANS:
arithmetic, ,
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 8.1
NAT: HSF-IF.A.3 KEY: terms of a sequence | sequence | writing rules for sequences
NOT: Example 2
7. ANS:
geometric, ,
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 8.1
NAT: HSF-IF.A.3 KEY: terms of a sequence | sequence | writing rules for sequences
NOT: Example 2
8. ANS:
72
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 8.1
NAT: HSF-IF.A.3 KEY: finding sums of series | series NOT: Example 5
9. ANS:
–57
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 8.1
NAT: HSF-IF.A.3 KEY: finding sums of series | series NOT: Example 5
10. ANS:
–45
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 8.3
NAT: HSA-SSE.B.4 KEY: geometric series | finding sums of finite geometric series
NOT: Example 5
11. ANS:
2186 books
PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 8.1
NAT: HSF-IF.A.3 KEY: finding sums of series | series | application
NOT: Example 6
12. ANS:
,
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 8.2
NAT: HSF-IF.A.3 | HSF-BF.A.2 | HSF-LE.A.2
KEY: arithmetic sequence | writing rules for arithmetic sequences
NOT: Example 2
13. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 8.4
NAT: HSA-SSE.B.4
KEY: infinite geometric series | finding sums of infinite geometric series
NOT: Example 2
14. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 8.4
NAT: HSA-SSE.B.4
KEY: infinite geometric series | finding sums of infinite geometric series
NOT: Example 2
15. ANS:
,
PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 8.5
NAT: HSF-IF.A.3 | HSF-BF.A.1a | HSF-BF.A.2
KEY: recursive rule | writing recursive rules for sequences NOT: Example 2
16. ANS:
PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 8.5
NAT: HSF-IF.A.3 | HSF-BF.A.1a | HSF-BF.A.2
KEY: recursive rule | writing recursive rules for sequences NOT: Example 2
17. ANS:
PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 8.5
NAT: HSF-IF.A.3 | HSF-BF.A.1a | HSF-BF.A.2
KEY: recursive rule | writing explicit rules for sequences | translating between recursive rules and explicit rules NOT: Example 5
18. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 9.1
NAT: HSF-TF.A.1 | HSF-TF.A.2 | HSF-TF.B.5 | HSF-TF.C.8
KEY: evaluating trigonometric functions of acute angles | sine | cosine | tangent | cosecant | secant | cotangent NOT: Example 2
19. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 9.1
NAT: HSF-TF.A.1 | HSF-TF.A.2 | HSF-TF.B.5 | HSF-TF.C.8
KEY: evaluating trigonometric functions of acute angles | sine | cosine | tangent | cosecant | secant | cotangent NOT: Example 2
20. ANS:
PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 9.1
NAT: HSF-TF.A.1 | HSF-TF.A.2 | HSF-TF.B.5 | HSF-TF.C.8 KEY: solving right triangles
NOT: Example 4
21. ANS:
PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 9.1
NAT: HSF-TF.A.1 | HSF-TF.A.2 | HSF-TF.B.5 | HSF-TF.C.8 KEY: solving right triangles
NOT: Example 4
22. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 9.2
NAT: HSF-TF.A.1 KEY: drawing angles in standard position | standard position | measure of an angle
NOT: Example 1
23. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 9.2
NAT: HSF-TF.A.1 KEY: drawing angles in standard position | standard position | measure of an angle
NOT: Example 1
24. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 9.2
NAT: HSF-TF.A.1 KEY: drawing angles in standard position | standard position | measure of an angle
NOT: Example 1
25. ANS:
rad
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 9.2
NAT: HSF-TF.A.1 KEY: degrees | radians | converting between degrees and radians
NOT: Example 3
26. ANS:
–6°
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 9.2
NAT: HSF-TF.A.1 KEY: degrees | radians | converting between degrees and radians
NOT: Example 3
27. ANS:
31°
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 9.3
NAT: HSF-TF.A.2 KEY: reference angle | finding reference angles
NOT: Example 3
28. ANS:
3
The graph of g is a vertical stretch by a factor of 3 of the graph of f.
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 9.4
NAT: HSF-IF.C.7e | HSF-BF.B.3
KEY: graphing sine functions |sine function | graph of a periodic function | describing transformations of graphs of periodic functions | amplitude | periodic function | period
NOT: Example 1
29. ANS:
The graph of g is a vertical shrink by a factor of of the graph of f.
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 9.4
NAT: HSF-IF.C.7e | HSF-BF.B.3
KEY: graphing cosine functions | cosine function | graph of a periodic function | describing transformations of graphs of periodic functions | amplitude | period | periodic function
NOT: Example 2