PreCalc 11 Chapter 1 Review Pack v1 Answer Section

Transcription

1 PreCalc 11 Chapter 1 Review Pack v1 Answer Section MULTIPLE CHOICE 1. ANS: A PTS: 1 DIF: Easy REF: 1.1 Arithmetic Sequences. ANS: A PTS: 1 DIF: Easy REF: 1.1 Arithmetic Sequences 3. ANS: B PTS: 1 DIF: Easy REF: 1.1 Arithmetic Sequences 4. ANS: B PTS: 1 DIF: Easy REF: 1.1 Arithmetic Sequences 5. ANS: C PTS: 1 DIF: Moderate REF: 1. Arithmetic Series 6. ANS: A PTS: 1 DIF: Difficult REF: 1. Arithmetic Series 7. ANS: D PTS: 1 DIF: Easy REF: 1.3 Geometric Sequences KEY: Conceptual Understanding 8. ANS: C PTS: 1 DIF: Easy REF: 1.3 Geometric Sequences 9. ANS: A PTS: 1 DIF: Difficult REF: 1.3 Geometric Sequences 10. ANS: B PTS: 1 DIF: Easy REF: 1.3 Geometric Sequences 11. ANS: C PTS: 1 DIF: Easy REF: 1.3 Geometric Sequences 1. ANS: A PTS: 1 DIF: Difficult REF: 1.3 Geometric Sequences KEY: Problem-Solving Skills Procedural Knowledge 13. ANS: D PTS: 1 DIF: Moderate REF: 1.4 Geometric Series 14. ANS: D PTS: 1 DIF: Easy REF: 1.4 Geometric Series 15. ANS: C PTS: 1 DIF: Moderate REF: 1.5 Graphing Geometric Sequences and Series KEY: Conceptual Understanding 16. ANS: C PTS: 1 DIF: Easy REF: 1.5 Graphing Geometric Sequences and Series KEY: Conceptual Understanding 17. ANS: B PTS: 1 DIF: Easy REF: 1.5 Graphing Geometric Sequences and Series KEY: Procedural Knowledge 18. ANS: C PTS: 1 DIF: Moderate REF: 1.5 Graphing Geometric Sequences and Series KEY: Conceptual Understanding 1

2 19. ANS: D PTS: 1 DIF: Moderate REF: 1.5 Graphing Geometric Sequences and Series KEY: Conceptual Understanding Procedural Knowledge 0. ANS: A PTS: 1 DIF: Easy REF: 1.6 Infinite Geometric Series 1. ANS: B PTS: 1 DIF: Easy REF: 1.6 Infinite Geometric Series KEY: Conceptual Understanding Procedural Knowledge. ANS: A PTS: 1 DIF: Easy REF: 1.6 Infinite Geometric Series 3. ANS: B PTS: 1 DIF: Easy REF: 1.6 Infinite Geometric Series 4. ANS: B PTS: 1 DIF: Moderate REF: 1.6 Infinite Geometric Series SHORT ANSWER 5. ANS: No, this could not be an arithmetic sequence because the difference between consecutive terms is not constant. PTS: 1 DIF: Easy REF: 1.1 Arithmetic Sequences LOC: 11.RF9 KEY: Conceptual Understanding 6. ANS: PTS: 1 DIF: Difficult REF: 1. Arithmetic Series LOC: 11.RF9 KEY: Conceptual Understanding 7. ANS: r = 1 5, t 5 = 5, t 6 = 1 PTS: 1 DIF: Moderate REF: 1.3 Geometric Sequences 8. ANS: PTS: 1 DIF: Moderate REF: 1.4 Geometric Series 9. ANS: The common ratio is 1, which is between 0 and 1, so the partial sums increase and approach a constant value. 3 PTS: 1 DIF: Moderate REF: 1.5 Graphing Geometric Sequences and Series KEY: Conceptual Understanding

3 30. ANS: r =1.7, so the sum is not finite. PTS: 1 DIF: Easy REF: 1.6 Infinite Geometric Series KEY: Conceptual Understanding Procedural Knowledge PROBLEM 31. ANS: a) 4, d 4 t is d 4, or 6 t 3 is t d 6, or 8 t 4 is t 3 d 8, or 10 t 5 is t 4 d 10, or 1 The first 5 terms are:4, 6, 8,10, 1 b) The arithmetic sequence has 4, d, and n 10. t n d(n 1) Substitute: 4, d, n (10 1) Solve for 0. 0 There are seats when 10 tables are arranged in a single row. PTS: 1 DIF: Moderate REF: 1.1 Arithmetic Sequences LOC: 11.RF9 KEY: Communication Problem-Solving Skills 3

4 3. ANS: a) Use:S n n È t ÎÍ 1 d(n 1) È ÎÍ (1) 3( 1) S S 715 Substitute: n, 1, d 3 b) Use:S n n È t ÎÍ 1 d(n 1) Substitute: n, t 1 7, d 4 È ÎÍ ( 7) ( 4)( 1) S S 1078 PTS: 1 DIF: Moderate REF: 1. Arithmetic Series LOC: 11.RF9 KEY: Conceptual Understanding Procedural Knowledge 33. ANS: The prices of the tickets form an arithmetic sequence with first 3 terms $95, $89, $83,... The total cost of Joe s tickets is the sum of the firs0 terms of the arithmetic series: $95 $89 $83... Use:S n n[ d(n 1)] Substitute: n 10, 95, d 6 10[(95) 6(10 1)] S 10 S To buy 1 ticket from each section, Joe will have to spend $680. PTS: 1 DIF: Difficult REF: 1. Arithmetic Series LOC: 11.RF9 KEY: Communication Conceptual Understanding Problem-Solving Skills 4

5 34. ANS: a) r is Use:t n r n 1 Substitute: t n 8, r 1 4, n Ê 1 ˆ 8 Á 4 51 Ê t 51 1 ˆ Á 4 18 Ê t ˆ Á 4 3 The first 3 terms are: 51, t 18, t 3 3 b) The sequence is convergent because the terms approach a constant value of 0. PTS: 1 DIF: Moderate REF: 1.3 Geometric Sequences KEY: Communication Conceptual Understanding Problem-Solving Skills 35. ANS: The geometric sequence has first term and common ratio. Use:t n r n 1 Substitute: , r, n 5 t () 5 1 t Term 5 is PTS: 1 DIF: Moderate REF: 1.3 Geometric Sequences KEY: Communication Problem-Solving Skills 5

6 36. ANS: Car When the value of the car decreases by 13.5%, the new value is 86.5% of the original value. To determine a depreciation value of 13.5%, multiply by The initial cost of the car is the first term. So, the value of the car at the end of 10 years is the 11th term. The values, in dollars, at the end of each year form a geometric sequence with first term and common ratio Use:t n r n 1 Substitute: , r 0.865, n (0.865) At the end of 10 years, the value of the car is $ Truck When the value of the truck decreases by 7.0%, the new value is 93% of the original value. To determine a depreciation value of 7.0%, multiply by The initial cost of the truck is the first term. So, the value of the truck at the end of 10 years is the 11th term. The values, in dollars, at the end of each year form a geometric sequence with first term and common ratio Use:t n r n 1 Substitute: 6 500, r 0.93, n (0.93) At the end of 10 years, the value of the truck is $ The truck will be worth more at the end of 10 years. PTS: 1 DIF: Difficult REF: 1.3 Geometric Sequences KEY: Communication Problem-Solving Skills 6

7 37. ANS: Use:S n (1 r n ) 1 r t Ê ˆ Á (1 64) So, the first term is 5., r 1 Substitute: n 6, S n 315, r PTS: 1 DIF: Moderate REF: 1.4 Geometric Series KEY: Problem-Solving Skills Procedural Knowledge 7

8 38. ANS: To determine, use: S n t (1 r n 1 ) 1 r Ê Á , r 1 Substitute:S 1 1, n 1, r 1 4 ˆ Ê 1 ˆ 1 Á The 1st jump is approximately 9.00 m. To determine t, use: t n r n 1 Substitute: , r 1 4, n Ê t ˆ Á 4 1 t.500 The nd jump is approximately.5 m. To determine t 3, use: t n r n 1 Substitute: , r 1 4, n 3 Ê t ˆ Á t The 3rd jump is approximately 0.56 m. PTS: 1 DIF: Difficult REF: 1.4 Geometric Series KEY: Communication Conceptual Understanding Problem-Solving Skills 8

9 39. ANS: Sample response: For the term values to alternate between positive and negative,and increase in numerical value, the common ratio must be less than 1; for example, with r 5, a possible sequence is: 4, 5, 5 4 4, 15 16, 65 64, ,... PTS: 1 DIF: Moderate REF: 1.5 Graphing Geometric Sequences and Series KEY: Communication Conceptual Understanding Procedural Knowledge 9

10 40. ANS: a) The common ratio is 3, which is greater than 1, so the term values increase. b) The common ratio is 3, which is greater than 1, so the partialsums increase. c) To graph the geometric series, determine the partial sums. S 1 S S 3 S 4 S 5 S 6 3 S S 1 t S 3 S t 3 S 4 S 3 t 4 S 5 S 4 t 5 S 6 S 5 t 6 S 3 (9) S 3 1 (7) S 4 39 (81) S 5 10 (43) S (79) S 1 S 3 39 S 4 10 S S

11 PTS: 1 DIF: Moderate REF: 1.5 Graphing Geometric Sequences and Series KEY: Communication Conceptual Understanding Procedural Knowledge 11