Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question

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1 Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 11, Lesson 1 1. Warm up 2. Notes Review 3. ICA QUIZ 57 Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up: 1

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4 QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ US Dollar 1.00 USD Euro (EUR) British Pound (BPS) Indian Rupee 61.4 (INR) Australian Dollar 1.14 (AUS) Canadian Dollar 1.13 (CAD) Emirati Dirham 3.67 (AED) Swiss Franc (CHF) Chinese Yuan 6.13 (CNY) Malaysian Ringgit 3.27 (MYR) New Zealand Dollar 1.26 (NZD) Mexican Pesos 13.5 (MXP) If you see: 1 lb = kg 4

5 Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 11, Lesson 2 1. Warm up Quiz 2. Notes Arithmetic Sequences 3. ICA Wk 11 L 2 Standard Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up: Complete Week 10 Quiz 5

6 Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Arithmetic Sequence A sequence in which each term differs from the previous one by the same fixed number. General Term Formula For an arithmetic sequence with the first term and common difference d, the general term or the nth term is Example 1 Given the sequence u n = 2, 9, 16, 23, 30, a. Show that the sequence is arithmetic b. Find a formula for the nth term of the sequence c. Find the 57th term of the sequence d. Find the 100th term of the sequence Example 2 Consider the sequence un = 87, 83, 79, 75, a. Show that the sequence is arithmetic b. Find a formula for the n th term of the sequence c. Find the 16th term of the sequence d. Find the 40th term of the sequence Example 3 Mr. Henderson is also a cartoonist. His comic strip has just been bought by a newspaper, so he sends them the 28 comics he has already drawn. Each week after the first he sends 3 new comic strips. a. List the number of comic strips he sent after 1, 2, 3, and 4 weeks b. Find the formula for the n th term of the sequence c. Find the number of comic strips sent after 15 weeks d. Find the number of comic strips sent after 39 weeks e. When does Mr. Henderson send his 120 th comic? Example 4 A luxury car maker sets up a factory for a new model. In the first month, only 5 cars are produced. After this, 13 cars are assembled each month. a. List the number of cars made in the first 4 months b. Find the formula for the n th term of the sequence c. How many cars are assembled in the first year? d. How long is it until the 250th car is produced? Summary: 6

7 ity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity Which One? Which sequence has a 14 th term of 207? Which sequence has a 9 th term of 55? Which sequence has a 10 th term of 175? 7

8 Are all sequences arithmetic? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 11, Lesson 3 1. Warm up 2. Notes Geometric Sequences 3. ICA Wk 11, L3 Handout Standard Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up: Determine whether the following sequences are Arithmetic. Justify your answer. u n = 3, 11, 19, 27,... a n = 77, 75, 73, 71,... b n = 2, 4, 8, 16,... c n = 1, 4, 9, 16,... p n = 100, 200, 300, 400,... 8

9 Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Geometric Sequences A sequence is geometric if each term can be obtained from the previous one by multiplying by the same non zero number. Ex: The sequence 2, 10, 50, 250,... is geometric as each term is being multiplied by 5 Common Ratio The number we multiply by is called the common ratio General Term Formula For a geometric sequence with the first term and common ratio r, the general term or nth term is Example 1 u n = 5, 10, 20, 40,... a. Show that the sequence is geometric b. Find the first term u 1 and the common ratio r for the sequence. c. Find the general term formula. d. Find the 28th term of the sequence. e. Find the 52nd term of the sequence. Example 2 a n = 8, 4, 2, 1... a. Show that the sequence is geometric b. Find the first term a 1 and the common ratio r for the sequence. c. Find the general term formula. d. Find the 8th term of the sequence. e. Find the 1200th term of the sequence. Example 3 Show that the sequence is geometric. un = 2, 4, 8, 16,... Find the 10th term of the sequence Summary: 9

10 ity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity 1. For the following geometric sequences, find terms b and c a. 40, 20, b, c b. 6, 12, b, c c. 2, b, 18, c 2. Find the 6th term of the geometric sequence: 3, 6, 12, 24, Find the 9th term of the geometric sequence: 512, 256, 128,... 10

11 How do sequences apply to real life scenarios? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 11, Lesson 4 1. Warm up 2. Notes Tougher Sequences 3. ICA Practice Problems Standards 1.7 & Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up: Identify the sequence as arithmetic or geometric. Explain why. a n = 7, 15, 23, 31,... b n = 100, 75, 56.25, 42.19,... 11

12 Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Notes Tougher Sequences Word Problems Identify what the starting amount is This is u 1 Identify how the values are changing This determines arithmetic or geometric Identify what the change is This is d or r Percent Increases Terms changing by a percent are always geometric If something is decreasing by a percent, subtract that rate from 100 and change it to a decimal If something is increasing by a percent, add 100 percent and change it to a decimal. i.e. Increase of 15% means r = 1.15 Decrease of 15% means r = 0.85 Example 1 Julia makes $2.00 an hour for the first hour of work, $4.00 for her second hour, $6.00 for her third hour and so on... How much money is her 12th hour of work worth? Example 2 Each year, a teacher's salary increases by 1.8%. Mr. Henderson currently makes $48,500 annually. How much will his annual salary be in 6 years? Example 3 A car depreciates (decreases) in value at a rate of 22% per year. A Honda Accord that was brand new in 2010 cost $23,000. How much is that car worth now, 4 years later? Summary: 12

13 Attachments W2L1.docx Project Survey.docx Project Survey.xlsx Project Questionnaire.docx Project Questionnaire.xlsx