MAC 1140 Test 4 Review and Practice Solutions. MAC 1140 Test 4 Review 12.1 – 12.5 You will need to have your own graphing calculator for the test. You.

Slides:

Advertisements

Similar presentations

Slide Copyright © 2009 Pearson Education, Inc. Active Learning Lecture Slides For use with Classroom Response Systems © 2009 Pearson Education, Inc.

Advertisements

Sequences, Induction and Probability

Essential Question: What is a sequence and how do I find its terms and sums? How do I find the sum & terms of geometric sequences and series?

Unit 7: Sequences and Series

7.2 Analyze Arithmetic Sequences & Series

Binomial Coefficient.

ARITHMETIC SEQUENCES AND SERIES

Geometric Sequences and Series Part III. Geometric Sequences and Series The sequence is an example of a Geometric sequence A sequence is geometric if.

Copyright © 2007 Pearson Education, Inc. Slide 8-1.

Sequences & Series ♥ By Jen, Cindy, Tommy & Samuel The cool people of group e ☻

1 © 2010 Pearson Education, Inc. All rights reserved 10.1 DEFINITION OF A SEQUENCE An infinite sequence is a function whose domain is the set of positive.

Rev.S08 MAC 1140 Module 12 Introduction to Sequences, Counting, The Binomial Theorem, and Mathematical Induction.

Instructions for using this template. Remember this is Jeopardy, so where I have written “Answer” this is the prompt the students will see, and where.

Class Opener: Identify each sequence as geometric, arithmetic, or neither, find the next two terms, if arithmetic or geometric write the equation for the.

THE BEST CLASS EVER…ERRR…. PRE-CALCULUS Chapter 13 Final Exam Review.

12-5 Warm Up Lesson Presentation Lesson Quiz

A summary of the algebra concepts. Sequences and Series Some sequences are arithmetic because there is a common difference between terms. We call the.

SEQUENCES AND SERIES Arithmetic. Definition A series is an indicated sum of the terms of a sequence.  Finite Sequence: 2, 6, 10, 14  Finite Series:2.

CHAPTER 10 Sequences, Induction, & Probability Sequences & Summation Notation Objectives –Find particular terms of sequence from the general term.

Copyright © 2007 Pearson Education, Inc. Slide 8-1.

6.8.2 Binomial Theorem. Before We Begin Find 4 C 0 ____________ Find 4 C 1 ____________ Find 4 C 2 ____________ Find 4 C 3 ____________ Find 4 C 4 ____________.

Warm Up Finish your open notes quiz from yesterday. When you come in, I will return your quiz to you. Remember, you may use your 4 pages of notes and the.

Standard 22 Identify arithmetic sequences Tell whether the sequence is arithmetic. a. –4, 1, 6, 11, 16,... b. 3, 5, 9, 15, 23,... SOLUTION Find the differences.

Review of Sequences and Series.  Find the explicit and recursive formulas for the sequence:  -4, 1, 6, 11, 16, ….

Topic 1 Arithmetic Sequences And Series

Lesson 6.8A: The Binomial Theorem OBJECTIVES:  To evaluate a binomial coefficient  To expand a binomial raised to a power.

Pascal’s Triangle and the Binomial Theorem Chapter 5.2 – Probability Distributions and Predictions Mathematics of Data Management (Nelson) MDM 4U.

Binomial – two terms Expand (a + b) 2 (a + b) 3 (a + b) 4 Study each answer. Is there a pattern that we can use to simplify our expressions?

Copyright © Cengage Learning. All rights reserved. 8 Sequences, Series, and Probability.

Binomial Theorem & Binomial Expansion

Definition of a Sequence

EXAMPLE 3 Find zeros when the leading coefficient is not 1

1Convergent, 0Divergent Convergent 150Convergent |r| < 1 459th term Examplea n = 3n 3 +3n 2n 628 terms 7Example5, 3.75, ,

Knight’s Charge 8/26/15 Review Have your homework out on your desk (including your triangle).

Review of Sequences and Series

Sequences and the Binomial Theorem Sequences Arithmetic Sequences Geometric Sequences & Series Binomial Theorem.

Geometric Sequence – a sequence of terms in which a common ratio (r) between any two successive terms is the same. (aka: Geometric Progression) Section.

APC Unit 2 CH-12.5 Binomial Theorem. Warm-up  Take your Homework out  Clearly Label 12.2, 12.3, and 12.4  Ask your Questions  While I’m Checking…

Infinite Geometric Series. Find sums of infinite geometric series. Use mathematical induction to prove statements. Objectives.

Section 9.2 Arithmetic Sequences and Partial Sums 1.

Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the.

PreCalculus 8-R Unit 8 Sequences, Series and Probability Review Problems.

The binomial expansions

Arithmetic Sequences and Series

Use the Binomial Theorem

The Binomial Expansion Chapter 7

What you need to know To recognise GP’s and use nth term and sum of n terms formulae to solve problems To know about the sum of an infinite GP where How.

8.1 and 8.2 Summarized.

Use the Binomial Theorem

Ch. 8 – Sequences, Series, and Probability

10.2b - Binomial Theorem.

Binomial Theorem Pascal’s Triangle

Use the Binomial Theorem

1.7 - Geometric sequences and series, and their

Grade 11 Functions (MCR3U)

Chapter 8: Further Topics in Algebra

Unit 1 Test #3 Study Guide.

Geometric Sequences and Series

Homework Log Fri. 4/8 Lesson Rev Learning Objective:

Objectives Find the indicated terms of an arithmetic sequence.

Functions as Infinite Series

11.6 Binomial Theorem & Binomial Expansion

Chapter 11: Further Topics in Algebra

Lesson 12–3 Objectives Be able to find the terms of an ARITHMETIC sequence Be able to find the sums of arithmetic series.

Warm Up Use summation notation to write the series for the specified number of terms …; n = 7.

Section 12.3 Geometric Sequences; Geometric Series

Presentation transcript:

MAC 1140 Test 4 Review and Practice Solutions

MAC 1140 Test 4 Review 12.1 – 12.5 You will need to have your own graphing calculator for the test. You may not share calculators or use any type of communication device in place of a calculator. Tests cannot be made up for any reason other than an NWFSC event for which you must miss class. If you miss one test, your final exam score will be substituted. A second missed test is a zero.

Exam Topics ObjectiveSectionSuggested Text Problems 1) Write out the first five terms of a sequence.12.1p. 838: 1, 3 2) Find the sum of a sequence.12.1p. 838: 13, 15 3) Find the indicated term of an arithmetic sequence.12.2p. 838: 17 4) Find a general formula for a given arithmetic sequence.12.2p. 838: 21 5) Work with applications of arithmetic sequences.12.2p. 839: 34 (a)8,(b)1100 6) Find the indicated term of a geometric series.12.3p. 838: 19 7) Determine whether a geometric series converges or diverges (and determine the sum if it converges). 12.3p. 838: 23, 25 8) Prove statements using mathematical induction.12.4p. 839: 27 9) Use the Binomial theorem to expand a binomial12.5p. 839: 31, 33 10) Use the Binomial theorem to find a particular coefficient in a binomial expansion. 12.5p. 836: 29, 31

To Study for the Test Complete all assigned homework. Remember that a score of at least 70% on each assignment gives you 10 bonus points on the test. Complete the practice test and check your solutions. Set up a study system (note cards for example) for each of the 10 objectives in the chart above. Review your notes and applicable problem set questions for each of the 10 objectives in the chart above. Work the suggested text problems for each of the 12 objectives in the chart above.

Things to Know

4) Find the first term, common difference, and a simplified formula for the nth term of the arithmetic sequence where the 7 th term is 4 and the 22 nd term is 34.

5) When Eric started work as an orange picker, he picked 10 oranges in the first minute, 12 in the second minute, 14 in the third minute, and so on. How many oranges did Eric pick in the first 30 minutes?

9) Expand each binomial using the binomial theorem. You may use your calculator to compute the combinations.

10) Use the binomial theorem to answer each question. You may use your calculator to compute the combinations.

Test 4 Extra Practice

3)A brick driveway has 50 rows of bricks. The first row has 16 bricks and the fiftieth row has 65 bricks. Assuming that the number of bricks in each row forms an arithmetic sequence, what is total number of bricks?

5) Use the binomial theorem to answer the question. You may use your calculator to compute the combinations.