math10 (mwf)course calendar 1 st qtr 2011 12

37
COURSE CALENDAR AND SUMMARY SCORE SHEET - DIFFERENTIAL EQUATIONS Second Qtr SY 2008 - 2009 Surname: ______________________Firstname___________________________MI_______ Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: ______________ DAY # DATE TOPICS READINGS PROBLEM SET AND PROJECT 1 9/29/2008 Orientation 2 10/1/2008 Definitions/Elimination of Arbitrary Consta pp. 1 - 5/pp. 6 - 10 7th ed A1 20/10, 24/10 3 10/3/2008 Families of Curves/ Separation of Variables 10 - 16 7th ed/ pp. 18 - 23 8th A2 15/15, 21/15 // 9/23, 21/ 4 10/6/2008 Equations with Homogeneous Coefficients pp. 25 - 29 A3 9/28, 17/28 5 10/8/2008 Exact Equations pp. 29 - 34 A4 15/34, 19/34 6 10/10/2008 The Linear Equation of Order One pp. 35 - 43 A5 21/40, 23/40 7 10/13/2008 Integrating Factors Found by Inspection pp. 75 - 79 A6 19/78, 25/78 8 10/15/2008 The Determination of Integrating Factors pp. 79 - 83 A7 11/83, 19/84 9 10/17/2008 LONG QUIZ 1 SCORE LQ1: /100 TOTAL PROBLEM SET A 10 10/20/2008 Substitution Suggested by the Equation pp. 84 - 86 11 10/22/2008 Bernoulli’s Equation pp. 86 - 89 B1 10/88, 15/89, 19/89 12 10/24/2008 Coefficients Linear in the Two Variables pp. 89 - 94 B2 9/93, 19/93 13 10/27/2008 Orthogonal Trajectories/ Newton's Law of Co . 59 - 62 7th ed/ pp.64 - 65 8th. B3 19/62, 23/62 // 7/66 14 10/29/2008 Law of Growth and Decay/ Simple Interest pp. 65 - 69 B4 9/66, 15/67 15 10/31/2008 Newtons Second law of Motion/ Mixture Probl pp. 65 - 69 B5 22/68 16 11/3/2008 Logistic Growth pp. 69 - 73 B6 3/72, 17 11/5/2008 Simple Electric Circuits pp. 68 # 20 and 21 18 11/7/2008 LONG QUIZ 2 SCORE LQ2: /100 TOTAL PROBLEM SET B 19 11/10/2008 Differential Operators pp. 109 - 116 20 11/12/2008 Linear Equations with Constant Coefficients pp. 117 - 133 P1 pp.131-132, all odd 21 11/14/2008 The Method of Undetermined Coefficients pp. 139 - 144 P2 pp.142-143, 1-43 all odd 22 11/17/2008 Variation of Parameters pp. 156 - 164 P3 pp.162, 1-18 all odd 23 11/19/2008 Inverse Differential Operators pp 152 - 158 7th ed. 24 11/21/2008 Laplace Transforms pp. 252 - 257 25 11/24/2008 Definition of an Inverse Transforms pp. 274 - 277 26 11/26/2008 Partial Fractions pp. 277 - 280 P4 pp.280, 1-10 27 11/28/2008 LONG QUIZ 3 SCORE LQ3: /100 TOTAL PROJECT 28 12/1/2008 Initial Value Problem pp. 280 - 285 29 12/3/2008 A Step Function pp. 286 - 293 30 12/5/2008 Submission of Portfolio and Grade Verificat /300 GRAND TOTAL 31 12/8/2008 FINAL EXAMS WEEK AVERAGE Mapua Institute of Technology - Mathematics Department Faculty in Charge: Dr. DANTE L. SILVA Textbook: ELEMENTARY DIFFERENTIAL EQUATIONS, 7th and

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Page 1: Math10 (mwf)course calendar 1 st qtr 2011 12

COURSE CALENDAR AND SUMMARY SCORE SHEET - DIFFERENTIAL EQUATIONSSecond Qtr SY 2008 - 2009

Surname: ______________________Firstname___________________________MI_______Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________

DAY # DATE TOPICS READINGS PROBLEM SET AND PROJECT SCORES1 9/29/2008 Orientation S A2 10/1/2008 Definitions/Elimination of Arbitrary Constants pp. 1 - 5/pp. 6 - 10 7th ed A1 20/10, 24/103 10/3/2008 Families of Curves/ Separation of Variables pp. 10 - 16 7th ed/ pp. 18 - 23 8th ed. A2 15/15, 21/15 // 9/23, 21/234 10/6/2008 Equations with Homogeneous Coefficients pp. 25 - 29 A3 9/28, 17/285 10/8/2008 Exact Equations pp. 29 - 34 A4 15/34, 19/346 10/10/2008 The Linear Equation of Order One pp. 35 - 43 A5 21/40, 23/407 10/13/2008 Integrating Factors Found by Inspection pp. 75 - 79 A6 19/78, 25/788 10/15/2008 The Determination of Integrating Factors pp. 79 - 83 A7 11/83, 19/84

9 10/17/2008 LONG QUIZ 1 SCORE LQ1: /100 TOTAL PROBLEM SET A10 10/20/2008 Substitution Suggested by the Equation pp. 84 - 86

11 10/22/2008 Bernoulli’s Equation pp. 86 - 89 B1 10/88, 15/89, 19/8912 10/24/2008 Coefficients Linear in the Two Variables pp. 89 - 94 B2 9/93, 19/9313 10/27/2008 Orthogonal Trajectories/ Newton's Law of Cooling pp. 59 - 62 7th ed/ pp.64 - 65 8th. Ed B3 19/62, 23/62 // 7/6614 10/29/2008 Law of Growth and Decay/ Simple Interest pp. 65 - 69 B4 9/66, 15/6715 10/31/2008 Newtons Second law of Motion/ Mixture Problems pp. 65 - 69 B5 22/6816 11/3/2008 Logistic Growth pp. 69 - 73 B6 3/72, 17 11/5/2008 Simple Electric Circuits pp. 68 # 20 and 21

18 11/7/2008 LONG QUIZ 2 SCORE LQ2: /100 TOTAL PROBLEM SET B19 11/10/2008 Differential Operators pp. 109 - 116

20 11/12/2008 Linear Equations with Constant Coefficients pp. 117 - 133 P1 pp.131-132, all odd21 11/14/2008 The Method of Undetermined Coefficients pp. 139 - 144 P2 pp.142-143, 1-43 all odd22 11/17/2008 Variation of Parameters pp. 156 - 164 P3 pp.162, 1-18 all odd23 11/19/2008 Inverse Differential Operators pp 152 - 158 7th ed.

24 11/21/2008 Laplace Transforms pp. 252 - 257

25 11/24/2008 Definition of an Inverse Transforms pp. 274 - 277

26 11/26/2008 Partial Fractions pp. 277 - 280 P4 pp.280, 1-10

27 11/28/2008 LONG QUIZ 3 SCORE LQ3: /100 TOTAL PROJECT28 12/1/2008 Initial Value Problem pp. 280 - 285

29 12/3/2008 A Step Function pp. 286 - 293

30 12/5/2008 Submission of Portfolio and Grade Verification /300 GRAND TOTAL

31 12/8/2008FINAL EXAMS WEEK AVERAGE

Mapua Institute of Technology - Mathematics DepartmentFaculty in Charge: Dr. DANTE L. SILVA

Textbook: ELEMENTARY DIFFERENTIAL EQUATIONS, 7th and 8th EDITION

Page 2: Math10 (mwf)course calendar 1 st qtr 2011 12

by: Rainville, Bedient, Bedient

Page 3: Math10 (mwf)course calendar 1 st qtr 2011 12

COURSE CALENDAR AND SUMMARY SCORE SHEET - DIFFERENTIAL EQUATIONSThird Qtr SY 2008 - 2009

Surname: ______________________Firstname___________________________MI_______Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________

DAY # DATE TOPICS READINGS PROBLEM SETS SCORES1 1/5/2009 Orientation S A2 1/7/2009 Definitions/Elimination of Arbitrary Constants pp. 1 - 5/pp. 6 - 10 7th ed A1 19/10, 21/103 1/9/2009 Families of Curves/ Separation of Variables pp. 10 - 16 7th ed/ pp. 18 - 23 8th ed. A2 16/15, 20/15 // 10/23, 32/234 1/12/2009 Equations with Homogeneous Coefficients pp. 25 - 29 8th ed A3 10/28, 20/285 1/14/2009 Exact Equations pp. 29 - 34 8th ed A4 16/34, 17/346 1/16/2009 The Linear Equation of Order One pp. 35 - 43 8th ed A5 22/40, 28/407 1/19/2009 Integrating Factors Found by Inspection pp. 75 - 79 8th ed A6 18/78, 20/788 1/21/2009 The Determination of Integrating Factors pp. 79 - 83 8th ed A7 12/83, 20/84

9 1/23/2002 LONG QUIZ 1 SCORE LQ1: /100 TOTAL PROBLEM SET A10 1/26/2009 Substitution Suggested by the Equation pp. 84 - 86 8th ed

11 1/28/2009 Bernoulli’s Equation pp. 86 - 89 8th ed B1 11/88, 20/8912 1/30/2009 Coefficients Linear in the Two Variables pp. 89 - 94 8th ed B2 10/93, 18/9313 2/2/2009 Orthogonal Trajectories/ Newton's Law of Cooling pp. 59 - 62 7th ed/ pp.64 - 65 8th. Ed B3 19/62, 23/62 // 7/6614 2/4/2009 Law of Growth and Decay/ Simple Interest pp. 65 - 69 8th ed B4 9/66, 15/6715 2/6/2009 Newtons Second law of Motion/ Mixture Problems pp. 65 - 69 8th ed B5 22/6816 2/9/2009 Logistic Growth/Prices of Commodities pp. 69 - 73 8th ed B6 3/72, 9/7317 2/11/2009 Simple Electric Circuits pp. 68 # 20 and 21 8th ed

18 2/13/2009 LONG QUIZ 2 SCORE LQ2: /100 TOTAL PROBLEM SET B19 2/16/2009 Uniqueness Theorem/Differential Operators pp. 100 - 109//pp. 109 - 116 8th ed C1 5/102, 7/105, 3/11520 2/18/2009 Linear Equations with Constant Coefficients pp. 117 - 133 8th ed C2 15/119, 18/123, 17/13021 2/20/2009 Construction of Homogeneous Equation pp. 134 - 136 8th ed C3 5/136, 18/13622 2/23/2009 The Method of Undetermined Coefficients pp. 139 - 144 8th ed C4 27/143, 39/14323 2/25/2009 Variation of Parameters pp. 156 - 164 8th ed C5 4/162, 6/16224 2/27/2009 Inverse Differential Operators pp 152 - 158 7th ed.

25 3/2/2009 Laplace Transforms pp. 252 - 257 8th ed

26 3/4/2009 Definition of an Inverse Transforms pp. 274 - 277 8th ed

27 3/6/2009 LONG QUIZ 3 SCORE LQ3: /100 TOTAL PROBLEM SET C28 3/9/2009 Partial Fractions pp. 277 - 280 8th ed P1 pp.280, 1-1029 3/11/2009 Initial Value Problem pp. 280 - 285 8th ed

30 3/13/2009 Submission of Portfolio and Grade Verification

31 3/16/2009 FINAL EXAM /300 GRAND TOTAL

Faculty in Charge: Dr. DANTE L. SILVA Textbook: ELEMENTARY DIFFERENTIAL EQUATIONS, 7th and 8th EDITION

Page 4: Math10 (mwf)course calendar 1 st qtr 2011 12

Mapua Institute of Technology - Mathematics Department by: Rainville, Bedient, Bedient

Page 5: Math10 (mwf)course calendar 1 st qtr 2011 12

COURSE CALENDAR AND SUMMARY SCORE SHEET - DIFFERENTIAL EQUATIONSFourth Qtr SY 2008 - 2009

Surname: ______________________Firstname___________________________MI_______Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________

DAY # DATE TOPICS READINGS PROBLEM SETS SCORES1 4/20/2009 Orientation S A2 4/22/2009 Definitions/Elimination of Arbitrary Constants pp. 1 - 5/pp. 6 - 10 7th ed A1 19/10, 21/103 4/24/2009 Families of Curves/ Separation of Variables pp. 10 - 16 7th ed/ pp. 18 - 23 8th ed. A2 16/15, 20/15 // 10/23, 32/234 4/27/2009 Equations with Homogeneous Coefficients pp. 25 - 29 8th ed A3 10/28, 20/285 4/28/2009 Exact Equations pp. 29 - 34 8th ed A4 16/34, 17/346 5/1/2009 The Linear Equation of Order One pp. 35 - 43 8th ed A5 22/40, 28/407 5/4/2009 Integrating Factors Found by Inspection pp. 75 - 79 8th ed A6 18/78, 20/788 5/6/2009 The Determination of Integrating Factors pp. 79 - 83 8th ed A7 12/83, 20/84

9 5/8/2009 LONG QUIZ 1 SCORE LQ1: /100 TOTAL PROBLEM SET A10 5/11/2009 Substitution Suggested by the Equation pp. 84 - 86 8th ed

11 5/13/2009 Bernoulli’s Equation pp. 86 - 89 8th ed B1 11/88, 20/8912 5/15/2009 Coefficients Linear in the Two Variables pp. 89 - 94 8th ed B2 10/93, 18/9313 5/18/2009 Orthogonal Trajectories/ Newton's Law of Cooling pp. 59 - 62 7th ed/ pp.64 - 65 8th. Ed B3 19/62, 23/62 // 7/6614 5/20/2009 Law of Growth and Decay/ Simple Interest pp. 65 - 69 8th ed B4 9/66, 15/6715 5/22/2009 Newtons Second law of Motion/ Mixture Problems pp. 65 - 69 8th ed B5 22/6816 5/25/2009 Logistic Growth/Prices of Commodities pp. 69 - 73 8th ed B6 3/72, 9/7317 5/27/2009 Simple Electric Circuits pp. 68 # 20 and 21 8th ed

18 5/29/2009 LONG QUIZ 2 SCORE LQ2: /100 TOTAL PROBLEM SET B19 6/1/2009 Uniqueness Theorem/Differential Operators pp. 100 - 109//pp. 109 - 116 8th ed C1 5/102, 7/105, 3/11520 6/3/2009 Linear Equations with Constant Coefficients pp. 117 - 133 8th ed C2 15/119, 18/123, 17/13021 6/5/2009 Construction of Homogeneous Equation pp. 134 - 136 8th ed C3 5/136, 18/13622 6/8/2009 The Method of Undetermined Coefficients pp. 139 - 144 8th ed C4 27/143, 39/14323 6/10/2009 Variation of Parameters pp. 156 - 164 8th ed C5 4/162, 6/16224 6/12/2009 Inverse Differential Operators pp 152 - 158 7th ed.

25 6/15/2009 Laplace Transforms pp. 252 - 257 8th ed

26 6/17/2009 Definition of an Inverse Transforms pp. 274 - 277 8th ed

27 6/19/2009 LONG QUIZ 3 SCORE LQ3: /100 TOTAL PROBLEM SET C28 6/22/2009 Partial Fractions pp. 277 - 280 8th ed P1 pp.280, 1-1029 6/24/2009 Initial Value Problem pp. 280 - 285 8th ed

30 6/26/2009 Submission of Portfolio and Grade Verification

31 6/29/2009 FINAL EXAM /300 GRAND TOTAL

Mapua Institute of Technology - Mathematics Department by: Rainville, Bedient, BedientFaculty in Charge: Dr. DANTE L. SILVA Textbook: ELEMENTARY DIFFERENTIAL EQUATIONS, 7th and 8th EDITION

Page 6: Math10 (mwf)course calendar 1 st qtr 2011 12

COURSE CALENDAR AND SUMMARY SCORE SHEET - DIFFERENTIAL EQUATIONSFirst Qtr SY 2009 - 2010

Surname: ______________________Firstname___________________________MI_______Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________

DAY # DATE TOPICS READINGS PROBLEM SETS SCORES1 7/20/2009 Orientation S A2 7/22/2009 Definitions/Elimination of Arbitrary Constants pp. 1 - 5/pp. 6 - 10 7th ed A1 11/10, 17/103 7/24/2009 Families of Curves/ Separation of Variables pp. 10 - 16 7th ed/ pp. 18 - 23 8th ed. A2 10/15, 16/15 // 7/23, 28/234 7/27/2009 Equations with Homogeneous Coefficients pp. 25 - 29 8th ed A3 5/28, 7/285 7/29/2009 Exact Equations pp. 29 - 34 8th ed A4 12/34, 14/346 7/31/2009 The Linear Equation of Order One pp. 35 - 43 8th ed A5 18/40, 20/407 8/3/2009 Integrating Factors Found by Inspection pp. 75 - 79 8th ed A6 6/78, 8/788 8/5/2009 The Determination of Integrating Factors pp. 79 - 83 8th ed A7 2/83, 10/83

9 8/7/2009 LONG QUIZ 1 SCORE LQ1: /100 TOTAL PROBLEM SET A10 8/10/2009 Substitution Suggested by the Equation pp. 84 - 86 8th ed

11 8/12/2009 Bernoulli’s Equation pp. 86 - 89 8th ed B1 4/88, 6/8812 8/14/2009 Coefficients Linear in the Two Variables pp. 89 - 94 8th ed B2 4/92, 8/9213 8/17/2009 Orthogonal Trajectories/ Newton's Law of Cooling pp. 59 - 62 7th ed/ pp.64 - 65 8th. Ed B3 4/61, 9/62 // 7/6614 8/19/2009 Law of Growth and Decay pp. 65 - 69 8th ed B4 9/66, 15/6715 8/21/2009 Simple Interest

16 8/24/2009 Newtons Second law of Motion pp. 65 - 69 8th ed B5 22/6817 8/26/2009 Mixture Problems

18 8/28/2009 LONG QUIZ 2 SCORE LQ2: /100 TOTAL PROBLEM SET B19 8/31/2009 Differential Operators pp. 100 - 109//pp. 109 - 116 8th ed C1 2/115, 4/11520 9/2/2009 The Method of Undetermined Coefficients pp. 139 - 144 8th ed C2 8/143, 10/14321 9/4/2009 Variation of Parameters pp. 156 - 164 8th ed C3 3/162, 7/16222 9/7/2009 Inverse Differential Operators pp 152 - 158 7th ed.

23 9/9/2009 Laplace Transforms pp. 252 - 257 8th ed

24 9/11/2009 Definition of an Inverse Transforms pp. 274 - 277 8th ed

25 9/14/2009 Partial Fractions pp. 277 - 280 8th ed

26 9/16/2009 Initial Value Problem pp. 280 - 285 8th ed

27 9/18/2009 LONG QUIZ 3 SCORE LQ3: /100 TOTAL PROBLEM SET C28 9/21/2009 Grade Verification29 9/23/2009 Submission of Project

30 9/25/2009 Submission of Portfolio

31 9/28/2009 FINAL EXAM /300 GRAND TOTAL

Mapua Institute of Technology - Mathematics Department by: Rainville, Bedient, BedientFaculty in Charge: Dr. DANTE L. SILVA Textbook: ELEMENTARY DIFFERENTIAL EQUATIONS, 7th and 8th EDITION

Page 7: Math10 (mwf)course calendar 1 st qtr 2011 12

COURSE CALENDAR AND SUMMARY SCORE SHEET - MATH 10-1First Quarter 2011 - 2012

Surname: ______________________Firstname___________________________MI_______Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________

DAY DATE TOPICS READINGS HOMEWORKS SCORES1 11-Jul Orientation S A2 13-Jul Sets and the Real Number System SEC 0.1 pp 4 - 15

3 15-Jul Alg Expressions, Properties of Exponents, Polynomials SEC0.1 p9/SEC0.3 pp27-30/SEC 4.3

4 18-Jul Operations on Polynomials, Synthetic Division SEC 0.1 p. 9 / SEC 0.3 pp 27 -30

5 20-Jul Special Products SEC 0.3 pp 31 - 34

6 22-Jul Common Factorsof Polynomials and Factors of Binomials SEC 0.4 pp 37 - 46

7 25-Jul Factors of Trinomials and Factoring by Grouping SEC 0.4 pp 37 - 46

8 27-Jul LONG QUIZ 1 SCORE LQ1: /100

9 29-Jul Simplify, Multiply, and Divide of Rational Expressions SEC0.1 pp 13 - 14/SEC0.5 pp 50 - 62

10 1-Aug Add and Subtract Rational Expressions/Complex Fractions SEC0.1 pp 13 - 14/SEC0.5 pp 50 - 62

11 3-Aug Rational Exponent and Radicals SEC 0.6 pp 63 - 71

12 5-Aug Linear Equations SEC1.1 pp 90-96/SEC1.2 pp 100-109

13 8-Aug Applications of Linear Equations SEC1.1 pp 90-96/SEC1.2 pp 100-109

14 10-Aug LONG QUIZ 2 SCORE LQ2: /10015 12-Aug Quadratic Equations SEC 1.3 pp 113-123

16 15-Aug Applications of Quadratic Equations SEC 1.3 pp 113-123

17 17-Aug Inequalities SEC 1.5, 1.6 and 1.7 pp 136 - 163

18 19-Aug Inequalities in Two Variables SEC 9.4 917 - 919

19 22-Aug Matrices and Determinants SEC 10.1 - 10.4 pp946 - 1017

20 24-Aug Systems of Linear Equations SEC 9.1 pp 876 - 892

21 26-Aug Systems of Inequalities SEC 9.4 pp 917 - 927

22 29-Aug App of Systems of Linear Equations and Inequalities SEC9.1pp876-829/SEC9.4pp917-927

23 31-Aug LONG QUIZ 3 SCORE LQ3: /10024 2-Sep Partial Fractions SEC 9.3 pp 905 - 913

25 5-Sep Functions and Relations, Operations on Functions SEC 3.1 - 3.5 pp 226 - 303

26 7-Sep Inverse of Functions, Graphs of Functions SEC 3.1 - 3.5 pp 226 - 303

27 9-Sep Ratio, Proportion, and Variation SEC 3.6 pp. 304 - 308

28 12-Sep Combinatorial Mathematics: Permutation SEC 12.6 pp 1169 - 1171, 1172 - 1173

29 14-Sep Combinatorial Mathematics: Combination SEC 12.6 pp 1171 - 1172

30 16-Sep LONG QUIZ 4 SCORE LQ4: /100

31 FINAL EXAM

Mapua Institute of Technology - Mathematics Department Student Signature: ____________________________

Faculty in Charge: Engr. Antonio D. Sayaboc, Jr. Textbook: Algebra and Trigonometry, 2nd ed., Cynthia Young

Page 8: Math10 (mwf)course calendar 1 st qtr 2011 12

COURSE CALENDAR AND SUMMARY SCORE SHEET - MATH 10-2First Quarter 2011 - 2012

Surname: ______________________Firstname___________________________MI_______Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________

DAY # DATE TOPICS READINGS HOMEWORKS SCORES1 12-Jul Orientation S A2 14-Jul The Real Number System SEC 0.1 pp 4 - 15

3 16-Jul Algebraic Expressions SEC 0.1 p. 9 / SEC 0.3 pp 27 -28

4 19-Jul Laws of Integer Exponents SEC 0.2 pp18 - 25

5 21-Jul Addition, Subtraction, and Simplifying Alg Expressions SEC 0.3 p 29

6 23-Jul Multiplication and Division of Algebraic Expressions SEC 0.3 p 30 / SEC 4.3 pp 358 - 363

7 26-Jul Binomial Special Products SEC 0.3 pp 31 - 34

8 28-Jul Cube of a Binomial and Square of a Trinomial SEC 0.3 pp 31 - 34

9 30-Jul Common Factors of Polynomials and Factors of Binomials SEC 0.4 pp 37 - 46

10 2-Aug Factoring Trinomials SEC 0.4 pp 37 - 46

11 4-Aug LONG QUIZ 1 SCORE LQ1: /100

12 6-Aug Rational Expressions SEC0.1 pp 13 - 14/SEC0.5 pp 50 - 52

13 9-Aug Multiplication and Division of Rational Expressions, LCM SEC 0.5 pp 52 - 59

14 11-Aug Addition and Subtraction of Rational Expressions SEC 0.5 pp 52 - 59

15 13-Aug Complex Fractions SEC 0.5 pp 52 - 59

16 16-Aug Radicals, Simplifying and Rationalizing Radical Expressions SEC 0.6 pp 63 - 71

17 18-Aug Operations Involving Radical Expressions SEC 0.6 pp 63 - 71

18 20-Aug LONG QUIZ 2 SCORE LQ2: /100

19 23-Aug Linear Equations and Properties of Equality

20 25-Aug Linear Eqns in One Variable, Equations Leading to ax+b=0 SEC1.1 pp 90-96/SEC1.2 pp 100-109

21 27-Aug Applications of Linear Equations in One Variable SEC1.1 pp 90-96/SEC1.2 pp 100-109

22 30-Aug Quadratic Equations 1 SEC 1.3 pp 113-123

23 1-Sep Systems of Linear Equations in One Variable SEC 9.1 pp 876 - 888

24 3-Sep Solving Systems of Linear Equations in One Variable SEC 9.1 pp 876 - 888

25 6-Sep Ratio and Proportion SEC 3.6 pp. 304 - 308

26 8-Sep Transformation of a Proportion SEC 3.6 pp. 304 - 308

27 10-Sep Variation SEC 3.6 pp. 304 - 308

28 13-Sep LONG QUIZ 3 SCORE LQ3: /100

29 15-Sep Review/Preparation of Portfolio

30 17-Sep Review/Preparation of Portfolio

31 FINAL EXAM

Mapua Institute of Technology - Mathematics Department Student Signature: ____________________________

Faculty in Charge: Engr. Antonio D. Sayaboc, Jr. Textbook: Algebra and Trigonometry, 2nd ed., Cynthia Young

Page 9: Math10 (mwf)course calendar 1 st qtr 2011 12
Page 10: Math10 (mwf)course calendar 1 st qtr 2011 12

COURSE CALENDAR AND SUMMARY SCORE SHEET - MATH 101st Qtr 2011 - 2012

Surname: ______________________Firstname___________________________MI_______Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________

DAY # DATE TOPICS READINGS HOMEWORKS SCORES1 11-Jul Orientation S A2 13-Jul Equations and Linear Equations in One Variable SEC 1.1 pp. 90 - 99

3 15-Jul Equations Leading to Linear Equations in One Variable SEC 1.1 pp. 90 - 99

4 18-Jul Number, Digit, Geometric, and Money and Coin Problems SEC 1.2 pp. 100 - 113

5 20-Jul Investment, Age, and Mixture Problems SEC 1.2 pp. 100 - 113

6 22-Jul Uniform Motion, Work, and Clock Problems SEC 1.2 pp. 100 - 113

7 25-Jul Ratio, Proportion, and Variation SEC 3.6 pp. 304 - 313

8 27-Jul LONG QUIZ 1 SCORE LQ1: /100

9 29-Jul Quadratic Equations in One Variable SEC 1.3 and 1.4 pp 113 - 135

10 1-Aug Equations Leading to Quadratic Equations in One Variable SEC 1.3 and 1.4 pp 113 - 135

11 3-Aug Equations Leading to Quadratic Equations in One Variable SEC 1.3 and 1.4 pp 113 - 135

12 5-Aug Applications of Quadratic Equations in One Variable SEC 1.3 and 1.4 pp 113 - 135

13 8-Aug Inequalities and Linear Equalities in One Variable SEC 1.5, 1.6 and 1.7 pp 136 - 163

14 10-Aug Nonlinear Inequalities in One Variable SEC 1.5, 1.6 and 1.7 pp 136 - 163

15 12-Aug LONG QUIZ 2 SCORE LQ2: /10016 15-Aug Systems of Equations/Systems of Linear Equations in Two Variables SEC 9.1 pp 876 - 892

17 17-Aug Systems of Nonlinear Equations in Two Variables SEC 9.1 pp 876 - 892

18 19-Aug Applications of Systems of Linear Equations SEC 9.1 pp 876 - 892

19 22-Aug Systems of Inequalities in Two Variables SEC 9.4 pp 917 - 927

20 24-Aug Applications of Systems of Inequalities in Two Variables SEC 9.4 pp 917 - 927

21 26-Aug LONG QUIZ 3 SCORE LQ3: /10022 29-Aug Functions and Relations, Types of Functions, Domain and Range SEC 3.1 - 3.5 pp 226 - 303

23 31-Aug Graphs of Functions, Operations on Functions, One-to-One Functions SEC 3.1 - 3.5 pp 226 - 303

24 2-Sep Synthetic Division, Remainder and Factor Theorems, Fundamental Theorem of Algebra SEC 4.1 - 4.5 pp 326 - 389

25 5-Sep Zeroes of Polynomials, Decartes Rule of Signs, Rational Zeroes SEC 4.1 - 4.5 pp 326 - 389

26 7-Sep LONG QUIZ 4 SCORE LQ4: /100

27 9-Sep Sequences and Series, Arithmetic Sequences SEC 12.1 - 12.4 pp 1122 - 1158

28 12-Sep Harmonic Sequences and Geometric Sequences SEC 12.1 - 12.4 pp 1122 - 1158

29 14-Sep Factorial of a Number, Binomial Theorem SEC 12.1 pp 1124 - 1125 / SEC 12.5

30 16-Sep LONG QUIZ 5 SCORE LQ5: /100

31 FINAL EXAM

Mapua Institute of Technology - Mathematics Department Student Signature: ____________________________

Faculty in Charge: Floro Deogracias G. Llacuna Textbook: Algebra and Trigonometry, 2nd ed., Cynthia YoungChairman, Mathematics Department: Dr. Lilibeth D. Sabino

Page 11: Math10 (mwf)course calendar 1 st qtr 2011 12

COURSE CALENDAR AND SUMMARY SCORE SHEET - MATH 10First Quarter 2011 - 2012

Surname: ______________________Firstname___________________________MI_______Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________

DAY # DATE TOPICS READINGS HOMEWORKS SCORES1 12-Jul Orientation S A2 14-Jul Equations and Linear Equations in One Variable SEC 1.1 pp. 90 - 99

3 16-Jul Equations Leading to Linear Equations in One Variable SEC 1.1 pp. 90 - 99

4 19-Jul Number, Digit, Geometric, and Money and Coin Problems SEC 1.2 pp. 100 - 113

5 21-Jul Investment, Age, and Mixture Problems SEC 1.2 pp. 100 - 113

6 23-Jul Uniform Motion, Work, and Clock Problems SEC 1.2 pp. 100 - 113

7 26-Jul Ratio, Proportion, and Variation SEC 3.6 pp. 304 - 313

8 28-Jul LONG QUIZ 1 SCORE LQ1: /100

9 30-Jul Quadratic Equations in One Variable SEC 1.3 and 1.4 pp 113 - 135

10 2-Aug Equations Leading to Quadratic Equations in One Variable SEC 1.3 and 1.4 pp 113 - 135

11 4-Aug Equations Leading to Quadratic Equations in One Variable SEC 1.3 and 1.4 pp 113 - 135

12 6-Aug Applications of Quadratic Equations in One Variable SEC 1.3 and 1.4 pp 113 - 135

13 9-Aug Inequalities and Linear Equalities in One Variable SEC 1.5, 1.6 and 1.7 pp 136 - 163

14 11-Aug Nonlinear Inequalities in One Variable SEC 1.5, 1.6 and 1.7 pp 136 - 163

15 13-Aug LONG QUIZ 2 SCORE LQ2: /10016 16-Aug Systems of Equations/Sys of Linear Eqns in Two Variables SEC 9.1 pp 876 - 892

17 18-Aug Systems of Nonlinear equations in Two Variables SEC 9.1 pp 876 - 892

18 20-Aug Applications of Systems of Linear Equations SEC 9.1 pp 876 - 892

19 23-Aug Systems of Inequalities in Two Variables SEC 9.4 pp 917 - 927

20 25-Aug Applications of Systems of Inequalities in Two Variables SEC 9.4 pp 917 - 927

21 27-Aug LONG QUIZ 3 SCORE LQ3: /10022 30-Aug Functions and Relations, Types of Fxns, Domain and Range SEC 3.1 - 3.5 pp 226 - 303

23 1-Sep Graphs of Fxns, Operations on Fxns, One-to-One Fxns SEC 3.1 - 3.5 pp 226 - 303

24 3-Sep Syn Div, Remdr and Factor Theorem, Fund Theorem of Alg SEC 4.1 - 4.5 pp 326 - 389

25 6-Sep Zeroes of Poly's, Decartes Rule of Signs, Rational Zeroes SEC 4.1 - 4.5 pp 326 - 389

26 8-Sep LONG QUIZ 4 SCORE LQ4: /100

27 10-Sep Sequences and Series, Arithmetic Sequences SEC 12.1 - 12.4 pp 1122 - 1158

28 13-Sep Harmonic Sequences and Geometric Sequences SEC 12.1 - 12.4 pp 1122 - 1158

29 15-Sep Factorial of a Number, Binomial Theorem SEC 12.1 pp 1124 - 1125/SEC 12.5

30 17-Sep LONG QUIZ 5 SCORE LQ5: /100

31 FINAL EXAM

Mapua Institute of Technology - Mathematics Department Student Signature: ____________________________

Faculty in Charge: Engr. Antonio D. Sayaboc, Jr. Textbook: Algebra and Trigonometry, 2nd ed., Cynthia Young

Page 12: Math10 (mwf)course calendar 1 st qtr 2011 12

COURSE CALENDAR AND SUMMARY SCORE SHEET - MATH 12First Quarter 2011 - 2012

Surname: ______________________Firstname___________________________MI_______Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________

DAY # DATE TOPICS READINGS HOMEWORKS SCORES1 11-Jul Orientation S A2 13-Jul Angle Measure, Standard Position, Coterminal Angles pp492-494, pp537-542, pp568-572

3 15-Jul Length of a Circular Arc, Linear and Angular Speeds pp 573-585

4 18-Jul Trigonometeric Ratios and Ratios for Special Angles pp509-512, pp516-519

5 20-Jul Solutions of Right Triangles pp495-503, pp524-527

6 22-Jul Angle of Elevation/Depression and Bearing and Course pp 528-530

7 25-Jul Signs of Trigo Fxns and Trigo Ratios of Quadrant Angles pp546-548, pp552-556, pp586-591

8 27-Jul Evaluating Trigonometric Fxns Using the Reference Angle pp556-563

9 29-Jul LONG QUIZ 1 SCORE LQ1: /10010 1-Aug Graphs of Sin and Cos Fxns/Tan and Cot Fxns pp595-618, pp624-638

11 3-Aug Graphs of Tan ans Cot Fxnx/Sec and Csc Fxns pp624-638

12 5-Aug Trigonometric Identities and Prooving pp660-716

13 8-Aug Definition of Inverse Trigonometric Functions pp719-734

14 10-Aug Graphs of Inverse Trigonometric Functions pp719-734

15 12-Aug Evaluating Inverse Trigonometric Functions pp719-734

16 15-Aug Solving Trigonometric Equations pp739-750

17 17-Aug Applications of Trigonometric Equations pp739-750

18 19-Aug LONG QUIZ 2 SCORE LQ2: /10019 22-Aug Solutions to Oblique Triangles and the Law of Sines pp770-781

20 24-Aug Applications of the Law of Sines, Law of Cosines pp770-781, pp785-791

21 26-Aug Applications of the Law of Cosines pp785-791

22 29-Aug Definitions in Spherical Trigonometry TBA

23 31-Aug Law of Sine and Cosine in Spherical Trigonometry TBA

24 2-Sep Napier's Analogies and The Terrestrial Sphere TBA

25 5-Sep LONG QUIZ 3 SCORE LQ3: /10026 7-Sep Exponential Functions and Their Graphs pp422-433

27 9-Sep Logarithmic Functions and Properties of Logarithms pp437-447, pp451-457

28 12-Sep Solving Exponential and Logarithmic Equations pp460-467

29 14-Sep Applications Involving Exponential and Logarithmic Fxns pp460-467

30 16-Sep LONG QUIZ 4 SCORE LQ4: /100

31 FINAL EXAM

Mapua Institute of Technology - Mathematics Department Student Signature: ____________________________

Faculty in Charge: Engr. Antonio D. Sayaboc, Jr. Textbook: Algebra and Trigonometry, 2nd ed., Cynthia Young

Page 13: Math10 (mwf)course calendar 1 st qtr 2011 12

COURSE CALENDAR AND SUMMARY SCORE SHEET - MATH 12-LFirst Quarter 2011 - 2012

Surname: ______________________Firstname___________________________MI_______Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________

DAY # DATE TOPICS READINGS HOMEWORKS SCORES1 12-Jul Orientation and Review of Basic Terms S A2 19-Jul Angle Measure

3 26-Jul Trigonometery of Right Triangles

4 2-Aug SCORE LQ1: /1005 9-Aug Graphs of Trigonometric Functions

6 16-Aug Trigonometric Identities

7 23-Aug Inverse Trigo Fxns and Trigonometric Equations

8 30-Aug SCORE LQ2: /100

9 6-Sep Appn's of Sin and Cos Laws and Spherical Trigo

10 13-Sep

Mapua Institute of Technology - Mathematics Department Student Signature: ____________________________

Trigo Functions and Angles / LONG QUIZ 1

LONG QUIZ 2 / Solutions to Oblique Triangles

FINAL EXAM / Exp and Log Equations

Faculty in Charge: Engr. Antonio D. Sayaboc, Jr. Textbook: Algebra and Trigonometry, 2nd ed., Cynthia Young

Page 14: Math10 (mwf)course calendar 1 st qtr 2011 12

COURSE CALENDAR AND SUMMARY SCORE SHEET - MATH 12-LFirst Quarter 2011 - 2012

Surname: ______________________Firstname___________________________MI_______Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________

DAY # DATE TOPICS READINGS HOMEWORKS SCORES1 16-Jul Orientation and Review of basic Terms S A2 23-Jul Angle Measure

3 30-Jul Trigonometery of Right Triangles

4 6-Aug SCORE LQ1: /1005 13-Aug Graphs of Trigonometric Functions

6 20-Aug Trigonometric Identities

7 27-Aug Inverse Trigo Fxns and Trigonometric Equations

8 3-Sep SCORE LQ2: /100

9 10-Sep Appn's of Sin and Cos Laws and Spherical Trigo

10 17-Sep

Mapua Institute of Technology - Mathematics Department Student Signature: ____________________________

Trigo Functions and Angles / LONG QUIZ 1

LONG QUIZ 2 / Solutions to Oblique Triangles

FINAL EXAM / Exp and Log Equations

Faculty in Charge: Engr. Antonio D. Sayaboc, Jr. Textbook: Algebra and Trigonometry, 2nd ed., Cynthia Young

Page 15: Math10 (mwf)course calendar 1 st qtr 2011 12

DAY # DATE1 11-Jul2 13-Jul3 15-Jul4 18-Jul5 20-Jul6 22-Jul7 25-Jul8 27-Jul9 29-Jul

10 1-Aug11 3-Aug12 5-Aug13 8-Aug14 10-Aug15 12-Aug

DAY # DATE1 11-Jul2 13-Jul3 15-Jul4 18-Jul5 20-Jul6 22-Jul7 25-Jul8 27-Jul9 29-Jul

10 1-Aug11 3-Aug12 5-Aug13 8-Aug14 10-Aug15 12-Aug

Page 16: Math10 (mwf)course calendar 1 st qtr 2011 12

DAY # DATE1 11-Jul2 13-Jul3 15-Jul4 18-Jul5 20-Jul6 22-Jul7 25-Jul8 27-Jul9 29-Jul

10 1-Aug11 3-Aug12 5-Aug13 8-Aug14 10-Aug15 12-Aug

DAY # DATE1 12-Jul2 14-Jul3 16-Jul4 19-Jul5 21-Jul6 23-Jul7 26-Jul8 28-Jul9 30-Jul

10 2-Aug11 4-Aug12 6-Aug13 9-Aug14 11-Aug15 13-Aug

Page 17: Math10 (mwf)course calendar 1 st qtr 2011 12

DAY # DATE1 12-Jul2 19-Jul3 26-Jul4 2-Aug5 9-Aug6 16-Aug7 23-Aug8 30-Aug9 6-Sep

10 13-Sep

DAY # DATE1 16-Jul2 23-Jul3 30-Jul4 6-Aug5 13-Aug6 20-Aug7 27-Aug8 3-Sep9 10-Sep

10 17-Sep

DAY # DATE1 12-Jul2 14-Jul3 16-Jul4 19-Jul5 21-Jul6 23-Jul7 26-Jul8 28-Jul9 30-Jul

10 2-Aug11 4-Aug

Page 18: Math10 (mwf)course calendar 1 st qtr 2011 12

12 6-Aug13 9-Aug14 11-Aug15 13-Aug

Page 19: Math10 (mwf)course calendar 1 st qtr 2011 12

TOPICS DAY # DATEOrientation 16 15-AugSets and the Real Number System 17 17-AugAlg Exp 1 (Concepts, Exponents, Polynomials) 18 19-AugAlg Exp 2 (Oper'ns on Polynomials and Syn Div) 19 22-AugSpecial Products 20 24-AugFactoring 1 21 26-AugFactoring 2 22 29-Aug

LONG QUIZ 1 23 31-AugRat'l Exp 1 (Simplifying, Multiplication and Division) 24 2-SepRat'l Exp 2 (Add'n, Sub'n, and Complex Fractions) 25 5-SepRational Exponent and Radicals 26 7-SepLinear Equations 27 9-SepApplications of Linear Equations 28 12-Sep

LONG QUIZ 2 29 14-SepQuadratic Equations 30 16-Sep

31

TOPICS DAY # DATEOrientation 16 15-AugEquations, Properties of Equality, Equivalent Eqn's 17 17-AugLinear Equations in One Variable 18 19-AugModelling/ Number, Digit, and Geometric Problems 19 22-AugMoney, Investment, Age, and Mixture Problems 20 24-AugUniform Motion, Work, and Clock Problems 21 26-AugRatio, Proportion, and Variation 22 29-Aug

LONG QUIZ 1 23 31-AugQuadratic Equations in One Variable 24 2-SepEquations Leading to Quadratic Equations 1 25 5-SepEquations Leading to Quadratic Equations 2 26 7-SepApplications of Quadratic Equations in One Variable 27 9-SepInequalities 1 28 12-SepInequalities 2 29 14-Sep

LONG QUIZ 2 30 16-Sep31

Page 20: Math10 (mwf)course calendar 1 st qtr 2011 12

TOPICS DAY # DATEOrientation 16 15-AugAngle Measure 1 17 17-AugAngle Measure 2 18 19-AugTrigonometry of Right Triangles 1 19 22-AugTrigonometry of Right Triangles 2 20 24-AugTrigonometry of Right Triangles 3 21 26-AugTrigonometric Functions of Angles 1 22 29-AugTrigonometric Functions of Angles 2 23 31-Aug

LONG QUIZ 1 24 2-SepGraphs of Trigonometric Functions 1 25 5-SepGraphs of Trigonometric Functions 2 26 7-SepTrigonometric Identities 27 9-SepInverse Trigonometric Functions 1 28 12-SepInverse Trigonometric Functions 2 29 14-SepInverse Trigonometric Functions 3 30 16-Sep

31

TOPICS DAY # DATEOrientation 16 16-AugThe Real Number System 17 18-AugAlgebraic Expressions 18 20-AugLaws of Integer Exponents 19 23-AugOperations on Alg Exp 1 (Add'n, Sub'n, Symplifying) 20 25-AugOperations on Alg Exp 2 (Mult, Div, and Syn Div) 21 27-AugSpecial Products 1 22 30-AugSpecial Products 2 23 1-SepFactoring 1 24 3-SepFactoring 2 25 6-Sep

LONG QUIZ 1 26 8-SepRational Expressions 27 10-SepOperations on Rational Expressions 1 28 13-SepOperations on Rational Expressions 2 29 15-SepOperations on Rational Expressions 3 30 17-Sep

31

Page 21: Math10 (mwf)course calendar 1 st qtr 2011 12

TOPICSOrientation and Review of basic TermsAngle MeasureTrigonometery of Right Triangles

Graphs of Trigonometric FunctionsTrigonometric IdentitiesInverse Trigo Fxns and Trigonometric Equations

Appn's of Sin and Cos Laws and Spherical Trigo

TOPICSOrientation and Review of basic TermsAngle MeasureTrigonometery of Right Triangles

Graphs of Trigonometric FunctionsTrigonometric IdentitiesInverse Trigo Fxns and Trigonometric Equations

Appn's of Sin and Cos Laws and Spherical Trigo

TOPICS DAY # DATEOrientation 16 16-AugEquations, Properties of Equality, Equivalent Eqn's 17 18-AugLinear Equations in One Variable 18 20-AugModelling/ Number, Digit, and Geometric Problems 19 23-AugMoney, Investment, Age, and Mixture Problems 20 25-AugUniform Motion, Work, and Clock Problems 21 27-AugRatio, Proportion, and Variation 22 30-Aug

LONG QUIZ 1 23 1-SepQuadratic Equations in One Variable 24 3-SepEquations Leading to Quadratic Equations 1 25 6-SepEquations Leading to Quadratic Equations 2 26 8-Sep

Trig of Right Triangles / LONG QUIZ 1

LONG QUIZ 2 / Solutions to Oblique Triangles

FINAL EXAM / Exp and Log Equations

Trig of Right Triangles / LONG QUIZ 1

LONG QUIZ 2 / Solutions to Oblique Triangles

FINAL EXAM / Exp and Log Equations

Page 22: Math10 (mwf)course calendar 1 st qtr 2011 12

Applications of Quadratic Equations in One Variable 27 10-SepInequalities 1 28 13-SepInequalities 2 29 15-Sep

LONG QUIZ 2 30 17-Sep31

Page 23: Math10 (mwf)course calendar 1 st qtr 2011 12

TOPICSApplications of Quadratic EquationsInequalitiesInequalities in Two VariablesMatrices and DeterminantsSystems of Linear Equations Systems of InequalitiesApp of Sys of Linear Equations and Inequalities

LONG QUIZ 3 Partial FractionsFunctions and Relations 1 (Def'ns and Oper'ns)Functions and Relations 2 (Inverse Fxn and Graphs)Ratio, Proportion, and VariationCombinatorial Mathematics: PermutationCombinatorial Mathematics: Combination

LONG QUIZ 4 FINAL EXAM

TOPICSSystems of Equations and Inequalities 1Systems of Equations and Inequalities 2Systems of Equations and Inequalities 3Systems of Equations and Inequalities 4Systems of Equations and Inequalities 5

LONG QUIZ 3 Relations Functions and Graphs 1

Relations Functions and Graphs 2Polynomial Functions 1Polynomial Functions 2

LONG QUIZ 4 Sequences and Series, Arithmetic SequencesHarmonic sequence, Geometric SequenceFactorial of a Number, Binomial Theorem

LONG QUIZ 5 FINAL EXAM

Page 24: Math10 (mwf)course calendar 1 st qtr 2011 12

TOPICSTrigonometric Equations 1Trigonometric Equations 2

LONG QUIZ 2 Solutions of Oblique Triangles 1Solutions of Oblique Triangles 2Solutions of Oblique Triangles 3Spherical Trigonometry 1Spherical Trigonometry 2Spherical Trigonometry 3

LONG QUIZ 3 Exponential FunctionsLogarithmic Function 1Logarithmic Function 2Exponential and Logarithmic Equations

LONG QUIZ 4 FINAL EXAM

TOPICSRational Exponents 1Rational Exponents 2

LONG QUIZ 2 Linear Equations 1Linear Equations 2Linear Equations 3Quadratic Equations 1Quadratic Equations 2Quadratic Equations 3Ratio, Proportion, and Variation 1

Ratio, Proportion, and Variation 2Ratio, Proportion, and Variation 3

LONG QUIZ 3 Review/Preparation of PortfolioReview/Preparation of Portfolio

FINAL EXAM

Page 25: Math10 (mwf)course calendar 1 st qtr 2011 12

TOPICSSystems of Equations and Inequalities 1Systems of Equations and Inequalities 2Systems of Equations and Inequalities 3Systems of Equations and Inequalities 4Systems of Equations and Inequalities 5

LONG QUIZ 3 Relations Functions and Graphs 1

Relations Functions and Graphs 2Polynomial Functions 1Polynomial Functions 2

LONG QUIZ 4

Page 26: Math10 (mwf)course calendar 1 st qtr 2011 12

Sequences and Series, Arithmetic SequencesHarmonic sequence, Geometric SequenceFactorial of a Number, Binomial Theorem

LONG QUIZ 5 FINAL EXAM