SlideShare a Scribd company logo
Rectangular 
Coordinate 
Sys tem 
Relations and 
Functions 
Representations of 
Relations and 
Functions 
Ordered Pairs 
Equations/ 
Formulas 
Domain and 
Dependent 
Independent 
Variables 
Slope and 
Intercepts 
6 5 4 3 2 1 
7 8 0 −1 2 0 
0 2 9 1 2 4 
1 
Paper #3a 
CARYL MAE S. PUERTOLLANO 
Subject: ICT in Mathematics Education 
Professor: Ms. Rosemarie Galvez 
* Create a Handout using MS Word 
1. SmartArt 
Here is a sample map of the lessons that will be covered in this module: 
2a. Linear Algebra 
Mapping 
Diagram 
Table 
Graphs 
Range 
and 
Appl ications 
PARTITION OF MATRICES; BLOCK MULTIPLICATION 
Linear 
Functions 
We now consider the following partitioned matrices of the same size to see how the operations work 
in practice: 
퐴 = [ 
1 2 3 4 6 0 
7 8 0 −3 1 6 
0 2 9 1 2 4 
], 퐵 = [ 
0 2 −1 0 −3 5 
1 −2 4 −2 2 −5 
4 −4 6 1 0 −4 
], 퐶 = 
[ 
] 
Now, A + B can be computed blockwise as A and B are partitioned the same way with 
corresponding blocks or submatrices having the same sizes. However, even though A and C are
matrices of the same size (so A + C can be computed adding elements entrywise) A + C cannot be 
computed blockwise as the blocks of A and C are not comparable. 
2b. Number Theory 
Properties of Summation 
1. Σ 푐 푛푖 
=1 = 푐 + 푐 + ⋯ + 푐 = 푐푛. 
2. Σ 푐푥푖 = 푐Σ 푥푖 . 푛푖 
=1 
2 
푛푖 
=1 
3. Σ (푥푖 + 푦푖 ) = Σ 푥푖 + Σ 푦푖 . 푛푖 
=1 
푛푖 
= 1 
푛푖 
=푛 
2c. Algebra 
Simplifying Rational Algebraic Expression 
푥2+3푥+2 
푥2−1 
Solution: 
푥2+3푥+2 
푥2−1 
= 
(푥+1)(푥+2) 
(푥+1)(푥−1) 
= 
푥+2 
푥−1 
2d. Calculus 
Evaluate ∫ 
푥2 
푥3 +1 
푑푥 
1 
0 
Solution: 푢 = 푥 3 + 1 
푑푢 = 3푥 2푑푥 
푑푢 
3푥2 = 푑푥 
∫ 
푥 2 
푥 3 + 1 
푑푥 = ∫ 
푥 2 
푢 
∙ 
푑푢 
3푥 2 = 
1 
3 
∫ 
1 
푢 
푑푢 = 
What factoring method 
is used in this step? 
1 
3 
푥=1 
푥=0 
푙푛|푢| = 
1 
3 
1 
푙푛|푥 3 + 1|| 
0 
푥=1 
푥=0 
1 
0 
= 
1 
3 
푙푛|1 + 1| − 
1 
3 
푙푛|0 + 1| = 
1 
3 
푙푛|2| − 
1 
3 
푙푛|1| = 
1 
3 
푙푛|2| − 0 = 
1 
3 
푙푛|2|
3 
2e. Trigonometry 
The graph of 푦 = 푠푖푛푥 is shown below. 
3. Geometric figures with labels. 
1. Name the parts of the circle. 
F G 
H 
D K 
L 
M 
A 
B 
C 
E 
1 
-1 
휋 
2 
3휋 2휋 3휋 
2 
● 
● 
●

More Related Content

What's hot

Lecture 5 (solving simultaneous equations)
Lecture 5 (solving simultaneous equations)Lecture 5 (solving simultaneous equations)
Lecture 5 (solving simultaneous equations)
HarithaRanasinghe
 
Lesson 4 b special matrix multiplication
Lesson 4 b  special matrix multiplicationLesson 4 b  special matrix multiplication
Lesson 4 b special matrix multiplication
Jonathan Templin
 
Lesson 5 b solving matrix equations
Lesson 5 b   solving matrix equationsLesson 5 b   solving matrix equations
Lesson 5 b solving matrix equations
Jonathan Templin
 
E. math
E. mathE. math
Mathematics magazine
Mathematics magazineMathematics magazine
Mathematics magazine
Directorate of Education Delhi
 
Evaluating an Algebraic Expression
Evaluating an Algebraic ExpressionEvaluating an Algebraic Expression
Evaluating an Algebraic Expression
JC Alisasis
 
Graphing Simple Quadratic Functions
Graphing Simple Quadratic FunctionsGraphing Simple Quadratic Functions
Graphing Simple Quadratic Functions
Bitsy Griffin
 
A1 Chapter 5 Study Guide
A1 Chapter 5 Study GuideA1 Chapter 5 Study Guide
A1 Chapter 5 Study Guide
vhiggins1
 
(8) Lesson 3.2
(8) Lesson 3.2(8) Lesson 3.2
(8) Lesson 3.2
wzuri
 
Discrete_Matrices
Discrete_MatricesDiscrete_Matrices
Discrete_Matrices
guest78c418
 
Matrices - Discrete Structures
Matrices - Discrete StructuresMatrices - Discrete Structures
Matrices - Discrete Structures
Bretz Harllynne Moltio
 
7-1 Exploring Quadratic Functions
7-1 Exploring Quadratic Functions7-1 Exploring Quadratic Functions
7-1 Exploring Quadratic Functions
Bitsy Griffin
 
Adding and subtracting matrices unit 3, lesson 2
Adding and subtracting matrices   unit 3, lesson 2Adding and subtracting matrices   unit 3, lesson 2
Adding and subtracting matrices unit 3, lesson 2
holmsted
 
Activity 5 (answer key)
Activity 5 (answer key)Activity 5 (answer key)
Activity 5 (answer key)
juljuliemer
 
Mat feb monthly paper 2
Mat feb monthly paper 2Mat feb monthly paper 2
Mat feb monthly paper 2
Murugamah Muru
 
Lesson 4a - permutation matrices
Lesson 4a - permutation matricesLesson 4a - permutation matrices
Lesson 4a - permutation matrices
Jonathan Templin
 
8th alg -l6.3
8th alg -l6.38th alg -l6.3
8th alg -l6.3
jdurst65
 
Material Didactico
Material DidacticoMaterial Didactico
Material Didactico
alexandra denos
 
Rational exponents and radicals
Rational exponents and radicals Rational exponents and radicals
Rational exponents and radicals
mooca76
 
Matrix multiplication
Matrix multiplicationMatrix multiplication
Matrix multiplication
Bobby Bloch
 

What's hot (20)

Lecture 5 (solving simultaneous equations)
Lecture 5 (solving simultaneous equations)Lecture 5 (solving simultaneous equations)
Lecture 5 (solving simultaneous equations)
 
Lesson 4 b special matrix multiplication
Lesson 4 b  special matrix multiplicationLesson 4 b  special matrix multiplication
Lesson 4 b special matrix multiplication
 
Lesson 5 b solving matrix equations
Lesson 5 b   solving matrix equationsLesson 5 b   solving matrix equations
Lesson 5 b solving matrix equations
 
E. math
E. mathE. math
E. math
 
Mathematics magazine
Mathematics magazineMathematics magazine
Mathematics magazine
 
Evaluating an Algebraic Expression
Evaluating an Algebraic ExpressionEvaluating an Algebraic Expression
Evaluating an Algebraic Expression
 
Graphing Simple Quadratic Functions
Graphing Simple Quadratic FunctionsGraphing Simple Quadratic Functions
Graphing Simple Quadratic Functions
 
A1 Chapter 5 Study Guide
A1 Chapter 5 Study GuideA1 Chapter 5 Study Guide
A1 Chapter 5 Study Guide
 
(8) Lesson 3.2
(8) Lesson 3.2(8) Lesson 3.2
(8) Lesson 3.2
 
Discrete_Matrices
Discrete_MatricesDiscrete_Matrices
Discrete_Matrices
 
Matrices - Discrete Structures
Matrices - Discrete StructuresMatrices - Discrete Structures
Matrices - Discrete Structures
 
7-1 Exploring Quadratic Functions
7-1 Exploring Quadratic Functions7-1 Exploring Quadratic Functions
7-1 Exploring Quadratic Functions
 
Adding and subtracting matrices unit 3, lesson 2
Adding and subtracting matrices   unit 3, lesson 2Adding and subtracting matrices   unit 3, lesson 2
Adding and subtracting matrices unit 3, lesson 2
 
Activity 5 (answer key)
Activity 5 (answer key)Activity 5 (answer key)
Activity 5 (answer key)
 
Mat feb monthly paper 2
Mat feb monthly paper 2Mat feb monthly paper 2
Mat feb monthly paper 2
 
Lesson 4a - permutation matrices
Lesson 4a - permutation matricesLesson 4a - permutation matrices
Lesson 4a - permutation matrices
 
8th alg -l6.3
8th alg -l6.38th alg -l6.3
8th alg -l6.3
 
Material Didactico
Material DidacticoMaterial Didactico
Material Didactico
 
Rational exponents and radicals
Rational exponents and radicals Rational exponents and radicals
Rational exponents and radicals
 
Matrix multiplication
Matrix multiplicationMatrix multiplication
Matrix multiplication
 

Viewers also liked

Unit 7.5
Unit 7.5Unit 7.5
Unit 7.5
Mark Ryder
 
6.6 Graphing Inequalities In Two Variables
6.6 Graphing Inequalities In Two Variables6.6 Graphing Inequalities In Two Variables
6.6 Graphing Inequalities In Two Variables
guestd1dc2e
 
Math Proj
Math ProjMath Proj
Math Proj
Micatine
 
Linear inequalities in two variables
Linear inequalities in two variablesLinear inequalities in two variables
Linear inequalities in two variables
christianjustine
 
Q2 l2 the centipede
Q2 l2 the centipedeQ2 l2 the centipede
Q2 l2 the centipede
Jareleny Nava
 
Q2 l4 the wedding dance
Q2 l4 the wedding danceQ2 l4 the wedding dance
Q2 l4 the wedding dance
Jareleny Nava
 
Solving of system of linear inequalities
Solving of system of linear inequalitiesSolving of system of linear inequalities
Solving of system of linear inequalities
Ricie Anne Palisoc
 
Linear Inequalities
Linear InequalitiesLinear Inequalities
Linear Inequalities
Justine Jose
 
Bandasan, renalyn. philippine literature
Bandasan, renalyn. philippine literatureBandasan, renalyn. philippine literature
Bandasan, renalyn. philippine literature
Jesullyna Manuel
 
Figurative language
Figurative language Figurative language
Figurative language
Chrissa Faith Mañego
 
Figurative Language
Figurative LanguageFigurative Language
Figurative Language
Emma B. Ward Elementary
 
Figurative language commericals
Figurative language commericalsFigurative language commericals
Figurative language commericals
mcpage85
 
Figurative Language
Figurative LanguageFigurative Language
Figurative Language
srabyy
 
Figures of speech : Basics
Figures of speech : BasicsFigures of speech : Basics
Figures of speech : Basics
Balqis Thaahaveettil
 
Figuresof speech
Figuresof speechFiguresof speech
Figuresof speech
Sanoy Jacob
 
The wedding dance summary
The wedding dance summaryThe wedding dance summary
The wedding dance summary
PRINTDESK by Dan
 

Viewers also liked (16)

Unit 7.5
Unit 7.5Unit 7.5
Unit 7.5
 
6.6 Graphing Inequalities In Two Variables
6.6 Graphing Inequalities In Two Variables6.6 Graphing Inequalities In Two Variables
6.6 Graphing Inequalities In Two Variables
 
Math Proj
Math ProjMath Proj
Math Proj
 
Linear inequalities in two variables
Linear inequalities in two variablesLinear inequalities in two variables
Linear inequalities in two variables
 
Q2 l2 the centipede
Q2 l2 the centipedeQ2 l2 the centipede
Q2 l2 the centipede
 
Q2 l4 the wedding dance
Q2 l4 the wedding danceQ2 l4 the wedding dance
Q2 l4 the wedding dance
 
Solving of system of linear inequalities
Solving of system of linear inequalitiesSolving of system of linear inequalities
Solving of system of linear inequalities
 
Linear Inequalities
Linear InequalitiesLinear Inequalities
Linear Inequalities
 
Bandasan, renalyn. philippine literature
Bandasan, renalyn. philippine literatureBandasan, renalyn. philippine literature
Bandasan, renalyn. philippine literature
 
Figurative language
Figurative language Figurative language
Figurative language
 
Figurative Language
Figurative LanguageFigurative Language
Figurative Language
 
Figurative language commericals
Figurative language commericalsFigurative language commericals
Figurative language commericals
 
Figurative Language
Figurative LanguageFigurative Language
Figurative Language
 
Figures of speech : Basics
Figures of speech : BasicsFigures of speech : Basics
Figures of speech : Basics
 
Figuresof speech
Figuresof speechFiguresof speech
Figuresof speech
 
The wedding dance summary
The wedding dance summaryThe wedding dance summary
The wedding dance summary
 

Similar to Paper3a puertollano

Rational Expressions
Rational ExpressionsRational Expressions
Rational Expressions
Lorie Jane Letada
 
Rational Expressions Module
Rational Expressions ModuleRational Expressions Module
Rational Expressions Module
Lorie Jane Letada
 
Solucao_Marion_Thornton_Dinamica_Classic (1).pdf
Solucao_Marion_Thornton_Dinamica_Classic (1).pdfSolucao_Marion_Thornton_Dinamica_Classic (1).pdf
Solucao_Marion_Thornton_Dinamica_Classic (1).pdf
FranciscoJavierCaedo
 
P1-Chp13-Integration.pptx
P1-Chp13-Integration.pptxP1-Chp13-Integration.pptx
P1-Chp13-Integration.pptx
YashTiwari512330
 
LEARNING PLAN IN MATH 9 Q1W1
LEARNING PLAN IN MATH 9 Q1W1LEARNING PLAN IN MATH 9 Q1W1
LEARNING PLAN IN MATH 9 Q1W1
Erwin Hilario
 
Lesson plan in mathematics 9 (illustrations of quadratic equations)
Lesson plan in mathematics 9 (illustrations of quadratic equations)Lesson plan in mathematics 9 (illustrations of quadratic equations)
Lesson plan in mathematics 9 (illustrations of quadratic equations)
Decena15
 
CP1-Chp6-Matrices (2).pptx used for revision
CP1-Chp6-Matrices (2).pptx used for revisionCP1-Chp6-Matrices (2).pptx used for revision
CP1-Chp6-Matrices (2).pptx used for revision
rachaelgiwa11
 
P2-Chp12-Vectors.pptx
P2-Chp12-Vectors.pptxP2-Chp12-Vectors.pptx
P2-Chp12-Vectors.pptx
StephenJude3
 
MATRICES-MATHED204.pptx
MATRICES-MATHED204.pptxMATRICES-MATHED204.pptx
MATRICES-MATHED204.pptx
ChristopherMaldicas
 
Direct solution of sparse network equations by optimally ordered triangular f...
Direct solution of sparse network equations by optimally ordered triangular f...Direct solution of sparse network equations by optimally ordered triangular f...
Direct solution of sparse network equations by optimally ordered triangular f...
Dimas Ruliandi
 
P1-Chp2-Quadratics.pptx
P1-Chp2-Quadratics.pptxP1-Chp2-Quadratics.pptx
P1-Chp2-Quadratics.pptx
BELLABELLA472963
 
Unidad 3 tarea 3 grupo208046_379
Unidad 3 tarea 3 grupo208046_379Unidad 3 tarea 3 grupo208046_379
Unidad 3 tarea 3 grupo208046_379
LAURAXIMENAMONTESEST
 
Unit-1 Basic Concept of Algorithm.pptx
Unit-1 Basic Concept of Algorithm.pptxUnit-1 Basic Concept of Algorithm.pptx
Unit-1 Basic Concept of Algorithm.pptx
ssuser01e301
 
CP2-Chp2-Series.pptx
CP2-Chp2-Series.pptxCP2-Chp2-Series.pptx
CP2-Chp2-Series.pptx
NasimSalim2
 
Chapter 2 - Types of a Function.pdf
Chapter 2 - Types of a Function.pdfChapter 2 - Types of a Function.pdf
Chapter 2 - Types of a Function.pdf
ManarKareem1
 
Advanced-Differentiation-Rules.pdf
Advanced-Differentiation-Rules.pdfAdvanced-Differentiation-Rules.pdf
Advanced-Differentiation-Rules.pdf
KyleBrianSLumanglas
 
2023 St Jospeh's College Geelong
2023 St Jospeh's College Geelong2023 St Jospeh's College Geelong
2023 St Jospeh's College Geelong
Andrew Smith
 
Other operations with exponents
Other operations with exponentsOther operations with exponents
Other operations with exponents
EdTechonGC Mallett
 
GraphTransformations.pptx
GraphTransformations.pptxGraphTransformations.pptx
GraphTransformations.pptx
SrideviNagarjuna
 
TABREZ KHAN.ppt
TABREZ KHAN.pptTABREZ KHAN.ppt
TABREZ KHAN.ppt
TabrezKhan733764
 

Similar to Paper3a puertollano (20)

Rational Expressions
Rational ExpressionsRational Expressions
Rational Expressions
 
Rational Expressions Module
Rational Expressions ModuleRational Expressions Module
Rational Expressions Module
 
Solucao_Marion_Thornton_Dinamica_Classic (1).pdf
Solucao_Marion_Thornton_Dinamica_Classic (1).pdfSolucao_Marion_Thornton_Dinamica_Classic (1).pdf
Solucao_Marion_Thornton_Dinamica_Classic (1).pdf
 
P1-Chp13-Integration.pptx
P1-Chp13-Integration.pptxP1-Chp13-Integration.pptx
P1-Chp13-Integration.pptx
 
LEARNING PLAN IN MATH 9 Q1W1
LEARNING PLAN IN MATH 9 Q1W1LEARNING PLAN IN MATH 9 Q1W1
LEARNING PLAN IN MATH 9 Q1W1
 
Lesson plan in mathematics 9 (illustrations of quadratic equations)
Lesson plan in mathematics 9 (illustrations of quadratic equations)Lesson plan in mathematics 9 (illustrations of quadratic equations)
Lesson plan in mathematics 9 (illustrations of quadratic equations)
 
CP1-Chp6-Matrices (2).pptx used for revision
CP1-Chp6-Matrices (2).pptx used for revisionCP1-Chp6-Matrices (2).pptx used for revision
CP1-Chp6-Matrices (2).pptx used for revision
 
P2-Chp12-Vectors.pptx
P2-Chp12-Vectors.pptxP2-Chp12-Vectors.pptx
P2-Chp12-Vectors.pptx
 
MATRICES-MATHED204.pptx
MATRICES-MATHED204.pptxMATRICES-MATHED204.pptx
MATRICES-MATHED204.pptx
 
Direct solution of sparse network equations by optimally ordered triangular f...
Direct solution of sparse network equations by optimally ordered triangular f...Direct solution of sparse network equations by optimally ordered triangular f...
Direct solution of sparse network equations by optimally ordered triangular f...
 
P1-Chp2-Quadratics.pptx
P1-Chp2-Quadratics.pptxP1-Chp2-Quadratics.pptx
P1-Chp2-Quadratics.pptx
 
Unidad 3 tarea 3 grupo208046_379
Unidad 3 tarea 3 grupo208046_379Unidad 3 tarea 3 grupo208046_379
Unidad 3 tarea 3 grupo208046_379
 
Unit-1 Basic Concept of Algorithm.pptx
Unit-1 Basic Concept of Algorithm.pptxUnit-1 Basic Concept of Algorithm.pptx
Unit-1 Basic Concept of Algorithm.pptx
 
CP2-Chp2-Series.pptx
CP2-Chp2-Series.pptxCP2-Chp2-Series.pptx
CP2-Chp2-Series.pptx
 
Chapter 2 - Types of a Function.pdf
Chapter 2 - Types of a Function.pdfChapter 2 - Types of a Function.pdf
Chapter 2 - Types of a Function.pdf
 
Advanced-Differentiation-Rules.pdf
Advanced-Differentiation-Rules.pdfAdvanced-Differentiation-Rules.pdf
Advanced-Differentiation-Rules.pdf
 
2023 St Jospeh's College Geelong
2023 St Jospeh's College Geelong2023 St Jospeh's College Geelong
2023 St Jospeh's College Geelong
 
Other operations with exponents
Other operations with exponentsOther operations with exponents
Other operations with exponents
 
GraphTransformations.pptx
GraphTransformations.pptxGraphTransformations.pptx
GraphTransformations.pptx
 
TABREZ KHAN.ppt
TABREZ KHAN.pptTABREZ KHAN.ppt
TABREZ KHAN.ppt
 

Recently uploaded

220711130100 udita Chakraborty Aims and objectives of national policy on inf...
220711130100 udita Chakraborty  Aims and objectives of national policy on inf...220711130100 udita Chakraborty  Aims and objectives of national policy on inf...
220711130100 udita Chakraborty Aims and objectives of national policy on inf...
Kalna College
 
Bonku-Babus-Friend by Sathyajith Ray (9)
Bonku-Babus-Friend by Sathyajith Ray  (9)Bonku-Babus-Friend by Sathyajith Ray  (9)
Bonku-Babus-Friend by Sathyajith Ray (9)
nitinpv4ai
 
Accounting for Restricted Grants When and How To Record Properly
Accounting for Restricted Grants  When and How To Record ProperlyAccounting for Restricted Grants  When and How To Record Properly
Accounting for Restricted Grants When and How To Record Properly
TechSoup
 
Pharmaceutics Pharmaceuticals best of brub
Pharmaceutics Pharmaceuticals best of brubPharmaceutics Pharmaceuticals best of brub
Pharmaceutics Pharmaceuticals best of brub
danielkiash986
 
Standardized tool for Intelligence test.
Standardized tool for Intelligence test.Standardized tool for Intelligence test.
Standardized tool for Intelligence test.
deepaannamalai16
 
How to Download & Install Module From the Odoo App Store in Odoo 17
How to Download & Install Module From the Odoo App Store in Odoo 17How to Download & Install Module From the Odoo App Store in Odoo 17
How to Download & Install Module From the Odoo App Store in Odoo 17
Celine George
 
HYPERTENSION - SLIDE SHARE PRESENTATION.
HYPERTENSION - SLIDE SHARE PRESENTATION.HYPERTENSION - SLIDE SHARE PRESENTATION.
HYPERTENSION - SLIDE SHARE PRESENTATION.
deepaannamalai16
 
Ch-4 Forest Society and colonialism 2.pdf
Ch-4 Forest Society and colonialism 2.pdfCh-4 Forest Society and colonialism 2.pdf
Ch-4 Forest Society and colonialism 2.pdf
lakshayrojroj
 
How to Fix [Errno 98] address already in use
How to Fix [Errno 98] address already in useHow to Fix [Errno 98] address already in use
How to Fix [Errno 98] address already in use
Celine George
 
Observational Learning
Observational Learning Observational Learning
Observational Learning
sanamushtaq922
 
Data Structure using C by Dr. K Adisesha .ppsx
Data Structure using C by Dr. K Adisesha .ppsxData Structure using C by Dr. K Adisesha .ppsx
Data Structure using C by Dr. K Adisesha .ppsx
Prof. Dr. K. Adisesha
 
skeleton System.pdf (skeleton system wow)
skeleton System.pdf (skeleton system wow)skeleton System.pdf (skeleton system wow)
skeleton System.pdf (skeleton system wow)
Mohammad Al-Dhahabi
 
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
indexPub
 
INTRODUCTION TO HOSPITALS & AND ITS ORGANIZATION
INTRODUCTION TO HOSPITALS & AND ITS ORGANIZATION INTRODUCTION TO HOSPITALS & AND ITS ORGANIZATION
INTRODUCTION TO HOSPITALS & AND ITS ORGANIZATION
ShwetaGawande8
 
CapTechTalks Webinar Slides June 2024 Donovan Wright.pptx
CapTechTalks Webinar Slides June 2024 Donovan Wright.pptxCapTechTalks Webinar Slides June 2024 Donovan Wright.pptx
CapTechTalks Webinar Slides June 2024 Donovan Wright.pptx
CapitolTechU
 
Educational Technology in the Health Sciences
Educational Technology in the Health SciencesEducational Technology in the Health Sciences
Educational Technology in the Health Sciences
Iris Thiele Isip-Tan
 
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
Nguyen Thanh Tu Collection
 
Brand Guideline of Bashundhara A4 Paper - 2024
Brand Guideline of Bashundhara A4 Paper - 2024Brand Guideline of Bashundhara A4 Paper - 2024
Brand Guideline of Bashundhara A4 Paper - 2024
khabri85
 
A Free 200-Page eBook ~ Brain and Mind Exercise.pptx
A Free 200-Page eBook ~ Brain and Mind Exercise.pptxA Free 200-Page eBook ~ Brain and Mind Exercise.pptx
A Free 200-Page eBook ~ Brain and Mind Exercise.pptx
OH TEIK BIN
 
Diversity Quiz Prelims by Quiz Club, IIT Kanpur
Diversity Quiz Prelims by Quiz Club, IIT KanpurDiversity Quiz Prelims by Quiz Club, IIT Kanpur
Diversity Quiz Prelims by Quiz Club, IIT Kanpur
Quiz Club IIT Kanpur
 

Recently uploaded (20)

220711130100 udita Chakraborty Aims and objectives of national policy on inf...
220711130100 udita Chakraborty  Aims and objectives of national policy on inf...220711130100 udita Chakraborty  Aims and objectives of national policy on inf...
220711130100 udita Chakraborty Aims and objectives of national policy on inf...
 
Bonku-Babus-Friend by Sathyajith Ray (9)
Bonku-Babus-Friend by Sathyajith Ray  (9)Bonku-Babus-Friend by Sathyajith Ray  (9)
Bonku-Babus-Friend by Sathyajith Ray (9)
 
Accounting for Restricted Grants When and How To Record Properly
Accounting for Restricted Grants  When and How To Record ProperlyAccounting for Restricted Grants  When and How To Record Properly
Accounting for Restricted Grants When and How To Record Properly
 
Pharmaceutics Pharmaceuticals best of brub
Pharmaceutics Pharmaceuticals best of brubPharmaceutics Pharmaceuticals best of brub
Pharmaceutics Pharmaceuticals best of brub
 
Standardized tool for Intelligence test.
Standardized tool for Intelligence test.Standardized tool for Intelligence test.
Standardized tool for Intelligence test.
 
How to Download & Install Module From the Odoo App Store in Odoo 17
How to Download & Install Module From the Odoo App Store in Odoo 17How to Download & Install Module From the Odoo App Store in Odoo 17
How to Download & Install Module From the Odoo App Store in Odoo 17
 
HYPERTENSION - SLIDE SHARE PRESENTATION.
HYPERTENSION - SLIDE SHARE PRESENTATION.HYPERTENSION - SLIDE SHARE PRESENTATION.
HYPERTENSION - SLIDE SHARE PRESENTATION.
 
Ch-4 Forest Society and colonialism 2.pdf
Ch-4 Forest Society and colonialism 2.pdfCh-4 Forest Society and colonialism 2.pdf
Ch-4 Forest Society and colonialism 2.pdf
 
How to Fix [Errno 98] address already in use
How to Fix [Errno 98] address already in useHow to Fix [Errno 98] address already in use
How to Fix [Errno 98] address already in use
 
Observational Learning
Observational Learning Observational Learning
Observational Learning
 
Data Structure using C by Dr. K Adisesha .ppsx
Data Structure using C by Dr. K Adisesha .ppsxData Structure using C by Dr. K Adisesha .ppsx
Data Structure using C by Dr. K Adisesha .ppsx
 
skeleton System.pdf (skeleton system wow)
skeleton System.pdf (skeleton system wow)skeleton System.pdf (skeleton system wow)
skeleton System.pdf (skeleton system wow)
 
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
 
INTRODUCTION TO HOSPITALS & AND ITS ORGANIZATION
INTRODUCTION TO HOSPITALS & AND ITS ORGANIZATION INTRODUCTION TO HOSPITALS & AND ITS ORGANIZATION
INTRODUCTION TO HOSPITALS & AND ITS ORGANIZATION
 
CapTechTalks Webinar Slides June 2024 Donovan Wright.pptx
CapTechTalks Webinar Slides June 2024 Donovan Wright.pptxCapTechTalks Webinar Slides June 2024 Donovan Wright.pptx
CapTechTalks Webinar Slides June 2024 Donovan Wright.pptx
 
Educational Technology in the Health Sciences
Educational Technology in the Health SciencesEducational Technology in the Health Sciences
Educational Technology in the Health Sciences
 
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
 
Brand Guideline of Bashundhara A4 Paper - 2024
Brand Guideline of Bashundhara A4 Paper - 2024Brand Guideline of Bashundhara A4 Paper - 2024
Brand Guideline of Bashundhara A4 Paper - 2024
 
A Free 200-Page eBook ~ Brain and Mind Exercise.pptx
A Free 200-Page eBook ~ Brain and Mind Exercise.pptxA Free 200-Page eBook ~ Brain and Mind Exercise.pptx
A Free 200-Page eBook ~ Brain and Mind Exercise.pptx
 
Diversity Quiz Prelims by Quiz Club, IIT Kanpur
Diversity Quiz Prelims by Quiz Club, IIT KanpurDiversity Quiz Prelims by Quiz Club, IIT Kanpur
Diversity Quiz Prelims by Quiz Club, IIT Kanpur
 

Paper3a puertollano

  • 1. Rectangular Coordinate Sys tem Relations and Functions Representations of Relations and Functions Ordered Pairs Equations/ Formulas Domain and Dependent Independent Variables Slope and Intercepts 6 5 4 3 2 1 7 8 0 −1 2 0 0 2 9 1 2 4 1 Paper #3a CARYL MAE S. PUERTOLLANO Subject: ICT in Mathematics Education Professor: Ms. Rosemarie Galvez * Create a Handout using MS Word 1. SmartArt Here is a sample map of the lessons that will be covered in this module: 2a. Linear Algebra Mapping Diagram Table Graphs Range and Appl ications PARTITION OF MATRICES; BLOCK MULTIPLICATION Linear Functions We now consider the following partitioned matrices of the same size to see how the operations work in practice: 퐴 = [ 1 2 3 4 6 0 7 8 0 −3 1 6 0 2 9 1 2 4 ], 퐵 = [ 0 2 −1 0 −3 5 1 −2 4 −2 2 −5 4 −4 6 1 0 −4 ], 퐶 = [ ] Now, A + B can be computed blockwise as A and B are partitioned the same way with corresponding blocks or submatrices having the same sizes. However, even though A and C are
  • 2. matrices of the same size (so A + C can be computed adding elements entrywise) A + C cannot be computed blockwise as the blocks of A and C are not comparable. 2b. Number Theory Properties of Summation 1. Σ 푐 푛푖 =1 = 푐 + 푐 + ⋯ + 푐 = 푐푛. 2. Σ 푐푥푖 = 푐Σ 푥푖 . 푛푖 =1 2 푛푖 =1 3. Σ (푥푖 + 푦푖 ) = Σ 푥푖 + Σ 푦푖 . 푛푖 =1 푛푖 = 1 푛푖 =푛 2c. Algebra Simplifying Rational Algebraic Expression 푥2+3푥+2 푥2−1 Solution: 푥2+3푥+2 푥2−1 = (푥+1)(푥+2) (푥+1)(푥−1) = 푥+2 푥−1 2d. Calculus Evaluate ∫ 푥2 푥3 +1 푑푥 1 0 Solution: 푢 = 푥 3 + 1 푑푢 = 3푥 2푑푥 푑푢 3푥2 = 푑푥 ∫ 푥 2 푥 3 + 1 푑푥 = ∫ 푥 2 푢 ∙ 푑푢 3푥 2 = 1 3 ∫ 1 푢 푑푢 = What factoring method is used in this step? 1 3 푥=1 푥=0 푙푛|푢| = 1 3 1 푙푛|푥 3 + 1|| 0 푥=1 푥=0 1 0 = 1 3 푙푛|1 + 1| − 1 3 푙푛|0 + 1| = 1 3 푙푛|2| − 1 3 푙푛|1| = 1 3 푙푛|2| − 0 = 1 3 푙푛|2|
  • 3. 3 2e. Trigonometry The graph of 푦 = 푠푖푛푥 is shown below. 3. Geometric figures with labels. 1. Name the parts of the circle. F G H D K L M A B C E 1 -1 휋 2 3휋 2휋 3휋 2 ● ● ●