General Mathematics Grade11 Syllabus.pdf

SENIOR HIGH SCHOOL BASIC EDUCATION DEPARTMENT Holy Angel University Angeles City FIRST SEMESTER SYLLABUS IN GENERAL MATHEMATICS FIRST QUARTER

CORE SUBJECT DESCRIPTION

The learner must know how to solve problems involving rational, exponential and logarithmic functions.

CONTENT

The learner demonstrates understanding of key concepts of functions, rational, inverse, exponential and

STANDARD

logarithmic functions.

PERFORMANCE STANDARD

The learner is able to accurately construct mathematical models to represent real-life situations using functions; to accurately formulate and solve real-life problems involving rational functions and to apply concepts of inverse, exponential and logarithmic functions to formulate and solve real-life problems with precision and accuracy.

TIME FRAME WEEK 1

TOPICS Review on Functions Evaluating Functions Domain and Range of a Function Operations on Functions Composite Functions  

LEARNING COMPETENCIES The learner… 1. M11GM-Ia-1: represents real-life situations using functions, including piecewise functions.

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Types of Functions and their Graphs

Values: Life-long learning In evaluating functions, one must specify values for expressions of

Formative: Quiz bee ( Function or not a function) Board work Recitation: Evaluating Functions 

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ASSESSMENT

2. M11GM-Ia-2: evaluates a function. 3. Enrichment: identifies the domain and range of functions. 4. M11GM-Ia-3: performs addition, subtraction, multiplication, division, and composition of functions.

Summative: LAS 1 ( Review on Functions) LAS 2 ( Operations of Functions) Quiz 1-1: Solve problems 

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WEEK 2

the form f(x) for it to become true and accurate. In our lives, we also need to identify our core values to live life with a purpose.

5. M11GM-Ia-4: solves problems involving functions.

Rational Functions Rational Function Solving Rational Equations and Inequalities

The learner… 1. M11GM-Ib-1: represents real-life situations using rational functions.

Formative: Recitation Board work

2. M11GM-Ib-2: distinguishes rational function, rational equation, and rational inequality.

Summative: Small group activity LAS 3 ( Solve rational equations) LAS 4 ( Representing rational equations)

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Values: Rational living in an irrational world. At times, life would give you undefined answers to questions. But this rationality will alert us when we have a false beli ef that’s making our life worse off.

involving functions

6. Enrichment: determines the different types of functions and their graphs.

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3. M11GM-Ib-3: solves rational equations and inequalities.

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4. M11GM-Ib-4: represents a rational function through its: (a) table of values, (b) graph, and (c) equation. 5. M11GM-Ib-5: finds the domain and range of a rational function.

WEEK 3

Rational Functions Solving Problems Involving Rational Functions Graphs and Properties of Rational Function 

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Values: Resilience Sometimes, life will challenge us and will make our lives undefined. However, the graphs or the right pathways will guide us to follow the

The learner… 1. M11GM-Ic-1: determines the: (a) intercepts (b) zeroes; and (c) asymptotes of rational functions.

2. M11GM-Ic-2: graphs rational functions. 3. M11GM-Ic-3: solves problems involving rational functions, equations, and inequalities.

Formative: Recitation Board work Mr. Dien’s Guide to Graphing Rational Functions   

Summative: LAS 5 ( Graphing rational functions using graphing papers) Quiz 1-2: Solve problems involving rational equations 

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trend of slopes of life. WEEK 4

Inverse Functions One-to-one Function Inverse of a Function Graphs and Properties of Inverse Functions  

The learner… 1. M11GM-Id-1: represents real-life situations using one-to one functions.

Formative: Recitation Board work

2. M11GM-Id-2: determines the inverse of a one-to-one function.

Summative: LAS 6 ( Determine the inverse of a function) Quiz 1-3: Solve problems involving inverse functions

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Values: Decision making Graphs and table of our values system will guide us to follow the right trend slopes of life.

3. M11GM-Id-3: represents an inverse function through its: (a) table of values, and (b) graph.

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4. M11GM-Id-4: finds the domain and range of an inverse function. 5. M11GM-Ie-1: graphs inverse functions. 6. M11GM-Ie-2: solves problems involving inverse functions. 1st MID-QUARTER EXAMINATION

WEEK 5 WEEK 6

Exponential Function Definition of Exponential Function Solving Exponential Equations and Inequalities

The learner… 1. M11GM-Ie-3: represents real-life situations using exponential functions.

Values: Self-Improvement Exponential function shows us how exponential growth functions work. Thus, it gives us an idea that we should ascend our lives when it’s descending. Furthermore, we

and exponential inequality.

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Formative: Board work Recitation Activity ( Complete the table of exponential functions)   

2. M11GM-Ie-4: distinguishes between exponential function, exponential equation,

Summative: LAS 7 & 8 ( Solve exponential equations) Quiz 1-4: Solve problems involving exponential functions 

3. M11GM-If-1: solves exponential equations and inequalities. 4. M11GM-If-2: represents an exponential function through its: (a) table of values, (b)

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WEEK 7

should learn how to divide our talents equally so that we can multiply them systematically.

graph, and (c) equation.

Exponential Function Graphs and Properties of Exponential Functions Solving Problems Involving Exponential Functions

The learner… 1. M11GM-If-4: determines the intercepts, zeroes, and asymptotes of an exponential function.

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Values: Decision Making In solving and graphing functions, a correct solution is rooted from an exact and accurate formula. To be able for us to solve the obstacles in life, we should also have the perfect formula for the problems that we have. WEEK 8

Logarithmic Definition of Logarithmic Function Solving Logarithmic Equations Properties of Logarithm 

5. M11GM-If-3: finds the domain and range of an exponential function.

2. M11GM-Ig-1: graphs exponential functions. 3. M11GM-Ig-2: solves problems involving exponential functions, equations, and inequalities.

The learner… 1. M11GM-Ih-1: represents real-life situations using logarithmic functions.

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Values: Life-long learning Logarithmic function is the inverse of exponential function. So, if we know that our lives are going in a descending direction, be mindful to make it ascend.

Formative: Recitation Board work  

Summative: LAS 9 ( Graphing exponential equations using graphing paper) Quiz 1-5: Solve problems involving exponential functions 

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Formative: Recitation Board work Reflect Upon Beyond Walls   

2. M11GM-Ih-2: distinguishes logarithmic function, logarithmic equation, and logarithmic inequality. 3. M11GM-Ih-3: illustrates the laws of logarithms. 4. M11GM-Ii-1: solves logarithmic equations and inequalities.

Summative: LAS 10 & 11 ( Solve logarithmic functions and equations) Quiz 1-6: Solve problems involving logarithmic functions 

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WEEK 9

Logarithmic Graphs and Properties of Logarithmic Function Solving Equations Involving Logarithms 

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The learner… 1. M11GM-Ii-2: represents a logarithmic function through its: (a) table of values, (b) graph, and (c) equation.

WEEK 10

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2. M11GM-Ii-3: finds the domain and range of a logarithmic function. Values: Life-long learning Logarithmic function is the inverse of exponential function. So, if we know that our lives are going in a descending direction, be mindful to make it ascend. Remember; be guided with its graph so that we could follow the right path.

Formative: Recitation Board work Summative: LAS 12 ( Graphing logarithmic equations using graphing papers) Quiz 1-7: Solve problems involving logarithmic functions 

3. M11GM-Ii-4: determines the intercepts, zeroes, and asymptotes of logarithmic functions. 4. M11GM-Ij-1: graphs logarithmic functions. 5. M11GM-Ij-2: solves problems involving logarithmic functions, equations, and inequalities. 1st QUARTER EXAMINATION

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SENIOR HIGH SCHOOL BASIC EDUCATION DEPARTMENT Holy Angel University Angeles City FIRST SEMESTER SYLLABUS IN GENERAL MATHEMATICS SECOND QUARTER

CORE SUBJECT

The learner must know how to solve business-related problems and to apply logic to real-life situations.

DESCRIPTION CONTENT STANDARD

The learner demonstrates understanding of key concepts of simple and compound interests; basic concepts of simple and general annuities; basic concepts of stocks and bonds; basic concepts of business and consumer loans; key concepts of propositional logic; syllogisms and fallacies and the key methods of proof and disproof.

PERFORMANCE STANDARD

The learner is able to investigate, analyze and solve problems involving simple and compound interests and simple and general annuities using appropriate business and financial instruments, use appropriate financial instruments involving stocks and bonds in formulating conclusions and making decisions, decide wisely on the appropriateness of business or consumer loan and its proper utilization, judiciously apply logic in real-life arguments , appropriately apply a method of proof and disproof in real-life situations.

TIME FRAME WEEK 11

TOPICS Simple and Compound Interest   

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What is Interest? Simple Interest Maturity Value, Future Value and Present Value for Simple Interest Compound Interest

LEARNING COMPETENCIES

ASSESSMENT Formative:

The learner…

1. M11GM-IIa-1: illustrates simple and compound interests.

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2. M11GM-IIa-2: distinguishes between simple and compound interests.

Recitation: Let’s talk about business Board work

Summative: LAS 1 ( Simple Interest) LAS 2 ( Compound 

3. M11GM-IIb-1: computes interest, maturity

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WEEK 12

Values: Good decision making Knowing the concept of simple and compound interest will help us decide whether a liability transaction (loan) is worth availing or an asset transaction (deposit or investment) is worth endowing.

value, future value, and present value in simple interest and compound interest environment.

Simple and General Annuities What is Annuity? Simple Annuity General Annuity

The learner… 1. M11GM-IIc-1: illustrates simple and general annuities.

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WEEK 13

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Summative: LAS 3 ( Simple and General Annuities) LAS 4 ( Survey) 

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The learner… 1. M11GM-IId-1: finds the future value and present value of both simple annuities and general annuities.

Values: Critical Thinking The concept of simple and general annuities will let us know some ideas for strategic options on where to effectively put our money.

3. M11GM-IId-3: calculates the present value and period of deferral of a deferred annuity.

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Formative: Recitation: Do you know what “paluwagan” is? Board work 

2. M11GM-IIc-2: distinguishes between simple and general annuities.

Simple and General Annuities Future and Present Values of Simple and General Annuities Fair Market Value of a Cash Flow Stream with Annuity Deferred Annuity 

Interest) Quiz 2-1: Solve problems involving Simple and Compound Interest

4. M11GM-IIb-2: solves problems involving simple and compound interests.

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Values: Setting plans and goals Annuities, whether simple or general, will help people to be knowledgeable of their financial situation especially in dealing with long-term financial plans.

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2. M11GM-IId-2: calculates the fair market value of a cash flow stream that includes an annuity.

Formative: Discussion: Survey Recitation: Recap  

Summative: LAS 5 ( Future and Present Values of Simple and General Annuities) 

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LAS 6 ( Fair Market Value and Deferred Annuity) Quiz 2-2: Solve problems involving Simple and General Annuities

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WEEK 14

Bonds and Stocks What are bonds? The Bond Market What are stocks? The Stock Market Computation on Bonds and Stocks Bond Valuation Stock Valuation Theory of Efficient Market 

The learner… 1. M11GM-IIe-1: illustrate stocks and bonds.

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2. M11GM-IIe-2: distinguishes between stocks and bonds.

Summative: LAS 7 ( Bonds and Stocks) LAS 8 ( Computation on Bonds and Stocks) Quiz 2-3: Solve problems involving Bonds and Stocks 

3. M11GM-IIe-3: describes the different markets for stocks and bonds. 4. M11GM-IIe-4: analyzes the different market indices for stocks and bonds.

Values:

5. M11GM-IIe-5: interprets the theory of

Decision Knowing Making the concept of bonds and stocks will give us examples of long-term investment. This way, people may be able to have a longer period to develop their choice of investments. Also, it could guide people in deciding whether a bond or stock is worth acquiring.

efficient markets.

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Ins ert 1 st P erforma nce

2ND MID-QUARTER EXAMINATION

WEEK 15 WEEK 16

Formative: Recitation: Board work

Basic and Consumer Loans Consumer Credit Business Loans Consumer Loans   

Values: Cautious Loans differ in purpose, terms and materiality. Hence, it is important to identify these before making a

The learner… 1. M11GM-IIf-1: illustrates business and consumer loans.

Formative: Recitation: Do you have some credit/loans? Reporting 

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2. M11GM-IIf-2: distinguishes between business and consumer loans.

Summative: LAS 9 ( Basic and Consumer Loans) Quiz 2-4: Solve problems involving Basic and 

3. M11GM-IIf-3: solves problems involving business and consumer loans (amortization, mortgage).

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loan. In real life, we must always be cautious and financially intelligent to discern which loan offers the best terms that will be more beneficial to us rather than harmful. WEEK 17

Logic  

What is Logic? Formal and Informal Reasoning

Consumer Loans

The learner… 1. M11GM-IIg-1: illustrates a proposition.

2. M11GM-IIg-3: distinguishes between simple and compound propositions.

What are Propositions? 

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Hypothetical Propositions: Simple and Compound Propositions Categorical Propositions Truth Values of Simple and Compound Propositions Truth Relations of the Standard-form of Categorical Proposition.

Formative: Recitation: Let’s expand the concept of common sense 

Summative: LAS 10 ( Talking about 

3. M11GM-IIg-4: performs the different types of operations on propositions. 4. M11GM-IIh-1: determines the truth values of propositions.

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Logical thinking) Quiz 2-5: Solve problems involving Logic and Propositions

Values: Resilient Everyone has a gift of natural logic and common sense, but problems in life are not all about common sense. Learning this lessons will help us evaluate such propositions that we may encounter in everyday life.

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WEEK 18

Categorical Syllogisms Categorical Syllogisms Validity of Categorical Syllogisms Rules in Establishing Validity

The learner… 1. M11GM-IIh-2: illustrates the different forms of conditional propositions.

Symbolic Representation of Propositions Symbolic Notation for Hypothetical Propositions Forms of Conditional

3. M11GM-IIg-2: symbolizes propositions.

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Formative: Recitation: What can you say? Board work 

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2. M11GM-IIi-2: determines the validity of categorical syllogisms.

Summative: LAS 11 ( Syllogisms) Quiz 2-6: Solve problems involving Syllogisms 

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4. M11GM-IIi-3: establishes the validity and falsity of real-life arguments using logical propositions, syllogisms and fallacies.

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Propositions Values: Life-long learning Syllogisms are statements which can be evaluated as true. By this concept, we will be guided on how to check if a given conclusion is valid or not. Whereas, this concept will be applied to some real-life situations.

WEEK 19

The Method of Deduction Argument and Argument Forms Truth Tables

The learner… 1. M11GM-IIj-1: illustrates the different methods of proof (direct and indirect) and disproof (indirect and by counterexample).

Formative: Recitation Board work LAS 12 ( Tautologies)

Tautologous Propositions Forms of Tautologies Direct Proof of Validity

2. M11GM-IIj-2: justifies mathematical and real life statements using the different methods of proof and disproof.

Summative: Quiz 2-7: Solve problems involving the Method of Deduction and Fallacies

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The Method of Proof and Disproof The Method of Induction 

3. M11GM-IIi-1: illustrates different types of tautologies and fallacies.

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Ins ert 2 nd Per formance

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Informal Fallacies Fallacies of relevance Fallacies of presumption Fallacies of ambiguity   

Values: Respect In the real world, there are lots of things needed to be proven so as well the things that are being disproved. Let us just be reminded that we have to respect each person’s statement for we follow a universal ruleopinion as a basis on or proving such as true not. WEEK 20

Prepared by Jeric Arrevado Merliza B. David Camille D. Franco Brielene T. Nacpil Lories D. Pingul

2ND QUARTER EXAMINATION

Reviewed and Checked by Brielene T. Nacpil SHS STEM Coordinator

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