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 STANDARD
The learner demonstrates understanding of key concepts of functions, rational, inverse, exponential and 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 Types of Functions and their Graphs
LEARNING COMPETENCIE COMPETENCIES S The learner … 1. M11GM-Ia-1: represents real-life situations using functions, including piecewise functions.
Values: Life-long learning In evaluating functions, one must specify values for expressions of
Formative: Quiz bee (Function or not a function) function) Board work Recitation: Evaluating Functions
ASSESSMENT
2. M11GM-Ia-2: 2. M11GM-Ia-2: evaluates a function. 3. Enrichment: identifies Enrichment: identifies the domain and range of functions. 4. M11GM-Ia-3: 4. M11GM-Ia-3: performs addition, subtraction, multiplication, division, and composition of functions.
Summative: LAS 1 (Review on Functions) Functions) LAS 2 (Operations of Functions) 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)
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 belief that’s making our life worse off.
involving functions
6. Enrichment: determines the different types of functions and their graphs.
3. M11GM-Ib-3: solves rational equations and inequalities.
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
The learner… 1. M11GM-Ic-1: determines the: (a) intercepts (b) zeroes; and (c) a symptotes of rational functions.
2. M11GM-Ic-2: graphs rational functions. Values: 3. M11GM-Ic-3: solves problems involving Resilience rational functions, equations, and Sometimes, life will challenge us and will make our lives undefined. inequalities. However, the graphs or the right pathways will guide us to follow the
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
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.
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. st
1 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
Formative: Board work Recitation Activity (Complete the table of exponential functions)
2. M11GM-Ie-4: distinguishes between exponential function, exponential equation, and exponential inequality.
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.
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.
Formative: Recitation Board work
Summative: LAS 9 (Graphing exponential equations using graphing paper ) Quiz 1-5: Solve problems involving exponential functions
Formative: Recitation Board work Reflect Upon Beyond Walls
2. M11GM-Ih-2: distinguishes logarithmic function, logarithmic equation, and logarithmic inequality.
Values: 3. M11GM-Ih-3: illustrates the laws of Life-long learning Logarithmic function is the inverse logarithms. of exponential function. So, if we 4. M11GM-Ii-1: solves logarithmic equations know that our lives are going in a descending direction, be mindful to and inequalities. make it ascend.
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
The learner… 1. M11GM-Ii-2: represents a logarithmic function through its: (a) table of values, (b) graph, and (c) equation.
WEEK 10
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. st
1 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 DESCRIPTION
The learner must know how to solve business-related problems and to apply logic to real-life situations.
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 What is Interest? Simple Interest Maturity Value, Future Value and Present Value for Simple Interest Compound Interest
LEARNING COMPETENCIES The learner… 1. M11GM-IIa-1: illustrates simple and compound interests.
Formative: Recitation: Let’s talk about business Board work
ASSESSMENT
2. M11GM-IIa-2: distinguishes between simple and compound interests.
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.
4. M11GM-IIb-2: solves problems involving simple and compound interests.
WEEK 13
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
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.
Formative: Recitation: Do you know what “paluwagan” is? Board work
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.
Interest ) Quiz 2-1: Solve problems involving Simple and Compound Interest
2. M11GM-IIc-2: distinguishes between simple and general annuities.
Summative: LAS 3 (Simple and General Annuities) LAS 4 (Survey )
The learner… 1. M11GM-IId-1: finds the future value and present value of both simple annuities and general annuities.
Formative: Discussion: Survey Recitation: Recap
Summative: LAS 5 (Future and Present Values of Simple and General Annuities) LAS 6 (Fair Market Value 3. M11GM-IId-3: calculates the present value and Deferred Annuity ) and period of deferral of a deferred annuity. Quiz 2-2: Solve problems involving Simple and General Annuities 2. M11GM-IId-2: calculates the fair market value of a cash flow stream that includes an annuity.
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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.
Values: Decision Making Knowing 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.
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. 5. M11GM-IIe-5: interprets the theory of efficient markets.
Ins ert 1 st P erformance
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WEEK 15 WEEK 16
Formative: Recitation: Board work
2 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
MID-QUARTER EXAMINATION
The learner… 1. M11GM-IIf-1: illustrates business and consumer loans.
Formative: Recitation: Do you have some credit/loans? Reporting
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
What are Propositions? Hypothetical Propositions: Simple and Compound Propositions Categorical Propositions Truth Values of Simple and Compound Propositions Truth Relations of the Standard-form of Categorical Proposition.
Consumer Loans
The learner… 1. M11GM-IIg-1: illustrates a proposition.
2. M11GM-IIg-3: distinguishes between simple and compound propositions.
Formative: Recitation: Let’s expand the concept of common sense
Summative: LAS 10 (Talking about Logical thinking ) Quiz 2-5: Solve problems involving Logic and Propositions
3. M11GM-IIg-4: performs the different types of operations on propositions. 4. M11GM-IIh-1: determines the truth values of 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 Propositions
3. M11GM-IIg-2: symbolizes propositions.
Formative: Recitation: What can you say? Board work
2. M11GM-IIi-2: determines the validity of categorical syllogisms.
Summative: LAS 11 (Syllogisms) Quiz 2-6: Solve problems involving Syllogisms
4. M11GM-IIi-3: establishes the validity and falsity of real-life arguments using logical propositions, syllogisms and fallacies.
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 Tautologous Propositions Forms of Tautologies Direct Proof of Validity
The Method of Proof and Disproof The Method of Induction
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)
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
3. M11GM-IIi-1: illustrates different types of tautologies and fallacies.
Ins ert 2nd 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 rule as a basis on proving such opinion as true or not. WEEK 20
Prepared by Jeric Arrevado Merliza B. David Camille D. Franco Brielene T. Nacpil Lories D. Pingul
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QUARTER EXAMINATION
Reviewed and Checked by Brielene T. Nacpil SHS STEM Coordinator
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