SENIOR HIGH SCHOOLBASIC EDUCATION DEPARTMENT Holy Angel University Angeles City FIRST SEMESTER SYLLABUS IN GENERAL MATHEMATICS FIRST QUARTER CORE SUBJECT The learner must know how to solve problems involving rational, exponential and logarithmic functions. DESCRIPTION CONTENT The learner demonstrates understanding of key concepts of functions, rational, inverse, exponential and STANDARD logarithmic functions. PERFORMANCE The learner is able to accurately construct mathematical models to represent real-life situations using STANDARD 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 TOPICS LEARNING COMPETENCIES ASSESSMENT FRAME WEEK 1 Review on Functions The learner… Formative: Evaluating Functions 1. M11GM-Ia-1: represents real-life Quiz bee (Function or not a Domain and Range of a situations using functions, including piece- function) Function wise functions. Board work Operations on Functions Recitation: Evaluating Composite Functions 2. M11GM-Ia-2: evaluates a function. Functions Types of Functions and their Graphs 3. Enrichment: identifies the domain and Summative: range of functions. LAS 1 (Review on Values: Functions) Life-long learning 4. M11GM-Ia-3: performs addition, LAS 2 (Operations of In evaluating functions, one must subtraction, multiplication, division, and Functions) specify values for expressions of composition of functions. Quiz 1-1: Solve problems First Semester: Syllabus in General Mathematics | 1 and (c) equation. 3. M11GM-Ic-1: determines the: (a) Recitation Rational Functions intercepts (b) zeroes. the form f(x) for it to become true 5. 6. papers) However. LAS 3 (Solve rational world. and (c) asymptotes of Board work Graphs and Properties of rational functions. we also functions. M11GM-Ib-1: represents real-life Recitation Solving Rational Equations situations using rational functions. 4. equations. M11GM-Ib-5: finds the domain and range of a rational function. At times. WEEK 2 Rational Functions The learner… Formative: Rational Function 1. Dien’s Guide to Rational Function Graphing Rational Functions 2. In our lives. M11GM-Ib-2: distinguishes rational Summative: Values: function. need to identify our core values to live life with a purpose. WEEK 3 Rational Functions The learner… Formative: Solving Problems Involving 1. M11GM-Ic-3: solves problems involving LAS 5 (Graphing rational Sometimes. Board work and Inequalities 2. M11GM-Ic-2: graphs rational functions. and functions using graphing and will make our lives undefined. life would give you equations) undefined answers to questions. M11GM-Ib-4: represents a rational function through its: (a) table of values. 5. the graphs or the right Quiz 1-2: Solve problems pathways will guide us to follow the involving rational equations First Semester: Syllabus in General Mathematics | 2 . rational equation. (b) graph. life will challenge us rational functions. M11GM-Ib-3: solves rational equations LAS 4 (Representing But this rationality will alert us and inequalities. and rational Small group activity Rational living in an irrational inequality. rational equations) when we have a false belief that’s making our life worse off. M11GM-Ia-4: solves problems involving involving functions and accurate. Mr. inequalities. Enrichment: determines the different types of functions and their graphs. Values: Summative: Resilience 3. M11GM-Ie-2: solves problems involving inverse functions. and inequalities. Quiz 1-4: Solve problems Thus. trend of slopes of life. it gives us an idea that we involving exponential should ascend our lives when it’s 4. 6. M11GM-Id-2: determines the inverse of a Summative: one-to-one function. M11GM-Ie-1: graphs inverse functions. we function through its: (a) table of values. Summative: Self-Improvement LAS 7 & 8 (Solve Exponential function shows us how 3. M11GM-Ie-4: distinguishes between of exponential functions) exponential function. M11GM-Id-4: finds the domain and range of an inverse function. Board work Graphs and Properties of Inverse Functions 2. M11GM-Id-3: represents an inverse Quiz 1-3: Solve problems Graphs and table of our values function through its: (a) table of values. (b) First Semester: Syllabus in General Mathematics | 3 . exponential equation. and involving inverse functions system will guide us to follow the (b) graph. M11GM-Id-1: represents real-life Recitation Inverse of a Function situations using one-to one functions. Values: and exponential inequality. M11GM-If-2: represents an exponential functions descending. M11GM-If-1: solves exponential equations exponential equations) exponential growth functions work. M11GM-Ie-3: represents real-life Board work Function situations using exponential functions. 4. WEEK 5 1st MID-QUARTER EXAMINATION WEEK 6 Exponential Function The learner… Formative: Definition of Exponential 1. 5. LAS 6 (Determine the Values: inverse of a function) Decision making 3. Furthermore. right trend slopes of life. Recitation Solving Exponential Activity (Complete the table Equations and Inequalities 2. WEEK 4 Inverse Functions The learner… Formative: One-to-one Function 1. and (c) equation. functions able for us to solve the obstacles in life. M11GM-Ig-2: solves problems involving Quiz 1-5: Solve problems a correct solution is rooted from an exponential functions. should learn how to divide our graph. M11GM-Ig-1: graphs exponential LAS 9 (Graphing Values: functions. 5. M11GM-If-4: determines the intercepts. So. and involving exponential exact and accurate formula. we should also have the perfect formula for the problems that we have. make it ascend. To be inequalities. logarithmic equation. 3. First Semester: Syllabus in General Mathematics | 4 . and asymptotes of an exponential Board work Solving Problems Involving function. exponential equations using Decision Making graphing paper) In solving and graphing functions. WEEK 8 Logarithmic The learner… Formative: Definition of Logarithmic 1. Board work Solving Logarithmic Reflect Upon Beyond Walls Equations 2. and Summative: logarithmic inequality. M11GM-Ii-1: solves logarithmic equations functions descending direction. equations. Exponential Functions Summative: 2. M11GM-Ih-2: distinguishes logarithmic Properties of Logarithm function. if we involving logarithmic know that our lives are going in a 4. Quiz 1-6: Solve problems of exponential function. talents equally so that we can multiply them systematically. LAS 10 & 11 (Solve Values: logarithmic functions and Life-long learning 3. M11GM-If-3: finds the domain and range of an exponential function. WEEK 7 Exponential Function The learner… Formative: Graphs and Properties of 1. M11GM-Ih-3: illustrates the laws of equations) Logarithmic function is the inverse logarithms. be mindful to and inequalities. Recitation Exponential Functions zeroes. M11GM-Ih-1: represents real-life Recitation Function situations using logarithmic functions. logarithmic functions. M11GM-Ii-4: determines the intercepts. and asymptotes of logarithmic functions of exponential function. be mindful to 4. be guided with its graph so that we 5. equations. Board work Solving Equations Involving (b) graph. M11GM-Ii-2: represents a logarithmic Recitation Logarithmic Function function through its: (a) table of values.WEEK 9 Logarithmic The learner… Formative: Graphs and Properties of 1. M11GM-Ii-3: finds the domain and range logarithmic equations using of a logarithmic function. WEEK 10 1st QUARTER EXAMINATION First Semester: Syllabus in General Mathematics | 5 . if we functions. make it ascend. and (c) equation. involving logarithmic Logarithmic function is the inverse zeroes. graphing papers) Values: Quiz 1-7: Solve problems Life-long learning 3. and inequalities. Summative: Logarithms LAS 12 (Graphing 2. M11GM-Ij-1: graphs logarithmic functions. know that our lives are going in a descending direction. So. M11GM-Ij-2: solves problems involving could follow the right path. Remember. DESCRIPTION CONTENT The learner demonstrates understanding of key concepts of simple and compound interests. M11GM-IIb-1: computes interest. 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. M11GM-IIa-1: illustrates simple and Recitation: Let’s talk about Simple Interest compound interests. syllogisms and fallacies and the key methods of proof and disproof. M11GM-IIa-2: distinguishes between Simple Interest simple and compound interests. TIME TOPICS LEARNING COMPETENCIES ASSESSMENT FRAME WEEK 11 Simple and Compound Interest The learner… Formative: What is Interest? 1. judiciously apply logic in real-life arguments . key concepts of propositional logic. Summative: Compound Interest LAS 1 (Simple Interest) 3. basic concepts of stocks and bonds. appropriately apply a method of proof and disproof in real-life situations. basic concepts of business and consumer loans. use appropriate financial instruments involving stocks and bonds in formulating conclusions and making decisions. PERFORMANCE The learner is able to investigate. business Maturity Value. analyze and solve problems involving simple and compound interests and STANDARD simple and general annuities using appropriate business and financial instruments. Future Board work Value and Present Value for 2. basic concepts of STANDARD simple and general annuities. decide wisely on the appropriateness of business or consumer loan and its proper utilization. maturity LAS 2 (Compound First Semester: Syllabus in General Mathematics | 6 . M11GM-IIc-1: illustrates simple and Recitation: Do you know Simple Annuity general annuities. WEEK 12 Simple and General Annuities The learner… Formative: What is Annuity? 1. what “paluwagan” is? General Annuity Board work 2. Quiz 2-2: Solve problems annuities will let us know some involving Simple and ideas for strategic options on General Annuities where to effectively put our money. M11GM-IId-3: calculates the present value and Deferred Annuity) The concept of simple and general and period of deferral of a deferred annuity. M11GM-IId-1: finds the future value and Discussion: Survey of Simple and General present value of both simple annuities and Recitation: Recap Annuities general annuities. WEEK 13 Simple and General Annuities The learner… Formative: Future and Present Values 1. or an asset transaction (deposit or investment) is worth endowing. and present value in Interest) Good decision making simple interest and compound interest Quiz 2-1: Solve problems Knowing the concept of simple and environment. Fair Market Value of a Cash Summative: Flow Stream with Annuity 2. involving Simple and compound interest will help us Compound Interest decide whether a liability 4. M11GM-IId-2: calculates the fair market LAS 5 (Future and Present Deferred Annuity value of a cash flow stream that includes an Values of Simple and annuity. First Semester: Syllabus in General Mathematics | 7 . Values: value. Summative: Setting plans and goals LAS 3 (Simple and General Annuities. future value. M11GM-IIc-2: distinguishes between Values: simple and general annuities. whether simple or Annuities) general. General Annuities) Values: LAS 6 (Fair Market Value Critical Thinking 3. M11GM-IIb-2: solves problems involving transaction (loan) is worth availing simple and compound interests. will help people to be LAS 4 (Survey) knowledgeable of their financial situation especially in dealing with long-term financial plans. Hence. involving Basic and First Semester: Syllabus in General Mathematics | 8 . M11GM-IIf-1: illustrates business and Recitation: Do you have Business Loans consumer loans. M11GM-IIe-3: describes the different LAS 8 (Computation on Bond Valuation markets for stocks and bonds. people may be able to have a longer period to develop their choice of investments. it is important business and consumer loans (amortization. Also. WEEK 15 2ND MID-QUARTER EXAMINATION WEEK 16 Basic and Consumer Loans The learner… Formative: Consumer Credit 1. Summative: Computation on Bonds and LAS 7 (Bonds and Stocks) Stocks 3. Values: Insert 1st Performance 5. some credit/loans? Consumer Loans Reporting 2. M11GM-IIe-1: illustrate stocks and bonds. terms and 3. Knowing the concept of bonds and stocks will give us examples of long-term investment. Quiz 2-4: Solve problems to identify these before making a mortgage). Recitation: The Bond Market Board work What are stocks? 2. M11GM-IIe-5: interprets the theory of Decision Making efficient markets. it could guide people in deciding whether a bond or stock is worth acquiring. Summative: Cautious LAS 9 (Basic and Loans differ in purpose. M11GM-IIf-3: solves problems involving Consumer Loans) materiality. This way. M11GM-IIe-2: distinguishes between The Stock Market stocks and bonds.WEEK 14 Bonds and Stocks The learner… Formative: What are bonds? 1. M11GM-IIf-2: distinguishes between Values: business and consumer loans. M11GM-IIe-4: analyzes the different Theory of Efficient Market involving Bonds and Stocks market indices for stocks and bonds. Bonds and Stocks) Stock Valuation Quiz 2-3: Solve problems 4. loan. we must always Consumer Loans be cautious and financially intelligent to discern which loan offers the best terms that will be more beneficial to us rather than harmful. Recitation: Let’s expand the Formal and Informal concept of common sense Reasoning 2. Values: Resilient Everyone has a gift of natural logic and common sense. WEEK 17 Logic The learner… Formative: What is Logic? 1. M11GM-IIg-4: performs the different types Logical thinking) Simple and Compound of operations on propositions. M11GM-IIh-1: determines the truth values Propositions Truth Values of Simple and of propositions. Learning this lessons will help us evaluate such propositions that we may encounter in everyday life. Summative: What are Propositions? LAS 10 (Talking about Hypothetical Propositions: 3. Compound Propositions Truth Relations of the Standard-form of Categorical Proposition. M11GM-IIg-1: illustrates a proposition. In real life. but problems in life are not all about common sense. Quiz 2-5: Solve problems Propositions involving Logic and Categorical Propositions 4. First Semester: Syllabus in General Mathematics | 9 . M11GM-IIg-3: distinguishes between simple and compound propositions. LAS 12 (Tautologies) Tautologous Propositions Forms of Tautologies 2.WEEK 18 Categorical Syllogisms The learner… Formative: Categorical Syllogisms 1. M11GM-IIh-2: illustrates the different Recitation: What can you Validity of Categorical forms of conditional propositions. this concept will be applied to some real-life situations. say? Syllogisms Board work Rules in Establishing 2. By this concept. Summative: LAS 11 (Syllogisms) Symbolic Representation of 3. M11GM-IIi-1: illustrates different types of The Method of Induction tautologies and fallacies. M11GM-IIi-3: establishes the validity and Hypothetical Propositions falsity of real-life arguments using logical Forms of Conditional propositions. we will be guided on how to check if a given conclusion is valid or not. Insert 2nd Performance First Semester: Syllabus in General Mathematics | 10 . Quiz 2-6: Solve problems Propositions involving Syllogisms Symbolic Notation for 4. syllogisms and fallacies. M11GM-IIi-2: determines the validity of Validity categorical syllogisms. WEEK 19 The Method of Deduction The learner… Formative: Argument and Argument 1. M11GM-IIj-2: justifies mathematical and Summative: Direct Proof of Validity real life statements using the different Quiz 2-7: Solve problems methods of proof and disproof. Propositions Values: Life-long learning Syllogisms are statements which can be evaluated as true. M11GM-IIj-1: illustrates the different Recitation Forms methods of proof (direct and indirect) and Board work Truth Tables disproof (indirect and by counterexample). Whereas. involving the Method of The Method of Proof and Deduction and Fallacies Disproof 3. M11GM-IIg-2: symbolizes propositions. WEEK 20 2ND QUARTER EXAMINATION Prepared by Reviewed and Checked by Jeric Arrevado Brielene T. there are lots of things needed to be proven so as well the things that are being disproved. Nacpil Merliza B. Pingul First Semester: Syllabus in General Mathematics | 11 . David SHS STEM Coordinator Camille D. Informal Fallacies Fallacies of relevance Fallacies of presumption Fallacies of ambiguity Values: Respect In the real world. 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. Nacpil Lories D. Franco Brielene T.