376 CURRICULUM AND SYLLABUS for Classes XI & XII

Size: px
Start display at page:

Transcription

1 376 CURRICULUM AND SYLLABUS for Classes XI & XII MATHEMATICS CLASS - XI One Paper Time : 3 Hours 100 Marks Units Unitwise Weightage Marks Periods I. Sets Relations and Functions [9 marks] 1. Sets Relations and Functions Trigonometric Functions 16 9 II. Algebra [37 marks] 1. Comple Number Quadratic Equations and Linear Inequalities Permutations Combinations Mathematical Induction and 15 7 Binomial Theorem 3. Sequence and Series 9 16 III. Co-ordinate Geometry [13 marks] 1. Locus and Equation Straight Lines Circle Conic Section and Introduction to 7 13 Three-dimension Geometry IV. Calculus [6 marks] Limits and Derivatives 6 11 V. Mathematical Reasoning [3 marks] 3 5 VI. Statistics and Probability [1 marks] 1 Total = Unit-I: Sets Relations and Functions [9 marks] 1. Sets Sets and their representations Finite and infinite sets Empty set Equal sets Subsets Subsets of the set of real numbers especially intervals (with notations) Power sets Universal set Venn diagrams Complements of a set Operation on sets (union intersection and difference of sets).. Relations and Functions Ordered pairs Cartesian product of sets Number of elements in the Cartesian product of two finite sets. The product sets R R (or R ) and R R R (or R 3 ) where R is the set of real numbers. Relation from one set to another Domain and range of a relation. Function as a special kind of relation from one set to another. Domain Co domain and range of a function. Diagramatic (Pictorial) representation of a function. Real valued function of a real variable and their domain and range. Some specific functions and their

2 378 CURRICULUM AND SYLLABUS for Classes XI & XII graphs including constant identity polynomial rational modulus signum and greatest integer function. Sum difference product and quotients of real valued functions. 3. Trigonometric functions Positive and negative angles Measurement of angles Seagesemal system and circular system Conversion from one system to another. Definition of trigonometric functions with the help of unit circle. Signs of trigonometric functions (Quadrant Rule). The identity Sin +Cos =1. Graphs of trigonometric functions. To epress Cos (±y) and Sin( ±y) in terms of Sin Sin y Cos and Cos y. Deduction of other addition and subtraction formulae. To epress Sin ± Sin y and Cos ± Cos y as products. Identities related to multiple and submultiple angles. General solution of trigonometric equations. Sine and Cosine formulae in a triangle and their simple applications. Unit-II: Algebra [37 marks] 1. Comple numbers and Quadratic Equations. Need for comple numbers. The fundamental imaginary unit 1(or i). Comple numbers in the form of a + ib Real and imaginary parts of a comple number Comple conjugates Representation of a comple number by a point in a plane Argand diagram Modulus and argument (or amplitude) of a comple numberalgebra of comple numbers Triangle inequality Polar representation of a comple number. Statement of Fundamental Theorem of Algebra Solution of quadratic equation in the comple number system. Square root of a comple number Cube root of unity and their properties.. Linear Inequalities. Linear inequalities Algebraic solution of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Solution of system of linear inequalities in two variables - graphically. Inequalities involving modulus functions. 3. Premutations and Combinations. Fundamental principle of counting Factorial n where n is a non-negative integer Permutation as an arrangement Meaning of n P r or P( nr) Permutations in which things (i) may be repeated (ii) are not all different. Combination Meaning of n C r or C(nr). Important properties of n P r and n C r. Applications of permutations and combinations. 4. Mathematical Induction. Principles of Mathematical Induction and its applications. 5. Binomial Theorem. Bionomial theorem for a positive integral inde. Pascal's triangle General term Middle terms Equidistant terms properties of Binomial co-efficients Simple Applications. 6. Sequence and Series. Sequence and Series Arithmetic Progression (A.P.) Arithmetic Mean (A.M.) Insertion of arithmetic means between two numbers Geometric progression (G.P.) First term Common ratio general term sum to n terms of a G.P. Geometric Mean (G.M.) Insertion of geometric means between two numbers. Relation between A.M. and G.M. sum to n terms of special series n n and n 3. Unit-III: Coordinate Geometry [13 marks] 1. Locus and equation of a locus : Brief recall of D geometry from earlier classes. Shifting of origin. Locus and equation of a locus.. Straight lines : Slope of a line and angle between two lines various forms of equation of a straight line Parallel to aes slope-intercept form point-slope form two point form intercepts form and normal form. General equation of first degree in two variables represents a straight line. Reduction of the general equation of a line to different forms. System of lines passing through the point of intersection of two lines. Distance of a point from a line. 3. Circle : Definition Equation of circle with given centre and radius General equation of a circle its centre and radius. Equation of a circle when the end points of a diameter are given. Interior and eterior of a circle. 4. Conic section : Sections of a cone. Definition of a conic section. Equation of a conic section having given eccentricity focus and directri. Standard equation and simple properties of parabola ellipse and hyperbola. 5. Introduction to Three-dimentional Geometry : Coordinate aes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula. Unit-IV: Calculus [06 marks] Limits and derivatives : Idea of limit Left hand and right hand limits conditions for eistence of limit. Fundamental Theorem on limit (statement only) and standard limits (i) (i) n n a n 1 lim = na (with Proof) a a sin lim = 1(with Proof) 0 Derivative introduced as rate of change both as that of distance function and geometrically. Definition of derivative relate it to slope of tangent to a curve; Derivative of sum difference product and quotient of functions. Derivative of polynomial and trigonometric functions.

3 CURRICULUM AND SYLLABUS for Classes XI & XII CURRICULUM AND SYLLABUS for Classes XI & XII Unit-V: Mathematical Reasoning : [03 marks] Mathematically acceptable statements. Basic connecting words or phrases. Simple and compound statements. Truth tables. Understanding of and or implies implies by if and only if there eists for all and their use through variety of eamples related to Mathematics. Negation of a statement. Contra positive and converse of an implication. Validating statement involving connecting words. Checking the truth of a statement by method of contradiction. Unit-VI: Statistics and Probability [1 marks] 1. Statistics : Measure of dispersion Mean deviation Variance and Standard deviation of ungrouped/grouped data. Analysis of frequency distribution with equal means but different variances.. Probability : Random eperiment Outcomes sample spaces (set representation) Events occurrence of events not and & or events ehaustive events mutually eclusive events Aiomatic (set theoretic) probability connections with the theories of earlier classes. Probability of an event probability of not and & or events. Appendi : 1. Infinite series : Eponential and Logarithmic series.. Mathematical Modelling : Consolidating the understanding developed upto Class X. Focus on modelling problems related to real life (like environment travel etc.) and connecting with other subjects of study where many constraints may really need to be ignored formulating the model looking for solutions interpreting them in the problems situation and evaluating the model. PRESCRIBED TEXTBOOK : Frank Senior Secondary Mathematics for Class XI (As per latest syllabus of the Council). By : S.N. Chhibber G.D. Dhall & J.C. Nijhawan. Published by : Frank Bros. & Co. (Publishers) Ltd. New Delhi REFERENCE BOOKS : 1. Mathematics (Tetbook for Class XI) Published by : NCERT New Delhi. Modern s abc of Mathematics for Class XI By : J.P. Mohindru Published by : Modern Publishers Jalandhar. DESIGN QUESTION PAPER/UNIT TEST Subject : MATHEMATICS Class : XI Time : 3 Hours Full Marks : 100 I. WEIGHTAGE TO OBJECTIVES : Objectives K U A S Total Percentage of Marks 0 to to 55 6 to 18 0 to Marks 0 to to 55 6 to 18 0 to II. WEIGHTAGE TO FORM OF QUESTIONS : Forms of Questions E SA-I SA-II VSA O Total No. of Questions Marks Allotted Estimated Time (in Minutes) III. WEIGHTAGE TO CONTENT : Units Topics Marks Unit-I 1. Sets Relations and Functions 13. Trigonometric Functions 16 Unit-II 1. Comple numbers Quadratic equation and Linear Inequalities 13. Permutations and Combinations Mathematical Induction and Binomial Theorem Sequence and Series 9 Unit-III 1. Locus and equation Straight lines 6. Circle Conic section & Introduction to 3 Dimension Geometry 7 Unit-IV Limits and Derivatives 6 Unit-V Mathematical Reasoning 3 Unit-VI Statistics and Probability 1 Total : 100 IV. SCHEME OF SECTIONS : NIL V. SCHEME OF OPTIONS: Internal option in any two SA-I type and in any three Essay Type VI. DIFFICULTY LEVEL : Difficult : 15% marks Average : 50% marks Easy : 35% marks Abbreviation : K (Knowledge) U (Understanding) A (Application) S (Skill) E (Essay Type) SA (Short Answer Type) VSA (Very Short Answer Type) O (Objective Type)

4 CURRICULUM AND SYLLABUS for Classes XI & XII 381 MATHEMATICS CLASS - XII One Paper Time : 3 Hours 100 Marks Units Unitwise Weightage Marks Periods I. Relations and Functions [10 marks] 1. Relations and Functions 5 9. Inverse Trigonometric Functions 5 9 II. Algebra [13 marks] 1. Matrices Determinants 6 11 III. Calculus [44 marks] 1. Continuity and Differentiability Applications of Derivatives Integrals Applications of Integrals Differential Equations 8 14 IV. Vectors and Three Dimensional Geometry [17 marks] 1. Vectors Three dimensional Geometry 9 16 V. Linear Programming [06 marks] 6 11 VI. Probability [10 marks] Total : Unit-I: Relations and Functions [10 marks] 1. Relations and Functions : Relation in a set. Types of relations refleive symmetric transitive and equivalence relations. Types of functions injective (one-one) subjective (onto) bijective functions. Inverse of a function Composite of functions. Binary operations.. Inverse Trigonometric Functions : Definition range domain principal value branches. Graphs of inverse trigonometric functions Elementary properties of inverse trigonometric functions. Unit-II: Algebra [13 marks] Matrices : Concept notation order equality types of matrices zero-matri transpose of a matri symmetric and skew symmetric matrices. Addition multiplication and scalar multiplication of matrices simple properties of addition multiplication and scalar multiplication. Non-commutativity of multiplication of matrices and eistence of nonzero matrices whose product is the zero matri (restrict to square matrices of order ) Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse if it eists : (Here all matrices will have real entries). Determinants : Determinant of a square matri (upto 33 matrices) properties of determinants minors cofactors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matri. Consistency inconsistency and number of solutions of system of linear equations by eamples solving system of linear equations in two or three variables (having unique solution) using inverse of a matri. Cramer s Rule and its applications. Unit-III: Calculus [44 marks] 1. Continuity and Differentiability : Continuity and differentiability derivative of composite functions chain rule derivatives of inverse trigonometric functions derivative of implicit function. Concept of eponential and logarithmic functions and their derivatives. Logarithmic functions as inverse of eponential functions log(1+ ) e 1 lim lim lim 1 + lim 1 + lim lim Logarithmic differentiation. Derivative of functions epressed in parametric forms. Second order derivatives. Rolle s and Lagrange s Mean Value Theorems (without proof) and their geometric interpretations and simple applications.. Applications of Derivatives : Applications of derivatives : rate of change increasing/decreasing functions tangents & normals approimation maima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations). 3. Integrals : Integration as inverse process of differentiation. Integration of a variety of functions by substitution by partial fractions and by parts only simple integrals of the type ± + + a ± a a a b c a + b+ c

5 CURRICULUM AND SYLLABUS for Classes XI & XII CURRICULUM AND SYLLABUS for Classes XI & XII + ( p q) a + b+ c ( p+ q) a + b+ c a ± and a a + b+ c ( p+ q) a + b+ c a+ b cos a+ to be evaluated. b sin Definite integrals as a limit of a sum. Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals. 4. Applications of Integrals : Application in finding the area under simple curves especially lines areas of circles parabolas/ellipses (in standard form only) area under the curves y = sin y = cos etc. area between the two above said curves (the region should be clearly identifiable). 5. Differential Equations : Definition order and degree general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables homogeneous differential equations of first order and first degree. Solutions of linear differential equations of the type : dy + p()y = q() where p() and q() are functions of and dy + p(y) = q(y) where p(y) and q(y) are functions of y. Unit-IV: Vectors and Three dimensional Geometry [17 marks] 1. Vectors Vectors and scalars magnitude and direction of a vector. Direction cosines/ ratios of vectors. Types of vectors (equal unit zero parallel and collinear vectors) position vector of a point negative of a vector components of a vector addition of vectors multiplication of a vector by a scalar position vector of a point dividing a line segment in a given ratio. Scalar (dot) product of vectors projection of a vector on a line. Vector (cross) product of vectors. Scalar triple product.. Three-dinensional Geometry : Orthogonal Projection Projection of a point on a line/plane. Direction cosines direction ratios; Projection of the joint of two given points on a line. Cartesian and Vector equation of a line Coplanar lines Skew lines Shortest distance between two lines. Cartesian and Vector equation of a plane. Angle between (i) two lines (ii) two planes (iii) a line and a plane. Conditions for perpendicularity and parallelism. Distance of a point from a plane. Unit-V: Linear Programming [6 marks] 1. Linear Programming : Introduction definition of related terminology such as constraints objective function optimization different types of linear programming (L.P.) problems mathematical formulation of L.P. problems graphical method of solution of problems in two variables feasible and infeasible regions feasible and infeasible solutions optimal feasible solutions (upto three non-trivial constraints). Unit-VI: Probability [10 marks] Appendi : 1. Probability : Multiplication theorem on probability Conditional probability independent events total probability Baye s theorem. Random variable and its probability distribution mean and variance of random variable. Repeated independent (Bernoulli) trails and Binomial distribution. 1. Proofs in Mathematics : Through a variety of eamples related to mathematics & already familiar to the learner bring out different kinds of proofs : direct contrapositive by contradiction by counter eample.. Mathematical Modelling : Modelling real-life problems where many constraints may really need to be ignored (continuing from Class XI). However now the models concerned would use techniques/results of matrices calculus and linear programming. PRESCRIBED TEXTBOOK : Frank Senior Secondary Mathematics for Class XII (As per latest syllabus of the Council). By : S.N. Chhibber G.D. Dhall & J.C. Nijhawan. Published by : Frank Bros. & Co. (Publishers) Ltd. New Delhi REFERENCE BOOKS : 1. Mathematics Part I & II (Tetbook for Class XII) Published by : NCERT New Delhi. Modern s abc of Mathematics for Class XII By : J.P. Mohindru Published by : Modern Publishers Jalandhar.

6 CURRICULUM AND SYLLABUS for Classes XI & XII 385 DESIGN QUESTION PAPER/UNIT TEST Subject : MATHEMATICS Class : XII Time : 3 Hours Full Marks : 100 I. WEIGHTAGE TO OBJECTIVES : Objectives K U A S Total Percentage of Marks 0 to to 55 6 to 18 0 to Marks 0 to to 55 6 to 18 0 to II. WEIGHTAGE TO FORM OF QUESTIONS : Forms of Questions E SA-I SA-II VSA O Total No. of Questions Marks Allotted Estimated Time (in Minutes) III. WEIGHTAGE TO CONTENT : Units Topics Marks Unit-I 1.1 Relations and Functions 5 1. Inverse Trigonometric functions 5 Unit-II.1 Matrices 7. Determinants 6 Unit-III 3.1 Continuity and Differentiability Applications of derivatives Integrals Applications of Integrals Differential Equations 8 Unit-IV 4.1 Vectors 8 4. Three-dimentional Geometry 9 Unit-V 5.1 Linear Programming 6 Unit-VI 6.1 Probability 10 Total : 100 IV. SCHEME OF SECTIONS : NIL V. SCHEME OF OPTIONS:Internal option in any two SA-I type and in any three Essay Type VI. DIFFICULTY LEVEL : Difficult : 15% marks Average : 50% marks Easy : 35% marks Abbreviation : K (Knowledge) U (Understanding) A (Application) S (Skill) E (Essay Type) SA (Short Answer Type) VSA (Very Short Answer Type) O (Objective Type)

Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks

Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks Welcome to Thinkwell s Homeschool Precalculus! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson

Algebra 2 Chapter 1 Vocabulary. identity - A statement that equates two equivalent expressions.

Chapter 1 Vocabulary identity - A statement that equates two equivalent expressions. verbal model- A word equation that represents a real-life problem. algebraic expression - An expression with variables.

MATH BOOK OF PROBLEMS SERIES. New from Pearson Custom Publishing!

MATH BOOK OF PROBLEMS SERIES New from Pearson Custom Publishing! The Math Book of Problems Series is a database of math problems for the following courses: Pre-algebra Algebra Pre-calculus Calculus Statistics

Precalculus REVERSE CORRELATION. Content Expectations for. Precalculus. Michigan CONTENT EXPECTATIONS FOR PRECALCULUS CHAPTER/LESSON TITLES

Content Expectations for Precalculus Michigan Precalculus 2011 REVERSE CORRELATION CHAPTER/LESSON TITLES Chapter 0 Preparing for Precalculus 0-1 Sets There are no state-mandated Precalculus 0-2 Operations

South Carolina College- and Career-Ready (SCCCR) Pre-Calculus

South Carolina College- and Career-Ready (SCCCR) Pre-Calculus Key Concepts Arithmetic with Polynomials and Rational Expressions PC.AAPR.2 PC.AAPR.3 PC.AAPR.4 PC.AAPR.5 PC.AAPR.6 PC.AAPR.7 Standards Know

Estimated Pre Calculus Pacing Timeline

Estimated Pre Calculus Pacing Timeline 2010-2011 School Year The timeframes listed on this calendar are estimates based on a fifty-minute class period. You may need to adjust some of them from time to

Appendix 3 IB Diploma Programme Course Outlines

Appendix 3 IB Diploma Programme Course Outlines The following points should be addressed when preparing course outlines for each IB Diploma Programme subject to be taught. Please be sure to use IBO nomenclature

NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS

NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS TEST DESIGN AND FRAMEWORK September 2014 Authorized for Distribution by the New York State Education Department This test design and framework document

Higher Education Math Placement

Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication

Accelerated Mathematics 3 This is a course in precalculus and statistics, designed to prepare students to take AB or BC Advanced Placement Calculus. It includes rational, circular trigonometric, and inverse

How To Understand And Solve A Linear Programming Problem

At the end of the lesson, you should be able to: Chapter 2: Systems of Linear Equations and Matrices: 2.1: Solutions of Linear Systems by the Echelon Method Define linear systems, unique solution, inconsistent,

Algebra and Geometry Review (61 topics, no due date)

Course Name: Math 112 Credit Exam LA Tech University Course Code: ALEKS Course: Trigonometry Instructor: Course Dates: Course Content: 159 topics Algebra and Geometry Review (61 topics, no due date) Properties

Prentice Hall Algebra 2 2011 Correlated to: Colorado P-12 Academic Standards for High School Mathematics, Adopted 12/2009

Content Area: Mathematics Grade Level Expectations: High School Standard: Number Sense, Properties, and Operations Understand the structure and properties of our number system. At their most basic level

Algebra 1 Course Title

Algebra 1 Course Title Course- wide 1. What patterns and methods are being used? Course- wide 1. Students will be adept at solving and graphing linear and quadratic equations 2. Students will be adept

Prentice Hall Mathematics: Algebra 2 2007 Correlated to: Utah Core Curriculum for Math, Intermediate Algebra (Secondary)

Core Standards of the Course Standard 1 Students will acquire number sense and perform operations with real and complex numbers. Objective 1.1 Compute fluently and make reasonable estimates. 1. Simplify

MATH. ALGEBRA I HONORS 9 th Grade 12003200 ALGEBRA I HONORS

* Students who scored a Level 3 or above on the Florida Assessment Test Math Florida Standards (FSA-MAFS) are strongly encouraged to make Advanced Placement and/or dual enrollment courses their first choices

MEMORANDUM. All students taking the CLC Math Placement Exam PLACEMENT INTO CALCULUS AND ANALYTIC GEOMETRY I, MTH 145:

MEMORANDUM To: All students taking the CLC Math Placement Eam From: CLC Mathematics Department Subject: What to epect on the Placement Eam Date: April 0 Placement into MTH 45 Solutions This memo is an

KEANSBURG SCHOOL DISTRICT KEANSBURG HIGH SCHOOL Mathematics Department. HSPA 10 Curriculum. September 2007

KEANSBURG HIGH SCHOOL Mathematics Department HSPA 10 Curriculum September 2007 Written by: Karen Egan Mathematics Supervisor: Ann Gagliardi 7 days Sample and Display Data (Chapter 1 pp. 4-47) Surveys and

PYTHAGOREAN TRIPLES KEITH CONRAD 1. Introduction A Pythagorean triple is a triple of positive integers (a, b, c) where a + b = c. Examples include (3, 4, 5), (5, 1, 13), and (8, 15, 17). Below is an ancient

Biggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress

Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation

Mathematics (MAT) MAT 061 Basic Euclidean Geometry 3 Hours. MAT 051 Pre-Algebra 4 Hours

MAT 051 Pre-Algebra Mathematics (MAT) MAT 051 is designed as a review of the basic operations of arithmetic and an introduction to algebra. The student must earn a grade of C or in order to enroll in MAT

DRAFT. Further mathematics. GCE AS and A level subject content

Further mathematics GCE AS and A level subject content July 2014 s Introduction Purpose Aims and objectives Subject content Structure Background knowledge Overarching themes Use of technology Detailed

Core Maths C2. Revision Notes

Core Maths C Revision Notes November 0 Core Maths C Algebra... Polnomials: +,,,.... Factorising... Long division... Remainder theorem... Factor theorem... 4 Choosing a suitable factor... 5 Cubic equations...

COURSE SYLLABUS Pre-Calculus A/B Last Modified: April 2015 Course Description: In this year-long Pre-Calculus course, students will cover topics over a two semester period (as designated by A and B sections).

Review of Intermediate Algebra Content

Review of Intermediate Algebra Content Table of Contents Page Factoring GCF and Trinomials of the Form + b + c... Factoring Trinomials of the Form a + b + c... Factoring Perfect Square Trinomials... 6

Polynomial Degree and Finite Differences

CONDENSED LESSON 7.1 Polynomial Degree and Finite Differences In this lesson you will learn the terminology associated with polynomials use the finite differences method to determine the degree of a polynomial

Algebra 2 Year-at-a-Glance Leander ISD 2007-08. 1st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks

Algebra 2 Year-at-a-Glance Leander ISD 2007-08 1st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks Essential Unit of Study 6 weeks 3 weeks 3 weeks 6 weeks 3 weeks 3 weeks

Essential Mathematics for Computer Graphics fast

John Vince Essential Mathematics for Computer Graphics fast Springer Contents 1. MATHEMATICS 1 Is mathematics difficult? 3 Who should read this book? 4 Aims and objectives of this book 4 Assumptions made

Math Course Descriptions & Student Learning Outcomes

Math Course Descriptions & Student Learning Outcomes Table of Contents MAC 100: Business Math... 1 MAC 101: Technical Math... 3 MA 090: Basic Math... 4 MA 095: Introductory Algebra... 5 MA 098: Intermediate

UNIVERSITY OF PUNE, PUNE 411007. BOARD OF STUDIES IN MATHEMATICS SYLLABUS

UNIVERSITY OF PUNE, PUNE 411007. BOARD OF STUDIES IN MATHEMATICS SYLLABUS F.Y.B.Sc (MATHEMATICS) PAPER 1 ALGEBRA AND GEOMETRY FIRST TERM 1) Sets (4 Lectures) 1.1 Power set of a set, Product of two sets.

04 Mathematics CO-SG-FLD004-03. Program for Licensing Assessments for Colorado Educators

04 Mathematics CO-SG-FLD004-03 Program for Licensing Assessments for Colorado Educators Readers should be advised that this study guide, including many of the excerpts used herein, is protected by federal

Content. Chapter 4 Functions 61 4.1 Basic concepts on real functions 62. Credits 11

Content Credits 11 Chapter 1 Arithmetic Refresher 13 1.1 Algebra 14 Real Numbers 14 Real Polynomials 19 1.2 Equations in one variable 21 Linear Equations 21 Quadratic Equations 22 1.3 Exercises 28 Chapter

Sequence of Mathematics Courses

Sequence of ematics Courses Where do I begin? Associates Degree and Non-transferable Courses (For math course below pre-algebra, see the Learning Skills section of the catalog) MATH M09 PRE-ALGEBRA 3 UNITS

Math Placement Test Study Guide. 2. The test consists entirely of multiple choice questions, each with five choices.

Math Placement Test Study Guide General Characteristics of the Test 1. All items are to be completed by all students. The items are roughly ordered from elementary to advanced. The expectation is that

POLYNOMIAL FUNCTIONS

POLYNOMIAL FUNCTIONS Polynomial Division.. 314 The Rational Zero Test.....317 Descarte s Rule of Signs... 319 The Remainder Theorem.....31 Finding all Zeros of a Polynomial Function.......33 Writing a

Indiana State Core Curriculum Standards updated 2009 Algebra I

Indiana State Core Curriculum Standards updated 2009 Algebra I Strand Description Boardworks High School Algebra presentations Operations With Real Numbers Linear Equations and A1.1 Students simplify and

Mathematics 31 Pre-calculus and Limits

Mathematics 31 Pre-calculus and Limits Overview After completing this section, students will be epected to have acquired reliability and fluency in the algebraic skills of factoring, operations with radicals

Expression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds

Isosceles Triangle Congruent Leg Side Expression Equation Polynomial Monomial Radical Square Root Check Times Itself Function Relation One Domain Range Area Volume Surface Space Length Width Quantitative

PRE-CALCULUS GRADE 12 [C] Communication Trigonometry General Outcome: Develop trigonometric reasoning. A1. Demonstrate an understanding of angles in standard position, expressed in degrees and radians.

Trigonometric Functions and Equations

Contents Trigonometric Functions and Equations Lesson 1 Reasoning with Trigonometric Functions Investigations 1 Proving Trigonometric Identities... 271 2 Sum and Difference Identities... 276 3 Extending

GEOMETRY CONCEPT MAP. Suggested Sequence:

CONCEPT MAP GEOMETRY August 2011 Suggested Sequence: 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons

How To Understand And Solve Algebraic Equations

College Algebra Course Text Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGraw-Hill, 2008, ISBN: 978-0-07-286738-1 Course Description This course provides

9 Multiplication of Vectors: The Scalar or Dot Product

Arkansas Tech University MATH 934: Calculus III Dr. Marcel B Finan 9 Multiplication of Vectors: The Scalar or Dot Product Up to this point we have defined what vectors are and discussed basic notation

Vocabulary Words and Definitions for Algebra

Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms

The program also provides supplemental modules on topics in geometry and probability and statistics.

Algebra 1 Course Overview Students develop algebraic fluency by learning the skills needed to solve equations and perform important manipulations with numbers, variables, equations, and inequalities. Students

HIGH SCHOOL: GEOMETRY (Page 1 of 4)

HIGH SCHOOL: GEOMETRY (Page 1 of 4) Geometry is a complete college preparatory course of plane and solid geometry. It is recommended that there be a strand of algebra review woven throughout the course

MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education)

MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,

Mean value theorem, Taylors Theorem, Maxima and Minima.

MA 001 Preparatory Mathematics I. Complex numbers as ordered pairs. Argand s diagram. Triangle inequality. De Moivre s Theorem. Algebra: Quadratic equations and express-ions. Permutations and Combinations.

Prerequisites: TSI Math Complete and high school Algebra II and geometry or MATH 0303.

Course Syllabus Math 1314 College Algebra Revision Date: 8-21-15 Catalog Description: In-depth study and applications of polynomial, rational, radical, exponential and logarithmic functions, and systems

GRADES 7, 8, AND 9 BIG IDEAS

Table 1: Strand A: BIG IDEAS: MATH: NUMBER Introduce perfect squares, square roots, and all applications Introduce rational numbers (positive and negative) Introduce the meaning of negative exponents for

Extra Credit Assignment Lesson plan. The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam.

Extra Credit Assignment Lesson plan The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam. The extra credit assignment is to create a typed up lesson

Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express

Big Ideas in Mathematics

Big Ideas in Mathematics which are important to all mathematics learning. (Adapted from the NCTM Curriculum Focal Points, 2006) The Mathematics Big Ideas are organized using the PA Mathematics Standards

Mathematics Georgia Performance Standards

Mathematics Georgia Performance Standards K-12 Mathematics Introduction The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by

Alabama Department of Postsecondary Education

Date Adopted 1998 Dates reviewed 2007, 2011, 2013 Dates revised 2004, 2008, 2011, 2013, 2015 Alabama Department of Postsecondary Education Representing Alabama s Public Two-Year College System Jefferson

Algebra I Vocabulary Cards

Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression

The Australian Curriculum Mathematics

The Australian Curriculum Mathematics Mathematics ACARA The Australian Curriculum Number Algebra Number place value Fractions decimals Real numbers Foundation Year Year 1 Year 2 Year 3 Year 4 Year 5 Year

Birmingham City Schools

Activity 1 Classroom Rules & Regulations Policies & Procedures Course Curriculum / Syllabus LTF Activity: Interval Notation (Precal) 2 Pre-Assessment 3 & 4 1.2 Functions and Their Properties 5 LTF Activity:

CRLS Mathematics Department Algebra I Curriculum Map/Pacing Guide

Curriculum Map/Pacing Guide page 1 of 14 Quarter I start (CP & HN) 170 96 Unit 1: Number Sense and Operations 24 11 Totals Always Include 2 blocks for Review & Test Operating with Real Numbers: How are

North Carolina Math 2

Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4.

Mathematics Pre-Test Sample Questions A. { 11, 7} B. { 7,0,7} C. { 7, 7} D. { 11, 11}

Mathematics Pre-Test Sample Questions 1. Which of the following sets is closed under division? I. {½, 1,, 4} II. {-1, 1} III. {-1, 0, 1} A. I only B. II only C. III only D. I and II. Which of the following

Advanced Math Study Guide Topic Finding Triangle Area (Ls. 96) using A=½ bc sin A (uses Law of Sines, Law of Cosines) Law of Cosines, Law of Cosines (Ls. 81, Ls. 72) Finding Area & Perimeters of Regular

Math 241, Exam 1 Information.

Math 241, Exam 1 Information. 9/24/12, LC 310, 11:15-12:05. Exam 1 will be based on: Sections 12.1-12.5, 14.1-14.3. The corresponding assigned homework problems (see http://www.math.sc.edu/ boylan/sccourses/241fa12/241.html)

Section 1: How will you be tested? This section will give you information about the different types of examination papers that are available.

REVISION CHECKLIST for IGCSE Mathematics 0580 A guide for students How to use this guide This guide describes what topics and skills you need to know for your IGCSE Mathematics examination. It will help

Mathematics Review for MS Finance Students

Mathematics Review for MS Finance Students Anthony M. Marino Department of Finance and Business Economics Marshall School of Business Lecture 1: Introductory Material Sets The Real Number System Functions,

FOREWORD. Executive Secretary

FOREWORD The Botswana Examinations Council is pleased to authorise the publication of the revised assessment procedures for the Junior Certificate Examination programme. According to the Revised National

BookTOC.txt. 1. Functions, Graphs, and Models. Algebra Toolbox. Sets. The Real Numbers. Inequalities and Intervals on the Real Number Line

College Algebra in Context with Applications for the Managerial, Life, and Social Sciences, 3rd Edition Ronald J. Harshbarger, University of South Carolina - Beaufort Lisa S. Yocco, Georgia Southern University

Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.

Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used

PCHS ALGEBRA PLACEMENT TEST

MATHEMATICS Students must pass all math courses with a C or better to advance to the next math level. Only classes passed with a C or better will count towards meeting college entrance requirements. If

Geometry. Higher Mathematics Courses 69. Geometry

The fundamental purpose of the course is to formalize and extend students geometric experiences from the middle grades. This course includes standards from the conceptual categories of and Statistics and

Mathematics Course 111: Algebra I Part IV: Vector Spaces

Mathematics Course 111: Algebra I Part IV: Vector Spaces D. R. Wilkins Academic Year 1996-7 9 Vector Spaces A vector space over some field K is an algebraic structure consisting of a set V on which are

Understanding Basic Calculus

Understanding Basic Calculus S.K. Chung Dedicated to all the people who have helped me in my life. i Preface This book is a revised and expanded version of the lecture notes for Basic Calculus and other

Current Standard: Mathematical Concepts and Applications Shape, Space, and Measurement- Primary

Shape, Space, and Measurement- Primary A student shall apply concepts of shape, space, and measurement to solve problems involving two- and three-dimensional shapes by demonstrating an understanding of:

APPLIED MATHEMATICS ADVANCED LEVEL INTRODUCTION This syllabus serves to examine candidates knowledge and skills in introductory mathematical and statistical methods, and their applications. For applications

Dear Accelerated Pre-Calculus Student:

Dear Accelerated Pre-Calculus Student: I am very excited that you have decided to take this course in the upcoming school year! This is a fastpaced, college-preparatory mathematics course that will also

Curriculum Map by Block Geometry Mapping for Math Block Testing 2007-2008. August 20 to August 24 Review concepts from previous grades.

Curriculum Map by Geometry Mapping for Math Testing 2007-2008 Pre- s 1 August 20 to August 24 Review concepts from previous grades. August 27 to September 28 (Assessment to be completed by September 28)

Core Maths C1. Revision Notes

Core Maths C Revision Notes November 0 Core Maths C Algebra... Indices... Rules of indices... Surds... 4 Simplifying surds... 4 Rationalising the denominator... 4 Quadratic functions... 4 Completing the

TSI College Level Math Practice Test

TSI College Level Math Practice Test Tutorial Services Mission del Paso Campus. Factor the Following Polynomials 4 a. 6 8 b. c. 7 d. ab + a + b + 6 e. 9 f. 6 9. Perform the indicated operation a. ( +7y)

Algebra Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the 2012-13 school year.

This document is designed to help North Carolina educators teach the Common Core (Standard Course of Study). NCDPI staff are continually updating and improving these tools to better serve teachers. Algebra

COLLEGE ALGEBRA LEARNING COMMUNITY

COLLEGE ALGEBRA LEARNING COMMUNITY Tulsa Community College, West Campus Presenter Lori Mayberry, B.S., M.S. Associate Professor of Mathematics and Physics lmayberr@tulsacc.edu NACEP National Conference

In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data.

MATHEMATICS: THE LEVEL DESCRIPTIONS In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. Attainment target

Algebra II. Weeks 1-3 TEKS

Algebra II Pacing Guide Weeks 1-3: Equations and Inequalities: Solve Linear Equations, Solve Linear Inequalities, Solve Absolute Value Equations and Inequalities. Weeks 4-6: Linear Equations and Functions:

DEFINITION 5.1.1 A complex number is a matrix of the form. x y. , y x

Chapter 5 COMPLEX NUMBERS 5.1 Constructing the complex numbers One way of introducing the field C of complex numbers is via the arithmetic of matrices. DEFINITION 5.1.1 A complex number is a matrix of

Algebra II and Trigonometry

Algebra II and Trigonometry Textbooks: Algebra 2: California Publisher: McDougal Li@ell/Houghton Mifflin (2006 EdiHon) ISBN- 13: 978-0618811816 Course descriphon: Algebra II complements and expands the

JUST THE MATHS UNIT NUMBER 8.5. VECTORS 5 (Vector equations of straight lines) A.J.Hobson

JUST THE MATHS UNIT NUMBER 8.5 VECTORS 5 (Vector equations of straight lines) by A.J.Hobson 8.5.1 Introduction 8.5. The straight line passing through a given point and parallel to a given vector 8.5.3

MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab

MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab MATH 0110 is established to accommodate students desiring non-course based remediation in developmental mathematics. This structure will

AMSCO S Ann Xavier Gantert

AMSCO S Integrated ALGEBRA 1 Ann Xavier Gantert AMSCO SCHOOL PUBLICATIONS, INC. 315 HUDSON STREET, NEW YORK, N.Y. 10013 Dedication This book is dedicated to Edward Keenan who left a profound influence

MATRIX ALGEBRA AND SYSTEMS OF EQUATIONS. + + x 2. x n. a 11 a 12 a 1n b 1 a 21 a 22 a 2n b 2 a 31 a 32 a 3n b 3. a m1 a m2 a mn b m

MATRIX ALGEBRA AND SYSTEMS OF EQUATIONS 1. SYSTEMS OF EQUATIONS AND MATRICES 1.1. Representation of a linear system. The general system of m equations in n unknowns can be written a 11 x 1 + a 12 x 2 +

SAT Subject Math Level 2 Facts & Formulas

Numbers, Sequences, Factors Integers:..., -3, -2, -1, 0, 1, 2, 3,... Reals: integers plus fractions, decimals, and irrationals ( 2, 3, π, etc.) Order Of Operations: Arithmetic Sequences: PEMDAS (Parentheses

Mathematics. GCSE subject content and assessment objectives

Mathematics GCSE subject content and assessment objectives June 2013 Contents Introduction 3 Subject content 4 Assessment objectives 11 Appendix: Mathematical formulae 12 2 Introduction GCSE subject criteria

National 5 Mathematics Course Assessment Specification (C747 75)

National 5 Mathematics Course Assessment Specification (C747 75) Valid from August 013 First edition: April 01 Revised: June 013, version 1.1 This specification may be reproduced in whole or in part for

Common Core Unit Summary Grades 6 to 8

Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity- 8G1-8G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations

x(x + 5) x 2 25 (x + 5)(x 5) = x 6(x 4) x ( x 4) + 3

CORE 4 Summary Notes Rational Expressions Factorise all expressions where possible Cancel any factors common to the numerator and denominator x + 5x x(x + 5) x 5 (x + 5)(x 5) x x 5 To add or subtract -

Gymnázium, Brno, Slovanské nám. 7, SCHEME OF WORK Mathematics SCHEME OF WORK. http://agb.gymnaslo. cz

SCHEME OF WORK Subject: Mathematics Year: Third grade, 3.X School year:../ List of topics Topics Time period 1. Revision (functions, plane geometry) September 2. Constructive geometry in the plane October

X On record with the USOE.

Textbook Alignment to the Utah Core Algebra 2 Name of Company and Individual Conducting Alignment: Chris McHugh, McHugh Inc. A Credential Sheet has been completed on the above company/evaluator and is

Section 1.1. Introduction to R n

The Calculus of Functions of Several Variables Section. Introduction to R n Calculus is the study of functional relationships and how related quantities change with each other. In your first exposure to

THREE DIMENSIONAL GEOMETRY

Chapter 8 THREE DIMENSIONAL GEOMETRY 8.1 Introduction In this chapter we present a vector algebra approach to three dimensional geometry. The aim is to present standard properties of lines and planes,