# Virtual University of Pakistan

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## MTH100 : General Mathematics

### Course Overview

#### Course Synopsis

This course contents are: Sets, Real Numbers , Complex Numbers, Functions, Quadratic Functions, Matrices, Inverse of a Matrix, Determinants, Arithmetic Progression and Arithmetic Series, Geometric progression and Geometric Series, Permutations and Combinations, Binomial theorem, Graphs and Functions, Straight Lines and Circles, Trigonometry, Statistics Introduction, Introduction to data, Frequency Distributions, Graphical representation of data, Measures Of Central Tendency, Range, inter quartile deviation mean deviation, Moments, Skewness and kurtosis.

#### Course Learning Outcomes

By the end of the course, students should be able to learn:

• Define sets, representation of sets, operations on sets.
• Natural Numbers, Integers, Rational Numbers, Irrational Numbers, Real Numbers. Properties of Real Numbers
• Need for complex numbers, definition of complex numbers, properties of complex numbers
• Definition of a function, types of functions, domain and range of a function, composition of functions, inverse functions
• Solution of quadratic equations, completing the square and quadratic formula, nature of the roots, equations reducible to quadratic equations
• Definition of a matrix, types of matrices, operations on matrices,Inverses, solving systems of equations using inverses,Definition of determinants, cofactors, evaluation of second and third order determinants, properties of determinants, Cramer’s Rule
• sequences. Arithmetic sequences, common difference and nth term. Sum of an arithmetic series. Applications, Geometric sequences, common ratio and nth term. Finite sum of a geometric series. Sum of an infinite geometric series. Applications
• Factorial notation. Permutations. Combinations. Applications.
• Binomial forms. Binomial theorem and the binomial formula.
• Basic concepts. Cartesian Coordinates. Use of symmetry, Distance formula ,Equation of a straight line, slopes and intercepts. Graphs of straight lines. Equation of a circle.,
• Radians and Degrees. Basic trigonometric functions – sine, cosine, tangent, secant, cosecant and cotangent - and their graphs. Inverse trigonometric functions. Solving trigonometric equations. Addition formulas. Double Angle formulas, trigonometric identities.Addition formulas. Double Angle formulas, trigonometric identities.
• Definition of statistics. Descriptive and Inferential statistics. Population and Sample. Limitations of statistics, Meaning of data. Types of data. Summation notation. Quantitative and qualitative data. Discrete and Continuous data. Types of intervals, Types of frequency distributions. Class intervals, class boundaries, class midpoints, frequencies, relative frequencies, Bar charts, histograms, frequency polygons, cumulative frequency polygon. Symmetry and skewness. Percentile, deciles and quartiles

#### Course Calendar

 Topic Lecture Resource Page Sets and Numbering Systems 1 Handouts 1-5 Sets and Numbering Systems 2 Handouts 1-5 Sets and Numbering Systems 3 Handouts 1-5 Function and Quadratics 4 Handouts 6-12 Function and Quadratics 5 Handouts 6-12 Function and Quadratics 6 Handouts 6-12 Function and Quadratics 7 Handouts 6-12 Assignment # 1 (Lecture 1 to Lecture 7) Matrices and Determinants 8 Handouts 13-21 Matrices and Determinants 9 Handouts 13-21 Matrices and Determinants 10 Handouts 13-21 Matrices and Determinants 11 Handouts 13-21 Matrices and Determinants 12 Handouts 13-21 Sequence and Series 13 Handouts 22-23 Sequence and Series 14 Handouts 22-23 Sequence and Series 15 Handouts 22-23 Quiz # 1 (From Lec 8 to Lec 12) Review of Sets 16 Handouts 1-5 Review of Functions 17 Handouts 6-12 Review of Matrices 18 Handouts 13-21 Quiz # 2 (From lec 13 to lec 15) Permutations 19 Handouts 24-25 Combinations 20 Handouts 24-25 Binomial theorem 21 Handouts 26-27 Coordinate Geometry 22 Handouts 28-30 Mid Term Examination Coordinate Geometry 23 Handouts 28-30 Coordinate Geometry and Trigonometry 24 Handouts 28-30 Trigonometry 25 Handouts 31-42 Trigonometry 26 Handouts 31-42 Trigonometry 27 Handouts 31-42 Trigonometry 28 Handouts 31-42 Trigonometry 29 Handouts 31-42 Trigonometry 30 Handouts 31-42 Assignment # 2 (Lecture 23 to Lecture 30) Review of Sequence and Series 31 Handouts 22-23 Review of Permutation and Combination, Binomial Theorem 32 Handouts 24-25 Review of Binomial Theorem, Coordinate Geometry 33 Handouts 26-27 Quiz # 3 (From Lec 23 to Lec 30) Review of Coordinate Geometry, Trigonometry 34 Handouts 28-30 Statistics 35 Handouts 43-46 Statistics 36 Handouts 43-46 Representation of Data 37 Handouts 47-51 Measures of Central Tendency 38 Handouts 52-55 Measures of Central Tendency 39 Handouts 52-55 Measures of Central Tendency and Measures of Dispersion 40 Handouts 56-62 Measures of Dispersion 41 Handouts 56-62 Measures of Dispersion 42 Handouts 56-62 Quiz#4(Lecture 35 to Lecture40) Skewness and Kurtosis 43 Handouts 63-67 Skewness and Kurtosis 44 Handouts 63-67 Probability Concepts 45 Handouts 68-69 Final Examination