## Applied Mathematics Class 11 Syllabus

There are eight units – (i) Numbers, Quantification and Numerical Applications, (ii) Algebra, (iii) Mathematical Reasoning, (iv) Calculus, (v) Probability, (vi) Descriptive Statistics, (vii) Basics of Financial Mathematics, and (viii) Coordinate Geometry.

### Course Structure

S.No. | Unit | Marks |

I | Numbers, Quantification and Numerical Applications | 9 |

II | Algebra | 10 |

III | Mathematical Reasoning | 6 |

IV | Calculus | 10 |

V | Probability | 10 |

VI | Descriptive Statistics | 12 |

VII | Basics of Financial Mathematics | 18 |

VIII | Coordinate Geometry | 5 |

Total | 80 |

### Unit I: Numbers, Quantification and Numerical Applications

- Prime Numbers, Encryptions using Prime Numbers
- Binary Numbers
- Complex Numbers (Preliminary idea only)
- Indices, Logarithm and Antilogarithm
- Laws and properties of logarithms
- Simple applications of logarithm and antilogarithm
- Numerical problems on averages, calendar, clock, time, work and distance, mensuration, seating arrangement

### Unit II: Algebra

- Sets
- Types of sets
- Venn diagram
- De Morgan’s laws
- Problem solving using Venn diagram
- Relations and types of relations
- Introduction of Sequences, Series
- Arithmetic and Geometric progression
- Relationship between AM and GM
- Basic concepts of Permutations and Combinations
- Permutations, Circular Permutations, Permutations with restrictions
- Combinations with standard results

### Unit III: Mathematical and Logical Reasoning

- Mathematically acceptable statements
- Connecting words/ phrases in Mathematical statement consolidating the understanding of “if and only if (necessary and sufficient) condition”, “implies”, “and/or”, “implied by”, “and”, “or”, “there exists” and their use through variety of examples related to real life and Mathematics
- Problems based on logical reasoning (coding-decoding, odd man out, blood relation, syllogism etc)

### Unit IV: Calculus

- Introducing functions
- Domain and Range of a function
- Types of functions (Polynomial function; Rational function; Composite function; Logarithm function; Exponential function; Modulus function; Greatest Integer function, Signum function)
- Graphical representation of functions
- Concept of limits and continuity of a function
- Instantaneous rates of change
- Differentiation as a process of finding derivative
- Derivatives of algebraic functions using Chain rule
- Tangent line and equations of tangents

### Unit V: Probability

- Random experiment, sample space, events, mutually exclusive events
- Independent and Dependent Events
- Law of Total Probability
- Bayes’ Theorem

### Unit VI: Descriptive Statistics

- Types of data (raw data, univariate data, bivariate and multi-variate data)
- Data on various scales (nominal, ordinal, interval and ratio scale)
- Data representation and visualization
- Data interpretation (central tendency, dispersion, deviation, variance, skewness and kurtosis)
- Percentile rank and quartile rank
- Correlation (Pearson and Spearman method of correlation)
- Applications of descriptive statistics using real time data

### Unit VII: Basics of Financial Mathematics

- Interest and interest rate
- Accumulation with simple and compound interest
- Simple and compound interest rates with equivalency
- Effective rate of interest
- Present value, net present value and future value
- Annuities, calculating value of regular annuity
- Simple applications of regular annuities (up to 3 period)
- Tax, calculation of tax and simple applications of tax calculation in Goods and service tax, Income Tax
- Bills, tariff rates, fixed charge, surcharge, service charge
- Calculation and interpretation of electricity bill, water supply bill and other supply bills

(Comparing interest rates on various types of savings; calculating income tax; electricity bills, water bill; service surcharge using realistic data)

### Unit VIII: Coordinate Geometry

- Straight Line
- Circles
- Parabola

(only standard forms and graphical representation on two-dimensional plane)

Applied Mathematics Class 11 Syllabus