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## Karnataka 1st PUC Basic Maths Question Bank with Answers

- Chapter 1 Number Theory
- Chapter 2 Sets, Relations and Functions
- Chapter 3 Theory of Indices
- Chapter 4 Logarithms
- Chapter 5 Progressions
- Chapter 6 Theory of Equations
- Chapter 7 Linear Inequalities
- Chapter 8 Simple Interest and Compound Interest
- Chapter 9 Annuities
- Chapter 10 Averages
- Chapter 11 Percentage, Profit and Loss sales tax, Vat
- Chapter 12 Linear Functions
- Chapter 13 Angles and Trigonometric Ratios
- Chapter 14 Standard Angles and Allied Angles
- Chapter 15 Co-Ordinate System in a Plane
- Chapter 16 Locus and its Equations
- Chapter 17 Straight Line

### Karnataka 1st PUC Basic Maths Syllabus and Marking Scheme

**Karnataka 1st PUC Basic Maths Blue Print of Model Question Paper**

**I PUC Basic Mathematics Weightage Given to the Curriculum**

**I PUC Basic Mathematics Unit Wise Weightage**

**I PUC Basic Mathematics Instructions to Question Paper Setters**

1. Part E : 2 marks Question must be from chapters

(i) Number theory (ii) Averages.

2. Part E : 4 marks from chapters

(i) Sets, Relation and Functions

(ii) Progressions

(iii) Linear Functions

(iv) Straight Lines.

3. The question paper consists of five parts A, B, C, D & E.

4. Part A carries 10 marks, Part B carries 20 marks, Part C carries 30 marks, Part D carries 30 marks and Part E carries 10 marks.

5. Write the question numbers properly as indicated in the question paper.

Unit I: Algebra

Chapter 1 Number Theory (Total – 8 hrs)

- 1.0 Introduction
- 1.1 Natural Numbers
- 1.2 Whole numbers
- 1.3 Integers
- 1.4 Odd and Even Numbers
- 1.5 Prime Numbers
- 1.6 Composite Numbers
- 1.7 Fundamental theorem of arithmetic
- 1.8 Least Common Multiple
- 1.9 Highest common factor
- 1.10 Finding H.C.F using the product of numbers given
- 1.11 Finding H.C.F of fractions
- 1.12 Rational Numbers
- 1.13 Irrational Numbers
- 1.14 Real Numbers
- 1.15 Complex numbers

Chapter 2 Sets, Relations and Functions (Total – 16 hrs)

- 2.0 Introduction
- 2.1 Sets
- 2.2 Methods of describing a set
- 2.3 Null set
- 2.4 Singleton set
- 2.5 Finite set and Infinite sets
- 2.6 Equal and equivalent sets
- 2.7 Subset
- 2.8 Universal Set
- 2.9 Operation on Sets
- 2.10 Complement set
- 2.11 Algebra of sets
- 2.12 Venn diagrams
- 2.13 Ordered pairs
- 2.14 Equality of ordered pairs
- 2.15 Cartesian product pairs
- 2.16 Worked examples
- 2.17 Relation
- 2.18 Domain and range of a relation
- 2.19 Inverse relation
- 2.20 Types of relation
- 2.21 Worked Examples
- 2.22 Functions
- 2.23 Domain, co-domain and range
- 2.24 Different types of functions
- 2.25 Worked Examples

Chapter 3 Theory of Indices (Total – 4 hrs)

- 3.1 Introduction
- 3.2 Meaning of a
^{n} - 3.3 Laws of Indices

Chapter 4 Logarithms (Total – 6 hrs)

- 4.1 Introduction
- 4.2 Definition of Logarithm
- 4.3 Laws of Logarithm
- 4.4 Common Logarithm

Chapter 5 Progressions (Total – 12 hrs)

- 5.1 Introduction
- 5.2 Sequences
- 5.3 Series
- 5.4 Arithmetic Progressions
- 5.5 nth term of an A.P
- 5.6 Sum to ‘n’ terms of an A.P
- 5.7 Geometric progression
- 5.8 nth term of GP
- 5.9 Sum to n terms of GP
- 5.10 Sum to infinite G.P
- 5.11 Harmonic progression
- 5.12 nth term of H.P

5.13 Arithmetic, Geometric and harmonic means

Chapter 6 Theory of Equations (Total – 12 hrs)

- 6.1 Introduction and definition of equation
- 6.2 Degrees of the equation and different types of equations
- 6.3 Linear equation in one variable
- 6.4 Simultaneous linear equation in two variables and different methods
- 6.5 Quadratic equation and its solution
- 6.6 Nature of the roots of the quadratic equation
- 6.7 Cubic equation, examples and solution
- 6.8 Synthetic division

Chapter 7 Linear Inequalities (Total – 6 hrs)

- 7.1 Introduction
- 7.2 Inequalities
- 7.3 Linear inequalities in one variable
- 7.4 System of linear inequations in one variable
- 7.5 Application of Linear inequalities
- 7.6 Linear inequalities in two variable
- 7.7 System of Linear Inequations in two variables and their graphical solution

Unit II: Commercial Arithmetic

Chapter 8 Simple Interest and Compound Interest (Total – 8 hrs)

- 8.1 Introduction
- 8.2 Simple interest
- 8.3 Compound Interest
- 8.4 Nominal and effective rate of interest
- 8.5 Varying rate of interest
- 8.6 Depreciation
- 8.7 Using compound interest formula for growth rate
- 8.8 Problems related to simple interest and compound interest

Chapter 9 Annuities (Total – 6 hrs)

- 9.1 Definition and types of annuity immediate
- 9.2 Future value of annuity immediate
- 9.3 Present value of annuity immediate
- 9.4 Future value of an annuity due
- 9.5 Present value of an annuity due
- 9.6 Perpetuity
- 9.7 Deferred annuity

Chapter 10 Averages (Total – 4 hrs)

- 10.1 Introduction
- 10.2 Types of Average
- 10.3 Simple Average
- 10.4 Weighted Average
- 10.5 Combined Average

Chapter 11 Percentage, Profit and Loss (Total – 6 hrs)

- 11.1 Conversion of the percentage to ratio fraction, decimal and vice versa
- 11.2 Percentage increase, the percentage decrease
- 11.3 Application problems involving percentages
- 11.4 Profit and Loss, Cost price, Selling price, Profit, Loss, Profit percentage, Loss percentage, definition and formula
- 11.5 Application problems

Chapter 12 Linear Functions (Total – 4 hrs)

- 12.1 Introduction
- 12.2 Definition
- 12.3 Linear Revenue, Cost and profit function
- 12.4 Break-Even Analysis

Unit III: Trigonometry

Chapter 13 Angles and Trigonometric Ratios (Total – 6 hrs)

- 13.1 Introduction
- 13.2 Measurement of angles
- 13.3 Trigonometric ratios of acute angle
- 13.4 Relation between the trigonometric ratios

Chapter 14 Standard Angles and Allied Angles (Total – 6 hrs)

- 14.1 Trigonometric Ratios of standard angles
- 14.2 Signs of Trigonometric ratios
- 14.3 Allied angles

Unit IV: Analytical Geometry

Chapter 15 Co-Ordinate System in a Plane (Total – 5 hrs)

- 15.1 Introduction
- 15.2 Rectangular Cartesian Co-ordinate system in a plane
- 15.3 Distance Formula
- 15.4 Section Formula
- 15.5 Centroid Formula, Midpoint formula
- 15.6 Area of the Triangle and quadrilateral

Chapter 16 Locus and its Equations (Total – 3 hrs)

- 16.1 Introduction
- 16.2 Equation of the locus of a point

Chapter 17 Straight Line (Total – 3 hrs)

- 17.1 Introduction
- 17.2 Slope or Gradient of a line
- 17.3 Slope of Parallel Lines and Perpendicular Lines
- 17.4 SJope of the line joining two points
- 17.5 Standard forms of Equation of straight lines
- 17.6 Equation of a line in general form
- 17.7 Intersection of two lines
- 17.8 Condition for concurrency of three lines
- 17.9 Length of the perpendicular from a point to a line
- 17.10 Distance between parallel lines

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