10th class Math solution chapter-wise solved exercises in pdf. Key Book of Mathematics in pdf. PTB 10th class maths solution pdf.

## 10th Class Math Solution:

Table of content and topics completely solved in 10th mathematics solution notes in pdf. Content table is given below.

- Quadratic Equations
- Theory of Quadratic Equations
- Variations
- Partial Fractions
- Sets and Functions
- Basic statistics
- Trigonometry Introduction
- Side of Triangle projection
- Chords of a circle
- Chords and ARCs
- Angle segment of a circle
- Geometry

### 10th Class Math Solution Unit 1 Quadratics Equations:

In this unit, students will learn how to

1 define quadratic equation.

2 solve a quadratic equation in one variable by factorization.

3 solve a quadratic equation in one variable by completing a square.

4 derive quadratic formula by using the method of completing the square.

5 solve a quadratic equation by using the quadratic formula.

6 solve the equations of the type ax4 + bx2 + c = 0 by reducing it to the quadratic form.

### Unit 2 Theory Of Quadratic Equations:

In this unit, students will learn how to

- define discriminant (b2 -4ac) of the quadratic expression ax2 + bx + c.

find the discriminant of a given quadratic equation. - discuss the nature of roots of a quadratic equation through discriminant. determine the nature of roots of a given quadratic equation and verify the result by solving the equation.
- determine the value of an unknown involved in a given quadratic

equation when the nature of its roots is given. - find cube roots of unity. recognize complex cube roots of unity as @ and w?
- prove the properties of cube roots of unity. use properties of cube roots of unity to solve appropriate problems.
- find the relation between the roots and the coefficients of a quadratic equation. find the sum and product of roots of a given quadratic equation without solving it.
- find the value(s) of unknown(s) involved in a given quadratic equation

when the sum of roots is equal to a multiple of the product of roots, the sum of the squares of roots is equal to a given number, roots differ by a given number, roots satisfy a given relation (e.g ., the relation 2 0 + 50 = 7 where a and Bare the roots of the given equation),. both sum and product of roots are equal to a given number. - define symmetric functions of roots of a quadratic equation.

### Chapter 3 Variations:

In this unit students will learn how to define ratio , proportions and variations ( direct and inverse) find 3,4, mean and continued proportion.

apply theorems of invertendo , alternendo , componendo , dividendo and

componendo dividendo to find proportions. define joint variation.

solve problems related to joint variation. use k-method to prove conditional equalities involving proportions. solve real-life problems based on variations.

#### Unit 4 Partial Fractions:

Define proper, improper, and rational fractions. a resolve an algebraic fraction into partial fractions when its denominator consists of

non-repeated linear factors, repeated linear factors, non-repeated quadratic factors, repeated quadratic factors.

#### Chapter 5 Sets and Functions:

perform operations on sets union, intersection, difference, complement.

give formal proofs of the following fundamental properties of union and

intersection of two or three sets. commutative property of union, commutative property of intersection,

associative property of union, associative property of intersection, distributive property of union over the intersection.

distributive property of intersection over union, De Morgan’s laws. a verify the fundamental properties for given sets. a use Venn diagram to represent union and intersection of sets.

#### Basic Statistics Unit 6:

construct grouped frequency table. construct histograms with equal and unequal class intervals. a construct a frequency polygon. & construct a cumulative frequency table.

draw a cumulative frequency polygon. a calculate (for ungrouped and grouped data)

arithmetic mean by definition and using deviations from assumed mean.

a calculate median, mode, geometric mean, harmonic mean. a recognize properties of the arithmetic mean. a calculate weighted mean and moving averages.

#### Introduction to Trigonometry Unit 7:

Trigonometry complete chapter solution with solved exercises are included in this pdf solution math.

#### Projection of a side of a Triangle Unit 8:

Projection a side Triangle unit with fully solved all exercises and explanation.

#### Chords of a circle Chapter 9:

In this chapter circle and chords all exercises are given with solution.

#### Chords and ARCs Chapter 10:

Completely solved chapter of chords and ARCs with exercises and explanations.

#### Angle segment of a circle Chapter 11:

Introduction and definition of Angle and its segments. Circle and its types with solved exercises.

#### Geometry Unit 12:

Introduction to Geometry and solved exercises with explanation.

You may also like to download 10th Mathematics Punjab text Book of Science Group from the link below.