Math 10 Class Notes | Punjab Board Easy Notes

10 Class Math Notes Chapter 1

       Quadratic Equation is the first chapter of Math 10 class notes. In this chapter, you will learn the definition of a quadratic equation, solve a quadratic equation in one variable by factorization, and the method of completing the square. 

       You will be able to solve a quadratic equation by formula. The equations of the type ax4+bx2+ c = 0 by reducing it to the quadratic form,  the reciprocal equations of the type ap(x)+bp(x) = c, the equation of the type  a(x2+1×2)+b(x+1x)+c=0, and also solve the equations of the types (x+a)(x+b)(x+c)(x+d)=k where a+b=c+d.

        You can also solve radical equations:

1.         ax+b =cx+d
2.        x+a + x+b = x+c
3.         x2+px+m +x2+px+n = q

Math 10 Class Notes Chapter 2

     Theory of Quadratic Equation is the second chapter of Math 10 class notes. In Math 10 class notes, you will be able to explain the discriminant of the quadratic equation, and also identify a given quadratic equation’s discriminant.

     Describe the characteristics of a quadratic equation’s roots through discrimination, the nature of the roots of a given quadratic equation, verify the result by solving the quadratic expression and also find the value of an unknown involved in a given equation. 

     You will also find the cube root of unity and its properties, and also recognize the complex cube root of unity as and 2, and also understand the relation between the roots and the coefficients of a quadratic equation.

      You can solve a quadratic equation without solving it, and find the sum, and the product of the roots. Evaluate the symmetric function of the roots of a quadratic equation in terms of the coefficients.

Math Class 10th Notes Chapter 3

       Variations is the third chapter of Math 10 class notes. You will learn about ratios, proportions, and variations. Find the 3rd and 4th continued proportion, mean, and also use the alternendo, dividendo, componendo, and invertendo theorems to determine proportions.

         You can also solve problems by considering joint variation and defining it. Explain the k-method to demonstrate conditional equality and to resolve practical issues based on variations.

10th Class Math Notes Chapter 4

      Partial Fractions is the fourth chapter of Math 10 class notes. You will be able to describe improper, proper, and rational fractions. When the denominator of an algebraic fraction has non-repeated linear elements, resolve it into a partial  percentage, non-repeated linear elements repeated quadratic elements and repeated quadratic factors.

Class 10th Math Notes Chapter 5

       Set & Functions is the fifth chapter of Math 10 class notes. You will learn in Math 10 class notes about sets, and perform operations on sets union, intersection, difference, and complement. Also, formal proofs of the following fundamental properties of union and intersection of more than one set,

1. Union’s commutative property.
2.  Intersection’s commutative property.
3. Union’s associative property.
4. Intersection’s associative property.
5. Distributive property of union over the intersection.
6. Distributive property of intersection over the union.
7. De Morgan’s laws.

      You can use a Venn diagram to explain the union and intersection of sets, the complement of a set, De Morgan’s laws, associative laws, and distributive laws. Also, recognize ordered pairs and cartesian products, and also define binary relations and identify their domain and range.

Math Class 10th Notes Chapter 6

      Basic Statistics is the sixth chapter of the Math 10 class notes. You will learn how to construct a grouped frequency table, and also construct histograms with equal and unequal class intervals. Construct a frequency polygon, a cumulative frequency table, and a cumulative frequency polygon.

       You can learn in Math 10 class notes arithmetic mean by definition and using deviations from assumed mean, and also calculate the median, mode, geometric mean, and harmonic mean. You can explain the characteristics of the mean of arithmetic, moving averages, and weighted mean. Calculate the mode graphically, median, quartiles, variance, range, and standard deviation. 

10 Class Math Notes Chapter 7

       Introduction to Trigonometry is the seventh chapter of Math 10 class notes. You will be able to measure an angle in degrees, minutes, and seconds and convert it into decimals forms and vice versa. Define radian and verify the relationship between radians and degrees.  

       Establish the rule  l=r. You can also prove that the area of a sector of a circle is  12r2,. Describe the general angle, and angle in standard position, and also define quadrantal and quadrants angles. We defined in Math 10 class notes using a unit circle, to find the reciprocals of trigonometric ratios.

       Also, describe the trigonometric ratio values for degrees 30,45,60, and also the signs of trigonometric ratios in different quadrants. You can find the angle of depression and elevation, and also practical-based problems involving the angle of elevation and depression. 

Math Notes 10th Class Chapter 8

       Projection of a Side of a Triangle is the eighth chapter of Math 10 class notes. 

1. The square on the side opposing the obtuse angle equals the squares on the sides containing the obtuse angle added to twice the rectangle encompassed by the oblique angle on one of the sides, and the projection on it of the other, in a triangle with an obtuse angle.
2. The square on the side opposite an acute angle equals the squares on the sides that include the acute angle multiplied by twice the rectangle that is encompassed by one of those sides, and the other’s projection upon it, in any triangle.
3. Any two sides’ square sum is equal to twice the side’s square, half of the third side along with twice the square on the third side’s median.

10th Class Math Notes Chapter 9

      Chords of a Circle is the ninth chapter of Math 10 class notes. You will learn that three noncollinear locations can only be passed through by a single circle, draw from the center a chord perpendicular to the chord by cutting the circle in half, a straight line. 

       We described in Math 10 class notes, a chord bisects a circle perpendicularly from the center, and also if two of a circle’s chords will be equidistant from the center, are congruent. 

Class 10th Math Notes Chapter 10

       Tangent to a Circle is the tenth chapter of Math 10 class notes. You will be able to prove that At a circle’s outer terminal, a line is drawn perpendicular to the circle’s radial segment, it is tangent to the circle at that point, and also the tangent of the radial segment connecting the point to a circle of contact and the center are perpendicular to each other.

       You will learn about the two tangents drawn to a circle from a point outside it, which are equal in length, and If two circles are internally tangent or externally, the difference between the radii of two circles is equal to the distance between their centers.

Math 10th Class Notes Chapter 11

      Chords & Arcs is the eleventh chapter of Math 10 class notes Punjab board. You will understand the corresponding chords are equal, if two arcs of a circle are congruent, and also prove that the corresponding arcs are congruent if two chords of a circle are equal.

       You can learn that congruent circles subtend equal angles at the center, and also prove that if the angles subtended by congruent circles at the corresponding centers are equal, the chords are equal. 

Class 10th Math Notes Chapter 12

         Chords & Arcs is the eleventh chapter of Math 10 class notes Punjab board. You will understand the corresponding chords are equal, if two arcs of a circle are congruent, and also prove that the corresponding arcs are congruent if two chords of a circle are equal.

       You can learn that congruent circles subtend equal angles at the center, and also prove that if the angles subtended by congruent circles at the corresponding centers are equal, the chords are equal. 

Math Notes 10 Class Chapter 13

        Practical Geometry (Circles) is the chapter of Math 10 class notes. You will learn how to locate the center of the given circle, and draw a circle passing through three non-collinear points. When a part of the circumference is given, by finding its center, complete the circle, and also prove without finding the center.

       You will also learn how to circumscribe, inscribe, and escribe a circle in a given triangle. Explain that circumscribe, inscribe an equilateral triangle in a given circle, and also prove that circumscribe, inscribe a square in a given circle. How to circumscribe, and inscribe a regular hexagon in a given circle.

 Math 10th Class Notes Exercise Wise Solution

      When you are starting to practice a chapter, start from the first topic of the chapter and learn every definition and concept. You should practice all the formulas and examples from the chapter, so that practice of these examples and formulas will help you to solve the exercise questions. 

       You should practice all the questions of each exercise completely. We are uploaded all chapter’s exercises solutions. During practice, if you find two or more questions are the same, then you should focus on the questions which are tough for you.

Advantages

1. Maths improve students’ analytical thinking.
2. Learning and solving math problems increases students’ confidence.
3. Math is a very important subject for careers, such as engineering, computer sciences, data analysis, etc.
4. Math improves the memory of the students.

Disadvantages

1. Math anxiety is a common issue in students.
2. Math requires a lot of practice to become an expert in the subject.

Conclusion

       We have provided Math10 class notes of the Punjab Board. You can take help from our notes and prepare your exam notes. We have all chapter exercises questions and answers in PDF form, you can download all exercises from Freeilmi.com and also read online these notes. If you find any mistake in our notes then you can comment on our site, and we will respond to you as soon as possible.