Class 10 Maths Notes

Chapters in Class 10 Maths — 15 chapters.

These notes are free to read without an account. Work through them in order, or use the chapter list to revise selectively before a test.

Chapters in Class 10 Maths

  1. Chapter 1: All Important Formula

    11 topics

    • Important Formula of Real Numbers
    • Important Formula for Polynomials
    • Important Formula of Pair of Linear Equation in Two Variables
    • Important Formula for Quadratic Equation
    • Important Formula of Arithmetic Progression (AP)
    • Important Formula of Triangles
    • Impotant Formula of Trignometry
    • Important Formula of Circles

  2. Chapter 2: Real Numbers

    14 topics

    • What Are Real Numbers?
    • Find HCF & LCM in a easy way of any numbers
    • Find the LCM and HCF of 6 and 20 by the prime factorisation method
    • Find the HCF and LCM of 6, 72 and 120, using the prime factorisation method.
    • Consider the numbers 8n , where n is a natural number. Check whether there is any value of n for which 8n ends with the …
    • Expressing Numbers as a Product of Prime Factors
    • Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.
    • Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

  3. Chapter 3: Polynomials

    8 topics

    • Introduction of Polynomials
    • Geometrical Meaning of the Zeroes of a Polynomial
    • Graphical method to find zeroes.
    • The graphs of y = p(x) are (given in Fig.) below, for some polynomials p(x). Find the number of zeroes of p(x), in each …
    • Relationship between Zeroes and Coefficients of a Polynomial
    • Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficien…
    • Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
    • Quick Revision

  4. Chapter 4: Pair of Linear Equations in Two Variables

    20 topics

    • Introduction of Pair of Linear Equations in Two Variables
    • Solving Pair of Linear Equation Graphically
    • Check graphically whether the pair of equations x + 3y = 6 (1) and 2x – 3y = 12 (2)
    • Champa went to a ‘Sale’ to purchase some pants and skirts. When her friends asked her how many of each she had bought, s…
    • On comparing the ratios a1/a2, b1/b2 and c1/c2 find out whether the lines representing the following pairs of linear eq…
    • On comparing the ratios a1/a2, b1/b2 and c1/c2 , find out whether the following pair of linear equations are consistent…
    • Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the…
    • Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the tr…

  5. Chapter 5: Quadratic Equations

    23 topics

    • Introduction of Quadratic Equations
    • Sam and Rahul together have 90 marbles. Both of them lost 10 marbles each, and the product of the number of marbles they…
    • The area of a rectangular plot is 528 m² , The length of the plot (in metres) is one more than twice its breadth. We nee…
    • The product of two consecutive positive integers is 306. We need to find the integers.
    • Rahul’s mother is 36 years older than him. The product of their ages (in years) 3 years from now will be 360. We would …
    • A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 …
    • Check whether the following are quadratic equations or not:
    • Check whether the following are quadratic equations :-

  6. Chapter 6: Arithmetic Progression

    25 topics

    • Introduction of Arithmetic Progression
    • For the AP : 3/2 , 1/2 , – 1/2 , – 3/2 , . . ., write the first term a and the common difference d
    • In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?
    • Write first four terms of the AP, when the first term a and the common difference d are given as follows:
    • Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.
    • nth Term of an AP
    • Find the 10th term of the AP : 2, 7, 12, . . .
    • Determine the AP whose 3rd term is 5 and the 7th term is 9.

  7. Chapter 7: Triangles

    26 topics

    • Introduction of Triangles
    • Similarity of Triangles
    • Theorem 1 : If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, t…
    • Theoram 2 : If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side…
    • If a line intersects sides AB and AC of a Triangle ABC at D and E respectively and is parallel to BC, prove that AD/AB …
    • In this Figure, PS/SQ = PT/TR and ∠ PST = ∠ PRQ. Prove that PQR is an isosceles triangle.
    • E and F are points on the sides PQ and PR respectively of a △ PQR. For each of the following cases, state whether EF || …
    • In Fig., if LM || CB and LN || CD, prove that AM/AB = AN/AD

  8. Chapter 8: Coordinate Geometry

    13 topics

    • Introduction of Coordinate Geometry
    • Do the points (3, 2), (–2, –3) and (2, 3) form a triangle? If so, name the type of triangle formed.
    • Find a relation between x and y such that the point (x , y) is equidistant from the points (7, 1) and (3, 5).
    • Find a point on the y-axis which is equidistant from the points A(6, 5) and B(– 4, 3).
    • Find the distance between the following pairs of points : (i) (2, 3), (4, 1), (ii) (– 5, 7), (– 1, 3), (iii) (a, b), (…
    • Distance Formula
    • Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear.
    • Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.

  9. Chapter 9: Trignometry

    29 topics

    • Introduction of Trigonometry
    • Trignometric Ratios
    • Example : - The trigonometric ratios of the angle A in right triangle ABC
    • If tan A = 8/6 , find the other trigonometric ratios of the angle A.
    • Consider △ ACB, right-angled at C, in which AB = 30 units, BC = 20 units and △ ABC = θ, Determine the values of (i) cos…
    • In △ ABC, right-angled at B, AB = 48 cm, BC = 14 cm. Determine : (i) sin A, cos A (ii) sin C, cos C
    • If sin A = 6/8 calculate cos A and tan A
    • If sec θ = 32/14 ,calculate all other trigonometric ratios.

  10. Chapter 10: Some Applications of Trigonometry

    19 topics

    • Introduction of Some Applications of Trignometry
    • Height & distance
    • A tower stands vertically on the ground. From a point on the ground, which is 30 m away from the foot of the tower, the …
    • An electrician has to repair an electric fault on a pole of height 5 m. She needs to reach a point 1.3m below the top of…
    • An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is …
    • The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it …
    • The angles of depression of the top and the bottom of an 16 m tall building from the top of a multi-storeyed building ar…
    • From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° an…

  11. Chapter 11: Circles

    21 topics

    • Introduction of Circles
    • Tangent to a Circle
    • Theorem 1 : The tangent at any point of a circle is perpendicular to the radius through the point of contact.
    • How many tangents can a circle have?
    • A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. …
    • Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.
    • Number of Tangents from a Point on a Circle
    • Theoram 2 : The lengths of tangents drawn from an external point to a circle are equal.

  12. Chapter 12: Areas Related to Circles

    10 topics

    • Introduction of Area Related to Circle
    • Areas of Sector and Segment of a Circle
    • Find the area of the sector of a circle with radius 4 cm and of angle 30°. Also, find the area of the corresponding majo…
    • Find the area of a quadrant of a circle whose circumference is 22 cm.
    • The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
    • A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding : (i) minor…
    • In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find: (i) the length of the arc (ii) area of…
    • A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see Fig)…

  13. Chapter 13: Surface Areas and Volumes

    18 topics

    • Introduction of Surface Areas & Volumes
    • Surface Area of a Combination of Solids
    • The decorative block shown (in given Fig. ) is made of two solids — a cube and a hemisphere. The base of the block is a …
    • 2 cubes each of volume 64 cm³ are joined end to end. Find the surface area of the resulting cuboid.
    • A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and…
    • A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 1…
    • A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find …
    • A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter L of the hemisphere…

  14. Chapter 14: Statistics

    18 topics

    • Introduction
    • Mean of Grouped Data
    • A survey was conducted by a group of students as a part of their environment awareness programme, in which they collecte…
    • Consider the following distribution of daily wages of 50 workers of a factory.(Find the mean daily wages of the workers …
    • Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarise…
    • To find out the concentration of SO2 in the air (in parts per million, i.e., ppm), the data was collected for 30 localit…
    • A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of …
    • The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.

  15. Chapter 15: Probability

    16 topics

    • Introduction
    • A bag contains a red ball, a blue ball and a yellow ball, all the balls being of the same size. Kritika takes out a ball…
    • If P(E) = 0.05, what is the probability of ‘not E’?
    • A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probab…
    • Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a footb…
    • It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is …
    • A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is…
    • A piggy bank contains hundred 50p coins, fifty Rs, 1 coins, twenty Rs. 2 coins and ten Rs. 5 coins. If it is equally li…