Chapter 5 : Arithmetic Progression Master Arithmetic Progressions (AP) | Class 10 Math Guide Have you ever noticed the spiral pattern on a pineapple, the petals of a sunflower, or the decreasing lengths of the rungs on a ladder? Mathematics is the hidden language behind these natural and man-made patterns. In Class 10, one of the most fascinating patterns we study is the Arithmetic Progression (AP). Whether you are figuring out a monthly savings plan or calculating compound interest, AP is an incredibly handy tool. Let’s break down the theory and tackle some practice questions! What is an Arithmetic Progression? An arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term. Common Difference ( d ) : This fixed number that we add is called the common difference of the AP. Remember, d can be positive, negative, or zero. First Term ( a ): The starting number of your sequence. The Ge...

Chapter 4 : Quadratic equation What is quadratic equation A quadratic equation in the variable x is an equation of the form ax 2 + bx + c = 0, where a, b, c are real numbers, a ≠ 0. Example 2x 2 + x – 300 = 0 , 2x 2 – 3x + 1 = 0, 4x – 3x 2 + 2 = 0 and 1 – x 2 + 300 = 0 In fact, any equation of the form p(x) = 0, where p(x) is a polynomial of degree 2, is a quadratic equation. But when we write the terms of p(x) in descending order of their degrees, then we get the standard form of the equation. That is, ax 2 + bx + c = 0, a ≠ 0 is called the standard form of a quadratic equation. How to check whether given equation is quadratic equation or not. Point 1 : After simplify the equation, highest power of variable should be 2. Point 2: After simplify the equation , equation can be represented in the form ax 2 +bx+c = 0 Example : a) (x – 2) 2 + 1 = 2x – 3 (x – 2) 2 + 1 = 2x – 3 can be rewritten as x 2 – 4x + 5 = 2x – 3 i.e., x 2 – 6...

Chapter 3 : PAIR OF LINEAR EQUATIONS IN TWO VARIABLES What is Linear Equation? A linear equation is an algebraic equation in which the highest power of the variable(s) is 1, and its graph always forms a straight line. Example : 3x + 4 = 0 , 3x + 4y = 6 Linear Equation in Two variable: A linear equation in two variables is an equation of the form ax+by+c=0, where a,b,c are real numbers and x,y are variables. Its graph is always a straight line in the coordinate plane. Example : a) 2x + 3y = 6 , b) 4x + 5y = 8. Solution of pair of linear equation in two variable: A pair of linear equations in two variables can be represented, and solved, by the: (i) graphical method (ii) algebraic method a) Graphical method 1. General Form A pair of linear equations in two variables can be written as: a 1 x + b 1 y + c 1 = 0 a 2 x + b 2 y + c 2 = 0 Here, x and y are variables, and (a 1 , b 1 , c 1 , a 2 , b 2 , c 2 ) are constants. 2. Steps in the...

Chapter 2 : Polynomial What is polynomial? A polynomial is an expression made up of variables and coefficients, combined using addition, subtraction, and multiplication, with non-negative integer exponents. Example : 3x 4 -2x 2 +7x-5. Key Features of Polynomial : let's discuss some features of polynomial: Take a polynomial : 3x 4 -2x 2 +7x-5. a) Degree: The highest power of the variable(x)(e.g. degree of 3x 4 -2x 2 +7x-5 is 4). b) Terms: Each part separated by + or – (e.g., 3x 4 , -2x 2 , 7x, -5). c) Coefficients: Numbers multiplying the variables (e.g., 3, -2, 7). d) Constant term: The standalone number (e.g. -5). Types of polynomial: a) Linear polynomial: A polynomial of degree 1.     Example : 2x – 3 , u + 5 , 3u+ 5 b) Quadratic polynomial : A polynomial of degree 2     Example : 3x 2 +2x – 3 ,3u 2 - u + 5 c) Cubic polynomial : A polynomial of degree 3     Example : 2...

Physics Question for revision 1. State any two properties of magnetic field lines. 2. What is a magnetic field ? How can the direction of magnetic field lines at a place be determined ? 3. Explain why, two magnetic field lines do not intersect each other. 4. State and explain Maxwell’s right-hand thumb rule. 5. Draw the magnetic lines of force due to a circular wire carrying current. 6. In the straight wire A, current is flowing in the vertically downward direction whereas in wire B the current is flowing in the vertically upward direction. What is the direction of magnetic field : (a) in wire A ? (b) in wire B ? Name the rule which you have used to get the answer. 7. A thick wire is hanging from a wooden table. An anticlockwise magnetic field is to be produced around the wire by passing current through this wire by using a battery. Which terminal of the battery should be connected to the : (a) top end of wire ? (b) bottom end of wire ? Giv...

Mathematics Question for revision | Area Related to circle There will be 10 questions and timing will be 1 hour. 1. Find the area of a quadrant of a circle whose circumference is 22 cm. 2. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes. 3. A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. 4. A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades. 5. To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned.(Use π = 3.14) 6. 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 below). Find (i...