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...