Basic Proportionality Theorem Basic Proportionality Theorem (BPT) The Basic Proportionality Theorem (also known as Thales’ theorem) states that if a line is drawn parallel to one side of a triangle to intersect the other two sides, then it divides those two sides proportionally. A B C D E In the diagram above, if line DE …
Master Triangles in 30 Minutes: A Quick Guide for CBSE Class 10 Students Q&A Style Revision 1. What is the Pythagoras Theorem? The Pythagoras Theorem states: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Mathematically: (c^2 = a^2 + b^2), where …
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Master Coordinate Geometry in 30 Minutes: A Quick Guide for CBSE Class 10 Students Q&A Style Revision 1. What is the Distance Formula in Coordinate Geometry? The distance between two points ((x_1, y_1)) and ((x_2, y_2)) is given by: (d = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}) 2. How do you calculate the Midpoint …
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Master Probability in 30 Minutes: A Quick Guide for CBSE Class 10 Students Q&A Style Revision 1. What is Probability? Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 means the event cannot happen, and 1 means the event is …
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Master Statistics in 30 Minutes: A Quick Guide for CBSE Class 10 Students Q&A Style Revision 1. What is the formula for calculating the Mean (Direct Method)? The formula is: Mean ((bar{x})) = (frac{sum f_i x_i}{sum f_i}) 2. How do you calculate the Mean using the Assumed Mean Method? The formula is: (bar{x} = A …
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Nationalism in Britain The concept of nationalism in Britain evolved differently compared to other parts of Europe. Unlike France or Germany, where nationalism was often tied to revolutions, the process in Britain was gradual and deliberate over centuries. 1. What was the state of Britain before it became a nation-state? Before the 18th century, there …
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Alternative Direct Substitution Approach Start from the given equation: [ costheta + sintheta = sqrt{2}costheta. ] Rearranging, we get: [ sintheta = (sqrt{2}-1)costheta. ] Now consider what we need to prove: [ costheta – sintheta = sqrt{2}sintheta. ] Substitute (sintheta = (sqrt{2}-1)costheta) into the left-hand side: [ costheta – sintheta = costheta – (sqrt{2}-1)costheta = …
Math Problems – Comprehensive Document Set Alpha – Formulas Set A Rectangle (text{Perimeter} = 2(l + b)) (text{Area} = l times b) Trapezium (text{Area} = frac{1}{2} times (a + b) times h) Parallelogram (text{Area} = sqrt{s(s-a)(s-b)(s-c)}) where ( s = frac{a + b + c}{2} ) Circles (text{Circumference} = 2 pi r) (text{Area} = pi …
Class VII – Science Chapter 2: Nutrition in Animals VI. Case Study Based Questions The small intestine is a highly coiled structure. It is about 7.5 meters long. It receives secretion from the liver and the pancreas. The liver is a reddish brown gland located in the upper part of the abdomen on the right …
Mathematics Reference Manual Quadratic Equations Forming Quadratic Polynomials A quadratic polynomial is of the form (ax^2 + bx + c). Example: Form a quadratic polynomial given the roots (alpha = 3) and (beta = -2). Sum of roots: (alpha + beta = 1) Product of roots: (alpha beta = -6) Quadratic polynomial: (x^2 – (alpha …
