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Congruent Triangles: An Introduction 150 150 SchoolTutoring Academy

Congruent Triangles: An Introduction

The two figures are congruent if they have exactly the same size and shape. The congruent figures have congruent sides and angles.  The congruence between two sides and angles is shown by the symbol . The two triangles ABC and XYZ shown below are congruent because their corresponding sides and angles are congruent. The table…

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Introduction to Probability 150 150 SchoolTutoring Academy

Introduction to Probability

Probability was introduced in seventeenth century by two French mathematicians, Blaise Pascal and Pierre de Fermat.  Probability deals with the likelihood of occurrence of an event. If can be expressed as a number between 0 and 1. It can also be expressed as equivalent fraction or percentage.  An event with Probability of one is certain…

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Quotient Rule of Differentiation 150 150 SchoolTutoring Academy

Quotient Rule of Differentiation

The quotient rule is a method of finding the derivative of a function that is the quotient of two other functions. If f(x) is the ratio of  two functions g(x) and h(x)     then,     In other words, if h and g are two functions of x, then the derivative of the ratio…

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Unit Circle and Trigonometric Ratios 150 150 SchoolTutoring Academy

Unit Circle and Trigonometric Ratios

The unit circle is a circle whose radius is one and center is at the origin.                     According to Pythagorean Theorem, p2 + q2 = 1 Also, the trigonometric functions cosine and sine may be defined on the unit circle. p = cos(θ) q = sin(θ)…

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Product Rule of Differentiation 150 150 SchoolTutoring Academy

Product Rule of Differentiation

The product rule of differentiation is a rule for differentiating problems where one function is multiplied by another function. According to this rule, first function times the derivative of second function is added to second function times the derivative of first function. If h and g are two functions of x, then the derivative of…

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Converting between Radians and Degrees 150 150 SchoolTutoring Academy

Converting between Radians and Degrees

Radian and Degree are the most commonly used units to measure angels. Angle in degrees is denoted by symbol °  e.g. 50°. The radian is represented by ‘rad’ or by superscript c e.g. 45 rad or 45c. To convert between radian and degree we make use of the fact that 360° is same as 2π…

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Derivative and Rules of Derivative 150 150 SchoolTutoring Academy

Derivative and Rules of Derivative

The derivative is a measure of change of one quantity in response to change in another quantity. The process of finding a derivative is called differentiation. The differentiation is used to find the rate of change of one quantity with respect to another quantity. For example, velocity is change of position with respect to time.…

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Rules of Exponents 150 150 SchoolTutoring Academy

Rules of Exponents

The exponent of a number tells how many times the number is to be multiplied by itself. An exponent can be both positive and negative. It is commonly called as power or index. In general, an = a × a × a × a……n times where, a is base and n is exponent (power or…

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Six Trigonometric Ratios 150 150 SchoolTutoring Academy

Six Trigonometric Ratios

In greek ‘Trig’ means triangle and ‘metic’ is for measurement. The Trigonometric rations are used to express relationship between angles and sides of a right triangle ( a triangle with one 90° angle). The non-right angle is usually designated by a greek letter θ (theta). The sides of the triangle are labeled according to the…

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The Coordinate Plane: Understanding Quadrants, Coordinates, and the Origin 150 150 SchoolTutoring Academy

The Coordinate Plane: Understanding Quadrants, Coordinates, and the Origin

The coordinate plane is a two-dimensional surface where we can plot points, lines, geometric shapes and curves. The coordinate plane is also called as Cartesian plane. It was invented by the French mathematician Rene Descartes in the 17th century. The coordinate plane has two scales (number lines) perpendicular (at right angle) to each other. The…

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