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Complementary and Supplementary Angles 150 150 SchoolTutoring Academy

Complementary and Supplementary Angles

In geometry two angles can be related to each other in several ways. Below are two of them Complementary angles A pair of angles is called complementary angles if their sum is 90°. One of the complementary angles is said to be the complement of the other. For example, an angle of 35° is complement…

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Introduction to Angles 150 150 SchoolTutoring Academy

Introduction to Angles

Angle is a geometric figure formed by two rays sharing a common endpoint called vertex. The two rays are called the sides of the angle. The size of an angle is measure using degree (represented by symbol °) and radian (abbreviated as rad). The table below shows the types of angles used in geometry. SchoolTutoring…

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Understanding the Nitrogen Cycle 150 150 SchoolTutoring Academy

Understanding the Nitrogen Cycle

Nitrogen gas is a major component of air. Nitrogen is used by living organisms to produce a number of complex organic molecules like amino acids, proteins, and nucleic acids. The main component of the nitrogen cycle starts with the element nitrogen in the air. Most organisms cannot use nitrogen in this form. Plants take nitrogen…

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The Carbon Cycle 150 150 SchoolTutoring Academy

The Carbon Cycle

All living things are made of carbon. Carbon is also a part of the ocean, air, and rocks. In the atmosphere, carbon is attached to some oxygen to form carbon dioxide. The movement of carbon, in its many forms, between the biosphere, atmosphere, oceans, and geosphere is described by the carbon cycle. The Carbon Cycle…

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Laws of Logarithm 150 150 SchoolTutoring Academy

Laws of Logarithm

Laws, also called as rules, of logarithm are set of relations which enable us to write logarithmic expressions in different, yet equivalent, ways. Below are the most commonly used rules of logarithm: Rule 1: loga(MN) = loga(M) + loga(N) Example:  log10(5 × 3) = log10(5) + log10(3) Rule 2: loga(M/N) = loga(M) – loga(N) Example:…

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Factoring Quadratic Equation 150 150 SchoolTutoring Academy

Factoring Quadratic Equation

A quadratic equation is a one-variable polynomial equation of the second degree whose general form is: ax2 + bx + c = 0, where a, b and c are constants with a ≠ 0, and x represents a variable. A quadratic equation has two solutions, called roots. The two solutions may be or may not…

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Completing the Square 150 150 SchoolTutoring Academy

Completing the Square

A quadratic equation is a one-variable polynomial equation of the second degree whose general form is: ax2 + bx + c = 0, where a, b and c are constants with a ≠ 0, and x represents a variable. A quadratic equation can be solved by factoring, completing the square method, graphing and using quadratic…

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Multiply and Divide Complex Numbers 150 150 SchoolTutoring Academy

Multiply and Divide Complex Numbers

Multiplication of Complex Numbers The product of complex numbers a + bi and c + di is given as: (a + bi) + (c + di) = (ac – bd) + (ad + bc)i Example: (4 – 2i)(3 + 5i) = 4(3 + 5i) – 2i(3 + 5i)                           (Using distributive property over addition) = 12…

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Conjugate, Addition and Subtraction of Complex Numbers 150 150 SchoolTutoring Academy

Conjugate, Addition and Subtraction of Complex Numbers

Conjugate of complex number The conjugate of a complex number z = a + bi is: a – bi Example: Conjugate of 7 – 5i = 7 + 5i Addition of Complex Numbers Sum of two complex numbers a + bi and c + di is given as: (a + bi) + (c + di)…

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Algebraic Identities 150 150 SchoolTutoring Academy

Algebraic Identities

Solving algebraic problems get easy with readily available expressions. These expressions are knows as algebraic identities or rules which makes the job of a person easy, fast and reduces the chances of error. Below are most commonly used algebraic identities: Square of a Binomial (a + b)2 = a2 + 2ab + b2 Example: (x…

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