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Trigonometric Ratios of Standard Angles 150 150 SchoolTutoring Academy

Trigonometric Ratios of Standard Angles

Usually, a calculator is used to find the trigonometric ratios at different values. But sometimes, the problem may ask to solve it without using a calculator where it involves some standard angles. The standard angles are 0, 300, 450, 600 and 900. Let us learn how to find the values of trigonometric ratios of these…

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Problem-Solving and Verbal Overshadowing 150 150 Suzanne

Problem-Solving and Verbal Overshadowing

Problem-solving is something we all do every day. In terms of what our brains are doing, there are two very distinct processes being used. We either analyze the problem or we have an insight about the problem. These are two totally different things and there are times when the processes confuse each other, so understanding…

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Finding the Inverse of a 2×2 Matrix 150 150 SchoolTutoring Academy

Finding the Inverse of a 2×2 Matrix

Two matrices A and B of same order 2 are said be inverses to each other if AB=BA=I, where ‘I’ is the unit matrix of same order 2. Here, A is called inverse of B and B is called inverse of A. i.e. A= B–1 and B= A-1.   Note 1: From the above definition,…

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Solution Set of an Inequality 150 150 SchoolTutoring Academy

Solution Set of an Inequality

A solution set is the set of values which satisfy a given inequality. It means, each and every value in the solution set will satisfy the inequality and no other value will satisfy the inequality. Example: Solve 2x + 3 ≤ 7, where x is a natural number. Solution: 2x + 3 ≤ 7 Subtracting…

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Algebra: Arithmetic Progression 150 150 SchoolTutoring Academy

Algebra: Arithmetic Progression

A sequence of numbers is said to be an arithmetic progression if the difference of any two successive terms in the sequence is always a constant. This constant difference is called “common difference” of the arithmetic progression. Usually, the first term and the common difference of the arithmetic sequence are denoted by a and d…

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Words That Express Comparison 150 150 Suzanne

Words That Express Comparison

To compare people, places or things (essentially, nouns) is to note distinctions based on similarities and/or differences between them relative to each other. The following are words commonly used to accomplish this, and that are often used interchangeably, and, more or less mistakenly. Farther vs. Further Farther refers to a comparative amount of literal distance,…

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Expanding Powers Through Binomial Theorem 150 150 SchoolTutoring Academy

Expanding Powers Through Binomial Theorem

Usually we will expand powers just by expanding it using normal multiplication or using the following formulae. (a+b)^2 = a^2 + 2ab + b^2 (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 Fine. We can use these formulae when the power is either 2 or 3. But, Is there any formula for the expansion…

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Sequences: Geometric Progression 150 150 SchoolTutoring Academy

Sequences: Geometric Progression

A sequence of numbers is said to be a geometric progression if the ratio of any two successive terms in the sequence is always a constant. This constant difference is called “common ratio” of the geometric progression. Usually, the first term and the common ratio of the geometric sequence are denoted by a and r…

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SchoolTutoring Academy Reviews Grammar – Affect/Effect and Assume/Presume 150 150 Suzanne

SchoolTutoring Academy Reviews Grammar – Affect/Effect and Assume/Presume

Effect vs. Affect Most people know what an effect is, but most do not know how to effectively use its very close lexical cousin, affect. The base grammatical rule is that when used as a noun (or adverb), the correct form is effect.  The boy’s speech in the lunchroom had a profound effect. When the…

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Solving Theorems: Mathematical Induction 150 150 SchoolTutoring Academy

Solving Theorems: Mathematical Induction

In Mathematics, we see many theorems which are true for all natural numbers. Sometimes, proving these theorems directly is not possible. For this purpose, we use a method of proof which is known as “Mathematical Induction”. The principal of Mathematical Induction is defined as follows. “Let S(n) be a certain statement involving n, where n…

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