Archive | Algebra

Simultaneous Equations With One a Quadratic

When solving ordinary – linear – simultaneous equations we multiply the equations by constant factors to make the coefficient of some variable the same in magnitude, then add or subtract the equations to eliminate that variable. For example, solve  (1)  (2) (1)*2-(2)*3 eliminatesto give Substitution of this value ofinto (1) to find a gives If […]

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The Ambiguous Case

The ambiguous case arises when using the Sine Rule to find an angle in a triangle. It occurs because the Sin function is symmetric about 90°, so that When we solve forthere is an acute solution,and an obtuse solution, Example: Find the angle A in the triangle below. The Sine Rule states Then This is […]

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The Difference Between an Expression, an Equation and a Formula

Many students get confused between anything in algebra involving‘s. Anything without an equals sign is an expression. are all expressions. The aim is always to simplify expressions. Anything with an equals sign containing x’s and no other letters, or containing more than two letters with no letter being the subject is an equation. are all […]

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Simple Interest

If you put money into a bank account, the bank will normally pay interest on the money in your account. If the interest is simple interest, then the yearly amount of interest will be calculated on the original deposit. This is unlike compound interest, for which the amount of interest is calculated on the balance […]

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Directed Numbers

Directed numbers are inequalities that describe a set of numbers. The inequalities may be represented on a number line. The diagram below represents the inequalityThe filled in black circle atindicates that 2 satisfies the inequality. The diagram below represents the inequalityThe white filled in circle atindicates thatdoes not satisfy the inequality. The above examples illustrate […]

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