# SIMPLE EQUATIONS AND VARIATIONS

CONTENT

1. Formulae, substitution and change of subject of formulae.
2. simple binary operations.
3. Variations (i) Direct and inverse, (ii) joint and partial.
4. Application of variation.

## SUBJECT OF A FORMULA

The subject of a formula is the variable that is expressed in terms of the other variables. In the relation $$y = x + 4$$, y is called the subject of the formula. To make x the subject means rewriting this relation in an equivalent form, where x will be alone on one side of the equality sign. The relation is normally written with the subject on the left-hand side of the formula. For example, $$y = 2 × -3$$, the x can be made subject of formula as follows, $$x = \frac{y + 3}{2}$$

## SUBSTITUTION

A formula is an equation in which letters represent quantities. The value of one variable in a formula or algebraic equation may be found by substituting (i.e replacing) known values in the same formula

Examples 1:  The sum of the squares of the first n integers is given by

$$s_n = \frac{n(n + 1)(2n + 1)}{6}$$

Calculate   (a) s20 (b) the sum of the squares from 21 to 40 inclusive.

Lesson tags: General Mathematics Lesson Notes, General Mathematics Objective Questions, SS1 General Mathematics, SS1 General Mathematics Evaluation Questions, SS1 General Mathematics Evaluation Questions First Term, SS1 General Mathematics First Term, SS1 General Mathematics Objective Questions, SS1 General Mathematics Objective Questions First Term
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