Algebra

NZ Level 6 (NZC) Level 1 (NCEA)

Substitute into common formulae

Lesson

Mathematicians love to write formulae as algebraic shorthand for expressions that we would otherwise have to write as a sentence.

For example, instead of writing, "The area of a rectangle is calculated by multiplying the length by the breadth," I can write the algebraic formula $A=lb$`A`=`l``b`. Much shorter right! Formulae also makes it easier to substitute values and evaluate equations.

There are lots of topics that have common formulae: simple interest, area, volume, perimeter and temperature conversions just to name a few. Make sure your familiar with the formulae for your topic before you start doing exercises.

Here are some examples to get you started.

The perimeter of a square with side lengths of $a$`a` is given by the formula $P=4\times a$`P`=4×`a`.

Find $P$`P` if the length of each side is $5$5 cm.

The area of a triangle is given by the formula $A=\frac{1}{2}$`A`=12$($(base$\times$×height$)$).

If the base of a triangle is $3$3 cm and its height is $10$10 cm, find its area.

The simple interest generated by an investment is given by the formula $I=\frac{P\times R\times T}{100}$`I`=`P`×`R`×`T`100.

Given that $P=1000$`P`=1000, $R=6$`R`=6 and $T=7$`T`=7, find the interest generated.

Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns

Apply algebraic procedures in solving problems