Formulae

Overview

This builds on the Basic Alge­bra sec­tion. It cov­ers; how to write your own alge­braic for­mu­lae, how to eval­u­ate expres­sions and for­mula by sub­sti­tut­ing val­ues for vari­ables and how to change the sub­ject of a formula.

For­mu­lae Questions

1. Each side of a hexa­gon mea­sure 4x +3. Write a for­mula for the perime­ter of the hexagon.

2. Cal­cu­late these expres­sions when x = 2, y = 3 and z = –4.

3. The area of a tri­an­gle can be cal­cu­lated from the formula:-

Area = √(s(s — x)(s — y)(s — z))

where s = (x + y + z)/2.

Find the area of a tri­an­gle which has sides of 6m, 8m and 10m.

4. Rearrange this for­mula to make x the subject:

y= (x³/6)  + 4z

5. Rearrange this for­mula to make z the subject:

y = √(x/(z+5))

For­mu­lae Approach

1. I find that if I get stuck on cre­at­ing a for­mula, it helps to jot down any rel­e­vant facts that I know. In this case it would be, “a hexa­gon has 6 sides” and “each side mea­sures 4x +3″. This approach is more help­ful the more com­pli­cated the question.

2. & 3. My approach is to re-write the for­mula sub­sti­tut­ing the num­bers for the vari­ables and then cal­cu­late the answer, tak­ing care to do these in the right order (e.g. cal­cu­lat­ing the brack­ets first). With a com­plex expres­sion I find it helps to re-write the expres­sion as I cal­cu­late each part of it (see answers below to see exactly what I mean).

4. & 5. Again I find a step by step approach (and writ­ing down each step) helps when rear­rang­ing for­mu­las (see answers below).

For­mu­lae Answers

1. 6(4x + 3)

2. Cal­cu­late these expres­sions when x = 2, y = 3 and z = –4.

3. s = (6 + 8 +10)/2 = 12

Area = √(12(12 — 6)(12 — 8)(12 — 10))

= √(12 x 6 x 4 x 2)

= √(24 x 24)

= 24m²

4. y — 4z = x³/6

6y — 24z= x³

x = ³√(6y — 24z)

5. y = √(x/(z+5))

y² = x/z+5

y²(z + 5) = x

z + 5 = x/y²

z = x/y²  -  5