2. Access Mathematics Transposition of Formulae

3. 2 Learning objectives After this session you should be able to: Recall simple formulae triangles to model simple engineering systems Transpose formulae in which the subject is contained in more than one term Transpose formulae which contain a root or a power

4. 3 Recap: Make x the subject Equation: 3x+2 = 23 3x+2 - 2= 23 -2 3x = 23 - 2 x = (23-2)/3 x=7 Formula: gx + h = k gx + h - h = k - h gx = k- h x = (k - h)/g Last lecture we examined the differences between equations and formulae and their subsequent solution protocols:

5. 4 Transposition Of Formulae The rules are exactly the same as for algebra, except the final result is an algebraic expression instead of a numerical answer.

6. 5 Simple Transposition In the Science units you will come across very simple formulae for instance Newton’s second law (mechanics) Electrical charge Ohms Law Density

7. 6 Recap: Simple Transposition Here the same rules apply as the letters in the formulae are just numbers in disguise

8. 7 Activity In groups make the subject of the following formulae the variable in parenthesis for: Density (m) Electrical Charge (t) Newton’s second law (a)

9. 8 Transposition of Elementary formulae Mathematical Systematic Try this one yourselves:

10. 9 Extra terms Mathematical v=u+at;t v-u=u+at-u v-u=at (v-u)/a=at/a t=(v-u)/a Systematic v=u+at;t v-u=at (v-u)/a=t Try this yourself but this time transpose for a instead

11. 10 Transposition & substitution Use any either of the methods to transpose find the the value of R given that: H=126, t=7 & I=3. Consider: What if m=2, v=5 and T=10

12. 11 Example: The pressure p in a fluid of density  at a depth h is given by: Where p a is the atmos pressure and g is gravitational acceleration. Make h the subject

13. 12 Group Activities Work in groups Discuss the solution for one the following problems Select a group member to share your solution with the class

14. 13 Class Discussion/Exercise (a,b)

15. 14 Subjects with Roots or Powers In these cases we proceed as before isolating the power or the root first Thereafter we simply us the inverse operation in order isolate the required variable i.e. take the root or raise to the power respectively e.g. Try

16. 15 Transposition inc. Roots/Powers The same procedure is employed where roots are involved. However to negate the root we raise to the appropriate power: E.g. or Try:

17. 16 Class Exercise

18. 17 Summary Have you met the learning objectives Specifically are you able to: Recall simple formulae triangles to model simple engineering systems Transpose formulae in which the subject is contained in more than one term Transpose formulae which contain a root or a power