Change Of Subject Of Formula JSS3 Mathematics Lesson Note

TOPIC: CHANGE OF SUBJECT OF FORMULA

A formula is a general equation involving two or more unknowns. An example is the formula a = ¶r2  which gives the area of the circle in terms of its radius r. In this formula, a is called the subject of the formula.

Simplifying a formula by substitution

Example:

Given mx+c=y, express x in terms of m,c, and y. Find the value of x if y=10, c=2 and m is 4

Solution: mx+c= y,    mx=y-c

                  X=  y-c

                                 M

To find the value of X, X=    10-2

                                                  4

X= 8/4 =2

Evaluation: If I=  PRT

1.         Make p the subject and find the value of p if I = 10, R = 4, and T = 5.

 CHANGING THE SUBJECT OF A FORMULA

When a variable that forms a part of the formula is made subject, we say we have changed the subject of the formula.

Examples:

1.         In the formula S=2¶r(r+h), make h the subject.
2.         Make m the subject if F= mv-mu     

 Solution:   S=2¶r(r+h)

                   S=2¶r 2 +2¶rh

                   S- 2¶r 2 =2¶rh

                    S-2¶r2 =h

                    2¶r                  

2.         F =mv-mu

            Cross multiply:  FT =mv-mu

             FT =m(v-u)

            FT v-u       = m

EVALUATION

1.         Make r the subject if V =¶r 2h
2.         Make u the subject if    1/f =1/v + 1/u

READING ASSIGNMENT

1.         Exam focus for J.S.C.E Pg 212 -216
2.         Essential Maths for J.S.S.3 Pg 47-54

WEEKEND ASSIGNMENT

Express an in terms of u, v, and t in v= u+at

1.         a = vu-t (b) a= v-u  (c) a = v+u tt
2.         If Z=2p +3, find the value of Z when p=1. (a) Z=2, (b) Z= 5, (c) Z =7
3.         In the relation X = m – 6y , how would you write m in terms of x and y?

           (a) m=x-6   (b) m = 6x -6y (c) m =6x +6y

4.         Express n in terms of s, a, and L if S=n/2(a+L)

          (a) n=2(a+L)    (b) n=  2S    (c) 2S-(a-L) d. Sa+L

5.         Make U the subject if V2 = U2  +2as.

     (a) U= V 2 -2as   (b) U = (V 2 -2as) 2     (c)       V2  – 2a

THEORY

1.         Given L = arn-1, make a the subject of the formula.
2.         If S +     2t, make t the subject of the formula. Find the value of t if S=1, d= 2.