Ch 1: 1.1 Transposition of Formula

Changing the Subject of the formula

Chapter 1: Algebra

Remember...There is greatness within each of us, we just need to find our way to unleash it!!!

Let us contextualize some things before we start

A formula is an equation,that shows how one amount depends on one or more amounts.

Formula

An equation is a mathematical statement that shows that two mathematical expressions are equal.

​Equation

What is an Equation/Formula

How are they related...

Discuss....

What is meant by "The Subject of the Formula"

Think about this.... Link it to English, What is the subject of the sentence?

When you are talking, what is the subject of your discussions?

What is the subject of our current discussion?

Well......

The subject of the formula is the variable that is being worked out. It can be recognised as the letter on it's own on one side of the equation.

Multiple Choice

What is the subject of the formula?

$$y\ =\ mx\ +\ c$$

• y

• m

• x

• c

Multiple Choice

What is the subject of the formula?

$$2\pi r\ =\ c$$

• 2

• $$\pi$$

• r

• c

Multiple Choice

What is the subject of the formula?

$$x\ =-b\pm\sqrt[]{\frac{b^2-4ac}{2a}}$$

• a

• b

• c

• x

What do we mean by 'transposing' or 'changing the subject of the formula'

You are absolutely correct!!!

Just as you'd rearrange your room, you can rearrange the variables in a formula.

• In math, transposition literally means moving variables from one side of an equation to the next.

How is this done?

A Formula is like a scale. To keep it balance, whatever you do to one side, you must do it to the next.

Equation Scale

The point is......

• To make a variable the subject of the formula, remove all other variables from around/beside the variable you want.

• To remove a variable, undo the current operation being done to it...example, if a variable is being multiplied, divide it by the variable you want to get rid of. If something is being added, subtract it to get rid of it.

• Always remember, whatever you do to one side of a formula, you MUST do it to the next...Otherwise, the scale will not be balanced.

Example

Multiple Choice

Make X the subject of the formula.

$$y\ =\ 3x$$

• $$x=y-3$$

• $$x=3-y$$

• $$x\ =\ \frac{y}{3}$$

• $$x=\frac{3}{y}$$

Multiple Choice

Make r the subject of the formula

$$c=2\pi r$$

• $$r=\frac{2\pi}{c}$$

• $$2\pi c=r$$

• $$\frac{c}{2\pi}=r$$

• $$\frac{c}{\pi}=2r$$

Multiple Choice

Make X the subject of the formula.

y=mx+c

• $$x\ =\frac{y-c}{m}$$

• $$x\ =\ \frac{y}{m+c}$$

• $$x\ =\ \frac{y}{m-c}$$

• $$x=\ \frac{y-m}{c}$$

Multiple Choice

Make 'm' the subject of the formula.

f=ma

• $$\frac{f}{a}=m$$

• $$f-a\ =m$$

• $$m=\ \frac{a}{f}$$

• $$a-f\ =m$$

Multiple Choice

$$a-3\ =\ m\ +4$$

Transpose the formula for 'a'

• a = m + 7

• a = m - 1

• a = m + 1

• a = m - 7

Multiple Choice

Given h= $$\frac{k^3}{4}+6,$$ express k in terms of h

• $$k=\frac{4h-24}{3}$$  

• $$k=\frac{4h-6}{3}$$  

• $$k=^3\sqrt{4h-24}$$  

• $$k=^{3\sqrt{4h-6}}$$  

Multiple Choice

Given $$T=\sqrt{\frac{3}{n}}+4m,$$  express n in term of T and m.

• $$n=3\left(T-4m\right)^2$$  

• $$n=9\left(T-4m\right)^2$$  

• $$n=\frac{3}{T^2-4m^2}$$  

• $$n=\frac{3}{\left(T-4m\right)^2}$$  

Multiple Choice

Given $$\frac{m-2n}{p}=n-4$$  , express n in terms of m and p.

• $$\frac{m-4p}{p-2}$$  

• $$\frac{m-4p}{p+2}$$  

• $$\frac{m+4p}{p-2}$$  

• $$\frac{m+4p}{p+2}$$  

Multiple Choice

Given $$\frac{p^2-3r}{2}=4$$  , express p in terms of r

• 8+6r

• 8+3r

• $$\sqrt{8+3r}$$  

• $$\sqrt{8+6r}$$  

Multiple Choice

Given $$2m=\frac{n}{n-5}$$  , express n in terms of m.

• $$n=\frac{2m+1}{10}$$  

• $$n=\frac{2m-1}{10m}$$  

• $$n=\frac{10m}{2m+1}$$  

• $$n=\frac{10m}{2m-1}$$  

Multiple Choice

Ungkapkan x dalam sebutan y dan w.

Express x in terms of y and w.

Multiple Choice

Ungkapkan x dalam sebutan y.

Express x in terms of y.

Multiple Choice

Given $$w=\frac{v\left(2-w\right)}{v-1}$$  , express v in terms of w.

• $$v=\frac{1+w}{w-2}$$  

• $$v=\frac{w}{2w-2}$$  

• $$v=\frac{1}{2w-2}$$  

• $$v=\frac{w-2}{w}$$  

Multiple Choice

Given $$\frac{6e-2f}{3}=ef+f$$ , express e in terms of f.

• $$e=\frac{3f}{5f-6}$$  

• $$e=\frac{3f}{6-3f}$$  

• $$e=\frac{5f}{3f-6}$$  

• $$e=\frac{5f}{6-3f}$$  

Multiple Choice

Given $$p=\sqrt{9q^2-3}$$ , express q in terms of p.

• $$q=\frac{p+3}{9}$$  

• $$q=\frac{p^2+3}{9}$$  

• $$q=\sqrt{\frac{p^2+3}{3}}$$  

• $$q=\frac{\sqrt{p^2+3}}{3}$$  

Multiple Choice

If $$m=\frac{n}{n-1}$$ , then n=

• $$\frac{m}{m-1}$$  

• $$\frac{m+1}{m}$$  

• $$\frac{1}{m-1}$$  

• $$\frac{m}{m+1}$$  

Multiple Choice

Given $$u=\sqrt{\frac{1+2t}{1-2t}}$$  , express t in terms of u.

• $$\frac{u^2-1}{4}$$  

• $$\frac{u-1}{4}$$  

• $$\frac{u-1}{2\left(u+1\right)}$$  

• $$\frac{u^2-1}{2\left(u^2+1\right)}$$  

Multiple Choice

Given that m = –3q + p , express q in terms of m and p.
Diberi m = –3q + p, ungkapkan q dalam sebutan m dan p.

• $$q\ =\ \frac{p\ +\ m}{3}$$  

• $$q\ =\ \frac{m\ -\ p}{3}$$  

• $$q\ =\ \frac{p\ -\ m}{3}$$  

• $$q\ =\ -\frac{p\ -\ m}{3}$$  

Multiple Choice

Which of the following is true?

• (a-b)² = a² - b²
• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab - b²
• (a + b) (a - b) = a² - 2ab + b²

Multiple Choice

A rectangle is r cm long, s cm wide and has an area of P cm². Express P in terms of r and s.

• P = rs
• P = r ∕ s
• P = 2rs
• P = (rs)²