Rearranging Formulae Flashcards

All 6 cards in this deck

What are the steps to change the subject of a formula where the new subject appears once?

e.g. make $x$ the subject of $y=\frac{3x+1}{5}$

1. Multiply both sides by the denominator: $5y=3x+1$
2. Undo the addition: $5y-1=3x$
3. Divide by the coefficient: $x=\frac{5y-1}{3}$

What are the steps to make a variable the subject of a formula written as a single algebraic fraction?

e.g. make $y$ the subject of $w=\frac{y^{2}+5}{y^{2}-2}$

1. Multiply both sides by the denominator: $w(y^{2}-2)=y^{2}+5$
2. Expand and collect the $y^{2}$ terms on one side, then factorise: $y^{2}(w-1)=2w+5$
3. Divide, then take the root: $y=\pm\sqrt{\frac{2w+5}{w-1}}$

What are the steps to make a letter the subject of a reciprocal formula?

e.g. make $u$ the subject of $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

1. Isolate the reciprocal of the new subject: $\frac{1}{u}=\frac{1}{f}-\frac{1}{v}$
2. Write the other side as a single fraction: $\frac{1}{u}=\frac{v-f}{fv}$
3. Take the reciprocal of both sides: $u=\frac{fv}{v-f}$

What are the steps to derive a printed result in a 'show that' rearrangement question?

e.g. four identical frames each use lengths $3x$, $2x$, $x$ and $2y$, and the total length is $300$. Show that $y=\frac{75-6x}{2}$

1. Form the equation from the information: $4(3x+2x+x+2y)=300$
2. Expand and collect like terms: $24x+8y=300$
3. Rearrange to the printed form: $8y=300-24x$, so $y=\frac{75-6x}{2}$

In a 'show that' rearrangement question, what must your working end with for the accuracy mark?

The printed result, fully simplified, with no incorrect equations seen in the working.

What are the steps to express one variable in terms of another from two given formulae?

e.g. a cone of radius $r$ and height $x$ has four times the volume of a prism of volume $\frac{1}{2}y^{2}x$; find $r$ in terms of $y$

1. Write each formula: cone $=\frac{1}{3}\pi r^{2}x$, prism $=\frac{1}{2}y^{2}x$
2. Form the equation with the multiplier processed: $\frac{1}{3}\pi r^{2}x=2y^{2}x$
3. Cancel the common variable and rearrange: $r=\sqrt{\frac{6y^{2}}{\pi}}$