Rearranging formulae

• What is a formula?

  A formula is a mathematical relationship consisting of variables, constants, and an equals sign.

  
• What are some examples of formulae you will encounter in the IGCSE course?

  Examples include formulae for areas and volumes of shapes, equations of lines and curves, and the relationship between speed, distance, and time.
• What is the equation of a straight line?


  The equation of a straight line is given by $y =$$mx +$$c$.

  
• What is the formula for the area of a trapezium?

  The area of a trapezium is given by $Area =$$\frac{(a + b)h}{2}$.
• What is Pythagoras' theorem?

  Pythagoras' theorem states that $a^2 +$$b^2 =$$c^2$.
• What does rearranging formulae mean?

  Rearranging formulae means changing the subject of the formula to isolate a specific variable.
• What is the first step in rearranging formulae?

  The first step is to remove any fractions or brackets.
• How do you remove fractions when rearranging a formula?

  You remove fractions by multiplying both sides by anything on the denominator.
• What should you do if expanding brackets does not help in rearranging a formula?

  If expanding brackets does not help, it may be easier to leave the bracket as is.
• What is the method for isolating a variable in a rearranged formula?

  You carry out inverse operations to isolate the variable you are trying to make the subject.
• How do you rearrange the formula $A =$$\frac{(a + b)h}{2}$ to make $h$ the subject?


  Multiply by 2 to get $2A =$$(a + b)h$ and then divide by $(a + b)$ to isolate $h$.
• How do you make $x$ the subject of the formula $y =$$ax^5$?


  First, divide both sides by $a$ to get $\frac{y}{a} =$$x^5$, then take the 5th root of both sides.
• What happens if $n$ is even when rearranging a formula?


  If $n$ is even, there will be two answers: a positive and a negative.
• How do you reverse an nth root in a formula?


  You reverse an nth root by raising both sides to the power of $n$.
• What are some common formulae for accelerating objects?

  Common formulae include $v =$$u +$$at$, $v^2 =$$u^2 +$$2as$, and $s =$$ut +$$\frac{1}{2}at^2$.
• What does the letter $t$ represent in the formulae for accelerating objects?


  $t$ stands for the amount of time something accelerates for (in seconds).
• What does the letter $u$ represent in the formulae for accelerating objects?


  $u$ stands for the initial speed (in m/s) - the speed at the beginning.
• What does the letter $v$ represent in the formulae for accelerating objects?


  $v$ stands for the final speed (in m/s) - the speed after $t$ seconds.
• What does the letter $a$ represent in the formulae for accelerating objects?


  $a$ stands for acceleration (in m/s²) during that time.
• What does the letter $s$ represent in the formulae for accelerating objects?


  $s$ stands for the distance covered in $t$ seconds.
• Do you need to memorize the common formulae for accelerating objects?

  No, you do not need to memorize these formulae, but you should know how to rearrange them.
• What is the difference between initial speed $(u)$ and final speed $(v)$?


  The initial speed $(u)$ is the speed at the beginning, while the final speed $(v)$ is the speed after $t$ seconds.
• What is the first step to rearranging the formula $y =$$\frac{ax^2 - b}{c}$ to make $x$ the subject?


  The first step is to square both sides.
• What should you do after squaring both sides in the rearrangement process?

  You should add $b$ to both sides.
• What is the final step to isolate $x$ in the rearrangement process?


  The final step is to square root both sides.
• What should you do if the subject appears twice in a formula?

  You will need to factorise at some point.
• How do you rearrange a formula where the subject appears inside a set of brackets?

  You will need to expand these brackets before you can begin rearranging.
• What should you do if the subject appears on two sides of a formula?

  You will need to bring those terms to the same side before you can factorise.
• How do you rearrange the formula $p =$$\frac{2 - ax}{x - b}$ to make $x$ the subject?


  Get rid of the fraction by multiplying both sides by the expression on the denominator.

  
• What is the next step after multiplying both sides by the denominator in the formula $p =$$\frac{2 - ax}{x - b}$?


  Expand the brackets on the left-hand side to 'release' the variable.

  
• What should you do after expanding the brackets in the rearrangement process?

  Bring the terms containing $x$ to one side of the equals sign and any other terms to the other side.
• How do you factorise the left-hand side of the equation to isolate $x$?


  Factorise the left-hand side to bring $x$ outside of the brackets, so that it appears only once.
• What is the final step to isolate $x$ in the formula $p =$$\frac{2 - ax}{x - b}$?


  Isolate $x$ by dividing by the whole expression.