Algebraic formulae

• What is a formula in mathematics?


  A formula is a mathematical rule that uses letters to represent changing amounts.
• How do formulae and equations differ?


  Formulae are always true, while equations only work for certain values.
• What is the formula for the area of a triangle?


  The area of a triangle is given by $\text{Area} =$$\frac{1}{2} b h$.
• What does substitution mean in mathematics?


  Substitution is the process of replacing letters with numbers to calculate the value of an expression.
• How would you substitute values into the expression $2b^2c$ if $b=$$4$ and $c=$$3$?


  By substituting, $2b^2c =$$2 \times 4^2 \times 3$.
• How do you evaluate the expression $d+$$(3e+f)$ if $d=$$2$, $e=$$3$, and $f=$$1$?


  First substitute: $d+$$(3e+f) =$$2+$$(3 \times 3 + 1)$, then follow BIDMAS.
• What is BIDMAS and how is it used?


  • BIDMAS stands for Brackets, Indices, Division and Multiplication, Addition and Subtraction.
  • It is used to determine the order of operations when evaluating expressions.
• How would you substitute $20°C$ into the formula $f =$$\frac{9}{5}c +$$32$?


  Substituting gives $f =$$\frac{9}{5}(20) +$$32$.
• Why are formulae created in mathematics?


  • Formulae are created for calculations that are performed frequently.
  • They help in simplifying complex calculations into a single expression.
• How would you write a formula to calculate the total cost of a job for a plumber with a call-out fee of £40 and an hourly rate of £8?


  The formula is $T =$$40 +$$8h$, where $h$ is the number of hours worked.
• If a plumbing job took 2 hours, what would be the total cost using the formula $T =$$40 +$$8h$?


  The total cost would be $T =$$40 +$$8 \times 2 =$$56$.
• What is the subject of a formula?


  • The subject of a formula is the variable that is being solved for.
  • It is represented by a letter that stands alone in the equation.
• How do you rearrange the formula $A =$$bh$ to make $b$ the subject?


  Rearranging gives $b =$$\frac{A}{h}$.
• How do you rearrange the formula $v =$$u +$$At$ to make $t$ the subject?


  Rearranging gives $t =$$\frac{v - u}{A}$.
• What are the steps to rearranging a formula?


  1. Simplify the formula.
  2. Perform the opposite operation to isolate the variable.
  3. Continue rearranging until the variable is alone.