Julie Beaumont
Use algebra in different contexts Create your own equation State two rules when using simple algebra
Algebra Algebra
We often use formulas without even noticing. For example, we might convert miles to km by multiplying by 1.6, or find the circumference of a circle by multiplying pi by the diameter. km = 1.6 x miles is an example of a formula.
We have already seen that km = 1.6 x miles and C = × d are examples of formulas. There are many others that we use regularly in other subjects. Sometimes we have to construct our own formula:
A taxi firm charges 50p per mile plus a fixed charge of £2.00. Write down a formula for the cost (C) of hiring this taxi to travel ‘n’ miles.
Travelling 1 mile would cost £2 + 50p. Travelling 2 miles would cost £2 + 2 x 50p. Travelling 3 miles would cost £2 + 3 x 50p. So travelling for 'n' miles will cost £2 + n x 50p. The formula is C = £2 + (n x 50p)
A rectangle has a width of x and a length of 2x. Write down a formula for the perimeter (P) in terms of x. Answer P = 2x + x + 2x + x Did you remember to include all 4 sides? So P= 6x
words and symbols in expressions and formulae represent variable quantities (i.e. numbers) not things ie 2a + 2b cannot be explained as 2 apples and 2 bananas the contents of brackets must be worked out first when there is no operator between a number and a variable, two variables, or a bracket, multiplication is implied
To recap, the cost (C) of hiring this taxi to travel ‘n’ miles, when a taxi firm charges 50p per mile plus a fixed charge of £2.00 is:- C = £2 + (n x 50p) To find the cost of the taxi for a journey of 20 miles, replace 'n' with 20. C = £2 + (20 x 50p) C = £2 + £10 C = £12
What is the cost of hiring this taxi for 16 miles? Remember the formula - C = £2 + (n x 50p) £10 Remember that C = £2 + (16 x 50p) = £2 + £8 = £10
Find the value of W using the given information T= 18 U = 3 W = T/U Answer = 6
Complete the worksheets given to you to practise your new skills