Today, we take a look at the topic of Functions. It is important to think of functions as a machine where a value is put into the function f(x) and an output is calculated. When using functions the key process is substituting the value into the function and yielding an output (imagine completing a table of values for a quadratic). You may be asked to calculate inverse functions which is the process of working backwards from the output to find the value of the number that has been put into the function. Composite functions is where you combine two or more functions to create a new (super) function.
On day 52 of the countdown, we approach the more complex topic of the Equation of a circle. There are a few areas of prior knowledge required to tackle the whole topic completely. You will need to be confident in calculating missing sides using Pythagoras' theorem (to find the radius), calculating the gradient (to find the equation of the radius and then the tangent). Knowledge of perpendicular lines will be required as well as memorising the general rule for the equation of a circle (x2+y2=r2)
Today we delve a little deeper into the topic of trigonometry, focusing on SohCahToa (mnemonic for the trig functions). You will use this when finding missing angles or side lengths in right angled triangles. The first step will be to accurately label the triangle with Opposite, Adjacent and Hypotenuse. We then have to decide which trig ratio to use to solve the problem.
You could use the formula triangles to instruct you or you could substitute values into the function and rearrange to solve.
Today we take a look at Formulae. There are many strands to Formulae that you need to be comfortable with. We take a look at creating a formula from some information given, paying particular attention to the operations that are involved.
You will be required to memorise formulae to help you solve problems and being able to substitute into a formula accurately is important in order to secure the right answer and marks.
There will be times that you will have to manipulate and rearrange the formula in order to work something else out. This is called changing the subject and is also the last thing we cover in this topic.