Essential prior knowledge:-

National 5 Maths; E+F 1.1b, E+F 1.2a, E+F 1.2b, APP 1.3b

• Laws of indices
• Multiplying out brackets
• Factorising expressions
• Adding, subtracting and multiplying fractions

Contents:-

6.1 - Learning to differentiate

6.2 - Rate of change

6.3 - Tangent to curve

6.4 - Increasing/decreasing functions

6.5 - Stationary points/curve sketching

6.6 - Closed intervals

6.7 - Optimisation

In this module we learn the process of differentiation. Bronze serves as a basic introduction and silver level moves onto fractional indices. Prior knowlesge of National 5 indice laws is essenntial here! At gold level we learn how to differentiate terms in brackets and we look at how to differentiate more complicated fractions.

Video 49: Outcome 1 - Basic differentiation. Grab a pen and your Rigour jotter. Make sure you try all the questions!

Video 50: Outcome 2 - Differentiation with fractions and indices. Remember to copy down the worked examples and take notes. These will help you revise and remember!

Video 51: Outcome 3 - Harder differentiation. This is the final video in this module. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?

In this module we learn how to calculate the derivative at a particular point starting off with nice easy derivatives for bronze level. After this, we look at harder differentiation at silver level - knowing your indice rules is a must for this section! We finish up at gold level where we learn how to calculate the rate of change of a function.

Video 52: Outcome 1 - Finding the derivative at a particular point. Grab a pen and your Rigour jotter. Make sure you try all the questions!

Video 53: Outcome 2 - Harder substitution. Remember to copy down the worked examples and take notes. These will help you revise and remember!

Video 54: Outcome 3 - Rates of change. This is the final video in this module. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?

In the bronze section of this module we learn how to calculate the gradient of the tangent to a curve. We build on this at silver level where we discover how to calculate the equation of the tangent. We finish up with our gold section where we learn how to calculate a point when given the gradient.

Video 55: Outcome 1 - The gradient of the tangent to a curve. Grab a pen and your Rigour jotter. Make sure you try all the questions!

Video 56: Outcome 2 - The equation of the tangent to a curve. Remember to copy down the worked examples and take notes. These will help you revise and remember!

Video 57: Outcome 3 - Calculating a point when given the gradient. This is the final video in this module. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?

In this module we learn how to calculate the range of values for x within increasing and decreasing functions. We also learn how to calculate the values of x where functions are stationary. After this, we learn how to sketch the graph of the derived function, i.e. the graph of y = f'(x). A simple procedure that is often forgotten so this practice is thoroughly recommended!

Video 58: Outcome 1 - Increasing/decreasing functions. Grab a pen and your Rigour jotter. Make sure you try all the questions!

Video 59: Outcome 2 - Stationary functions. Remember to copy down the worked examples and take notes. These will help you revise and remember!

Video 60: Outcome 3 - Sketching the graph of the derived function. This is the final video in this module. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?

In this tutorial we learn at bronze level how to calculate the coordinates of stationary points. At silver level we discover how to determine their nature. Well worth a watch! Remember to try ALL questions. At gold level, we take you through the whole 8-15 mark process of sketching a curve including calculating the y-intercept, finding the roots and calculating stationary points. This video is ESSENTIAL viewing!

Video 61: Outcome 1 - Calculating the coordinates of stationary points. Grab a pen and your Rigour jotter. Make sure you try all the questions!

Video 62: Outcome 2 - Determining the nature of stationary points. Remember to copy down the worked examples and take notes. These will help you revise and remember!

Video 63: Outcome 3 - Curve sketching. This is the final video in this module. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?

In this module we learn how to calculate the maximum and minimum values of a function within a given closed interval. Prior knowlege of stationary points is essential here!

Video 64: Outcome 1 - Maximum or minimum values within a closed interval. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?

In this module we learn about the idea of "opitimisation" within a variety of real life applications. Being able to find the coordinates of stationary points and to determine their nature is essential prior knowledge here!

Video 65: Outcome 1 - Optimisation. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?