Subject content
This is an extract of the full specification, which you can download from this page.
Specification
 Specification for pilot from 2009 (442.9 KB)
3.7 FSMQ Calculus (9998)
Calculus (9998)
This qualification has been developed to allow you to demonstrate your ability to use
 differentiation
 integration
 differential equations
to analyse, make sense of and describe real world situations and to solve problems. You will also investigate the use of numerical methods to find gradients and evaluate integrals and compare these with analytic methods.
Before you start this qualification  You must:  This includes: 
be able to use algebraic methods to rearrange and solve linear and quadratic equations  Solution of a quadratic equation by at least one of the following methods:
 
have knowledge of basic functions and how geometric transformations can be applied to them using
 being familiar with graphs and functions of:

Using calculators and computers
Using calculators and computers
When carrying out calculations, you may find the use of a standard scientific calculator sufficient.
You should learn to use your calculator effectively and efficiently. This will include learning to use:
 memory facilities
 function facilities (e.g., )
It is important that you are also able to carry out certain calculations without using a calculator, using both written methods and 'mental' techniques.
Whenever you use a calculator you should record your working as well as the result.
Understanding and using differentiation
Understanding and using differentiation  You should learn to:  This includes: 
understand and calculate gradient at a point,
, on a function
using the numerical approximation:
where is small  understanding how to improve the calculation of gradient at a point by using a smaller interval,  
understand and interpret gradients in terms of their physical significance  
understand and use the correct units with which to measure gradients /rates of change  
sketch graphs of gradient functions 
 
identify the key features of gradient functions in terms of the gradient of the original function 
 
understand how can be used to generate a gradient function  
differentiate functions 
 
Differentiate
 
find the second derivatives of functions  using notations and  
identify the key features of a second derivative 
 
Applications of differentiation to gradients, maxima and minima and stationary points, increasing and decreasing functions 

Understanding and using integration
Understanding and using integration  You should learn to:  This includes: 
estimate areas under graphs of functions using numerical methods 
 
understand and find areas under curves, between and using ,  
understand integration as the reverse process of differentiation  
understand and determine indefinite integrals of functions 
 
Integration by inspection and by one use of integration by parts 
 
understand the idea of constant of integration and be able to calculate this in known situations  
be able to determine definite integrals for functions 

Understanding and using differential equations
Understanding and using differential equations  You should learn to:  This includes: 
find families of solutions to first order differential equations with separable variables 
