First Principles Differentiation What is differentiation from first principles? Differentiation from first principles uses the definition of the derivative of a function f(x) The definition is How...
Limits What are limits in mathematics? When we consider a limit in mathematics we look at the tendency of a mathematical process as it approaches, but never quite reaches, an ‘end point’ of some so...
Differentiation for Kinematics How is differentiation used in kinematics? Displacement, velocity and acceleration are related by calculus In terms of differentiation and derivatives velocity is the...
Displacement, Velocity & Acceleration What is kinematics? Kinematics is the branch of mathematics that models and analyses the motion of objects Common words such as distance, speed and acceler...
Modelling with Differentiation What can be modelled with differentiation? Recall that differentiation is about the rate of change of a function and provides a way of finding minimum and maximum val...
Negative Integrals The area under a curve may appear fully or partially under the x-axis This is given in the formula booklet How do I find the area under a curve when the curve is fully under the ...
Definite Integrals What is a definite integral? The constant of integration (“+c”) is not needed in definite integration “+c” would appear alongside both F(a) and F(b) subtracting means the “+c”’s ...
Integrating Composite Functions (ax+b) What is a composite function? A composite function involves one function being applied after another A composite function may be described as a “function of a...
Integrating Trig Functions How do I integrate sin, cos and sec^2? The antiderivatives for sine and cosine are For calculus with trigonometric functions angles must be measured in radians Ensure you...
