Further Pure Maths 2 (FP2) Curriculum Map
Inequalities
Solving inequalities by manipulation
Solving inequalities graphically
Series
Using the method of differences to sum infinite series
Further complex numbers
The modulus-argument form
Euler's relation
Multiplying and dividing two complex numbers
De Moivre's theorem
De Moivre's theorem applied to trigonometric identities
Using de Moivre's theorem to find the nth roots of a complex number
Using complex numbers to represent a locus of points on an Argand diagram
Using complex numbers to represent regions on an Argand diagram
Applying transformations that map points on the z-plane to points on the w-plane by applying a formula relating z = x + iy to
w = u + iv
First order differential equations
Solving first order differential equations with separable variables and the formation of differential equations and sketching members
of the family of solution curves
Solving exact equations where one side is the exact derivative of a product and the other side can be integrated with respect to x
Solving first order linear differential equations of the type dy/dx + Py = Q, where P and Q are functions of x, by multiplying through
the equation by an integrating factor to produce an exact equation
Using a given substitution to reduce a differential equation into one of the above types of equation, which you can then solve.
Second order differential equations
2
Finding the general solution of the linear second order differential equation𝑎 𝑑𝑑𝑥𝑦2 + 𝑏
where a, b and c are constants and where b2 > 4ac
2
Finding the general solution of the linear second order differential equation𝑎 𝑑𝑑𝑥𝑦2 + 𝑏
𝑑𝑦
𝑑𝑥
𝑑𝑦
𝑑𝑥
+ 𝑐𝑦 = 0
+ 𝑐𝑦 = 0
where a, b and c are constants and where b2 = 4ac
2
Finding the general solution of the linear second order differential equation𝑎 𝑑𝑑𝑥𝑦2 + 𝑏 𝑑𝑦
+ 𝑐𝑦 = 0
𝑑𝑥
2
where a, b and c are constants and where b < 4ac
2
Finding the general solution of the linear second order differential equation 𝑎 𝑑𝑑𝑥𝑦2 + 𝑏 𝑑𝑦
+ 𝑐𝑦 = 𝑓(𝑥)
𝑑𝑥
where a, b and c are constants, by using y = complementary function + particular integral
Using boundary conditions, to find a specific solution of the linear second order differential equation
𝑑2 𝑦
𝑑𝑦
𝑎 2+ 𝑏
+ 𝑐𝑦 = 𝑓(𝑥), where a, b and c are constants, or initial conditions to find a specific solution of the linear second order
𝑑𝑥
𝑑𝑥
2
differential equation 𝑎 𝑑𝑑𝑡𝑥2 + 𝑏 𝑑𝑥
+ 𝑐𝑥 = 𝑓(𝑡)where a, b and c are constants
𝑑𝑡
Using a given substitution to transform a second order differential equation into one of the above types of equation, and solving it
Maclaurin and Taylor series
Finding and using higher derivatives of functions
Expressing functions of x as an infinite series in ascending powers of x using Maclaurin's expansion
Finding the series expansions of composite functions using known Maclaurin's expansions.
Finding an approximation to a function of x dose to x = a, where a ≠ 0, using Taylor's expansion of the function
Finding the solution, in the form of a series, to a differential equation using the Taylor series method
Polar coordinates
Polar and Cartesian coordinates
Polar and Cartesian equations of curves
Sketching polar equations
Areas using polar coordinates
Finding tangents parallel and perpendicular to the initial line
Revision using Past papers
Mock examination