EDEXCEL Further Pure Mathematics (4PM1) IGCSE Topic Questions

1 Logarithmic functions and indices

A: The functions ax and logb x (where b is a natural number greater than one)

B: Use and properties of indices and logarithms, including change of base

C: Simple manipulation of surds

D Rationalising the denominator

2 The quadratic function

A: The manipulation of quadratic expressions

B: The roots of a quadratic equation

C: Simple examples involving functions of the roots of a quadratic equation

3 Identities and inequalities

A: Simple algebraic division

B: The factor and remainder theorems

C: Solutions of equations, extended to include the simultaneous solution of one linear and one quadratic equation in two variables

D: Simple inequalities, linear and quadratic

E The graphical representation of linear inequalities in two variables

4 Graphs

A: Graphs of polynomials and rational functions with linear denominators

B: The solution of equations and transcendental functions by graphical methods

5 Series

A: Use of the ∑ notation

B: Arithmetic and geometric series

6 The binomial series

A: Use of the binomial series (1 + x) n

7 Scalar and vector quantities

A: The addition and subtraction of coplanar vectors and the multiplication of a vector by a scalar

B: Components and resolved parts of a vector

C: Magnitude of a vector

D:Position vector

E: Unit vector

F: Use of vectors to establish simple properties of geometrical figures

8 Rectangular Cartesian coordinates

A: The distance between two points

B: The point dividing a line in a given ratio

C: Gradient of a straight line joining two points

D: The straight line and its equation

E: The condition for two lines to be parallel or to be perpendicular

9 Calculus

A: Differentiation and integration of sums of multiples of powers of x (excluding integration of 1x),sin ,cos ,eax

B: Differentiation of a product, quotient and simple cases of a function of a function

C: Applications to simple linear kinematics and to determination of areas and volumes

D: Stationary points and turning points

E: Maxima and minima

F: The equations of tangents and normals to the curve y = f(x)

G: Application of calculus to rates of change and connected rates of change

10 Trigonometry

A: Radian measure, including use for arc length and area of sector

B: The three basic trigonometric ratios of angles of any magnitude (in degrees or radians) and their graphs

C: Applications to simple problems in two or three dimensions (including angles between a line and a plane and between two planes)

D: Use of the sine and cosine formulae

E: The identity 2 2 cos sin 1

F: Use of the identity tanθ = sinθ / cosθ

G: The use of the basic addition formulae of trigonometry

H: Solution of simple trigonometric equations for a given interval