Further Maths — Further Pure 1

Further Maths YFM01 — specification explorer

All 25 specification statements from the official Pearson Edexcel specification, as printed — filter by paper, unit or tier exactly as Pearson Edexcel assesses them.

Scope the specification

25 spec points

Unit

Every statement · FP1

Assessment homes come from the parsed Pearson specification (content summaries & assessment overviews). Hover a chip for the printed rule. Filters appear only where the qualification has that structure — a linear IGCSE has no unit scope, and only Maths A splits Foundation / Higher tiers.

1. Complex numbers

1.1
Definition of complex numbers in the form a + ib and r cos θ + i r sin θ.:
- The meaning of conjugate, modulus, argument, real part, imaginary part and equality of complex numbers should be known.
FP1
1.2Sum, product and quotient of |z 1 z 2| = |z 1| |z 2| complex numbers. Knowledge of the result arg( z z ) = arg z + arg z is not 1 2 1 2 required.FP1
1.3Geometrical representation of complex numbers in the Argand diagram. Geometrical representation of sums, products and quotients of complex numbers.FP1
1.4Complex solutions of quadratic equations with real coefficients.FP1
1.5Finding conjugate complex roots Knowledge that if z 1 is a root of f( z ) = 0 then z 1 * is and a real root of a cubic equation also a root. with integer coefficients.FP1
1.6
Finding conjugate complex roots and/or real roots of a quartic equation with real coefficients.:
- For example, (i) f(x) = x⁴ − x³ − 5x² + 7x + 10 Given that x = 2 + i is a root of f(x) = 0, use algebra to find the three other roots of f(x) = 0 (ii) g(x) = x⁴ − x³ + 6x² + 14x − 20 Given g(1) = 0 and g(−2) = 0, use algebra to solve g(x) = 0 completely.
FP1

2. Roots of quadratic equations

1. Roots of quadratic equations

2.1
Sum of roots and product of roots of a quadratic equation.:
- For the equation ax² + bx + c = 0, whose roots are α and β, then α + β = −b⁄a, αβ = c⁄a.
FP1
2.2
Manipulation of expressions involving the sum of roots and product of roots.:
- Knowledge of the identity α³ + β³ ≡ (α + β)³ − 3αβ(α + β).
FP1
2.3Forming quadratic equations with 3 3 1 1 1 1 2 new roots. For example, with roots α , β ; , ; 2 , 2 ; α + , α β α β β β + 2 ; etc. αFP1

3. Numerical solution of equations

1. Numerical solution of equations

3.1
Equations of the form f(x) = 0 solved numerically by:
- (i) interval bisection,(ii) linear interpolation,(iii) the Newton-Raphson process. rdinate systems
- f(x) will involve only functions used in P1 and P2. For the Newton-Raphson process, the only differentiation required will be as defined in unit P1 and P2.
FP1

4. Coordinate systems

1. Coordinate systems

4.1Cartesian equations for the parabola Students should be familiar with the equations: and rectangular hyperbola. 2 2 2 c y = 4 ax or x = at , y = 2 at and xy = c or x = ct , y = . tFP1
4.2
Idea of parametric equation for parabola and rectangular hyperbola.:
- The idea of (at², 2at) as a general point on the parabola is all that is required.
FP1
4.3
The focus-directrix property of the parabola.:
- Concept of focus and directrix and parabola as locus of points equidistant from focus and directrix.
FP1
4.4
Tangents and normals to these curves.:
- 1 12⁄2,y=c . Differentiation of y = 2a²x x Parametric differentiation is not required.
FP1

5. Matrix algebra integration

1. Matrix algebra integration

5.1Addition and subtraction of matrices.FP1
5.2Multiplication of a matrix by a scalar.FP1
5.3Products of matrices.FP1
5.4
Evaluation of 2 × 2 determinants.:
- Singular and non-singular matrices.
FP1
5.5
Inverse of 2 × 2 matrices. nsformations using matrices:
- Use of the relation (AB)⁻¹ = B⁻¹A⁻¹.
FP1

6. Transformations using matrices

1. Transformations using matrices

6.1
Linear transformations of column vectors in two dimensions and their matrix representation.:
- The transformation represented by AB is the transformation represented by B followed by the transformation represented by A.
FP1
6.2
Applications of 2 × 2 matrices to represent geometrical transformations.:
- Identification and use of the matrix representation of single transformations from: reflection in coordinate axes and lines y = ±x, rotation through any angle about (0, 0), stretches parallel to the x-axis and y-axis, and enlargement about centre (0, 0), with scale factor k, (k ≠ 0), where k ∈ ℝ.
FP1
6.3Combinations of transformations. Identification and use of the matrix representation of combined transformations.FP1
6.4The inverse (when it exists) of a given transformation or combination of transformations. Idea of the determinant as an area scale factor in transformations.FP1

7. Series

1. Series

7.1
Summation of simple finite series.:
- Students should be able to sum series such as ∑n r=1 r, ∑n r=1 r², ∑n r=1 r(r² + 2). The method of differences is not required.
FP1

8. Proof

1. Proof

8.1
Proof by mathematical induction. To include induction proofs for (i) summation of series n 3 1 2 2 e.g. show ∑ r = 4 n ( n + 1) or r = 1 n n ( n + 1)( n + 2) ∑ r ( r + 1) = r = 1 3 (ii) divisibility e.g. show 3 2 n + 11 is divisible by 4.
- (iii) finding general terms in a sequence e.g. if u n + 1 = 3 u n + 4 with u 1 = 1, prove that u n = 3 n − 2.
- (iv) matrix products n ( ) ( ) 1 − 3 n − n e.g. show ( − 2 − 1 ) = ( ) . ( 9 4 ) ( 9 n 3 n + 1 ) ( ) ( )
FP1