Note that this page is being decommissioned and will be deleted after the IGCSE Further Maths exams, instead replaced with Tiffin's existing Year 1011 scheme of work that combines GCSE and IGCSE Further Maths.
#  Topic  Resources 

1  Coordinate Geometry (IGCSEFM/C1) 

2  Equations of Circles (a) Determine the equation of a circle given its radius and centre, or give an equation in another form. (b) Use coordinate geometry/Pythagoras to establish the centre/radius of a circle. (c) Find the points of intersection of a circle with the coordinate axes or another line. (d) Determine the equation of the tangent of a circle. (e) (C1 only) Use the discriminant to prove that a line does not intersect a circle. (f) Determine the points where a straight line and circle intersect by solving simultaneous equations. 
#  Topic  Resources 

3  Indices (IGCSEFM/C1) (a) (GCSE) Know your laws of indices, including negative and fractional indices. (b) Be able to use laws of indices backwards, e.g. solve x^{(3/2)} = 1/27. 

4  Expanding Brackets and Collecting Terms (IGCSEFM/C1) (a) Be able to expand two brackets which have more than two terms in each, e.g. (x + y + 1)(y  1) (b) Be able to expand three (or more) brackets, e.g. (x + 1)(x + 2)(x  3) or (x + 2)^{3}. 

5  Surds (IGCSEFM/C1) (a) Be able to simplify surds as per GCSE, such as multiplying surds, expanding brackets with surds, and simplifying surds. (b) Rationalise denominators of fractions with surds, e.g. (3√2 + 4)/(5√2  7) 

6  Factorising (IGCSEFM/C1) (a) Be able to refactorise expressions where parts have been factorised, e.g. for (2x+3)^{2}  (2x5)^{2} using difference of two squares, or (x+1)^{2} + (x+1) = (x+1)(x+1+1) (b) Be able to factorise more complex expressions by 'intelligent guessing', e.g. 15x^{2}  34xy  16y^{2}. (c) Factorise expressions involving multiple factorisation steps, e.g. x^{4}  25x^{2} 

7  Completing the Square (IGCSEFM/C1) (a) As per GCSE, be able to put quadratics of form x^{2} + bx + c into the form (x+_)^{2} + _ (b) Also be able to complete the square when the coefficient of x^{2} is not 1, i.e. put in the form a(x+b)^{2} + c or c  a(x+b)^{2} 

8  Solving Equations (IGCSEFM/C1) (a) Solve linear equations, possibly involving fractions. (b) Be able to use the quadratic formula. (c) Solve equations involving algebraic fractions. 

9  The Discriminant (C1) (a) Understand that the value of discriminant b^{2}  4ac determines whether a quadratic has two distinct roots (if it is positive), equal roots (if it is 0) or no real real (if negative). (b) Understand how the discriminant relates to the sketch of a quadratic, e.g. the graph will 'touch' the xaxis if b^{2}  4ac = 0. (c) Solve discriminant problems involving unknown coefficients of a quadratic. 

10  Sketching Graphs (IGCSEFM/C1) (a) Recognise the shapes of different types of graphs (quadratic, cubic, reciprocal). (b) Understand the features that make up a graph, i.e. roots, yintercept, max/min points and asymptotes. Understand that an asymptote is a line that a graph approaches towards infinity. (c) Be able to sketch quadratic graphs, including using the completed square to identify the min/max point. (d) Be able to sketch cubics, recognising when the graph crosses at a root (nonrepeated factor), touches (squared factor) or has a point of intersection (cubed factor). (e) [IGCSEFM only] Be able to sketch and reason about functions defined in 'pieces', including finding possible inputs for a given output. (f) [C1 only] Sketch and reason about graph transformations (as per GCSE). 

11  Domain and Range of Functions (IGCSEFM) (a) Understand how functions work, e.g. find f(x^{2}) if f(x) = 3x  5. (b) Understand that the domain is the set of possible inputs of a function and the range the possible outputs. (c) Find the domain and range of common functions, particular quadratic and trigonometric. (d) Reason about the range of functions defined in pieces (see Topic 10). (e) Construct a function for a straight line based on a given domain/range. 
#  Topic  Resources 

12  Inequalities (IGCSEFM/C1) (a) Solve linear inequalities (as per GCSE). (b) Reason about a modified inequality, e.g. find the smallest and largest value of x^{2} if 3 <= x <= 2. (c) Solve quadratic inequalities, e.g. solve x^{2}  4x  5 < 0. (d) [C1 only] Solve quadratic inequalities in the context of discriminants. 

13  Differentiation (IGCSEFM/C1) (a) Understand that dy/dx is the gradient function, and allows us to find the gradient of a curve for any value of x. Understand that dy/dx means 'the rate of change of y with respect to x'. (b) Differentiate kx^{n} where n is a positive integer or 0, and the sum of such functions. (c) Find the equation of a tangent or normal of at any point on a curve. (d) State the equations of tangents and normals to a curve at stationary points. (e) Use differentiation to find stationary points on a curve: maxima, minima and points of inflection. (f) Find the point(s) on a curve where the curve has a given gradient. (g) Sketch a curve (e.g. a cubic) with known stationary points. 
#  Topic  Resources 

14  Simultaneous Equations (IGCSEFM/C1)


15  Sequences (IGCSEFM)


16  Matrix Transformations (IGCSEFM)

#  Topic  Resources 

17  Proof


18  Algebraic Manipulations Add, multiply, divide and add algebraic fractions. 
Slides 
19  Factor Theorem


20  Trigonometric Angles


21  3D Pythagoras, Trigonometry, Sine/Cosine Rules
