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Core-4-Mathematics---Kangaroo-Maths---Exciting-Resources-for-Maths-

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					                                                                                                       C4 (EDEXCEL)
                                                                                   ICT Resources                                                       Success For All
                                                                                       including                GlosMaths
Topic                                    Objectives                                                                            Assessment                    and
                                                                              Bring on the Maths (BOTM)         Resources
                                                                                Match Up Maths (MUM)                                                   other resources


                                                                                                        C4 Mindmap
                         Prior Knowledge:
                          Simplification of rational expressions including factorising and cancelling (C3)
                         Rational functions.                                    *BOTM*                                            On Target                       NRich
                         Partial fractions (denominators not more               Identifying partial fractions                                         Complex Partial Fractions
                         complicated than repeated linear terms).               Finding partial fractions                                             (first part of this problem)
                                                                                Improper partial fractions
                                                                                The mixed bag
 Algebra and Functions




                                                                                                                            True, Never, Sometimes;
                                                                                                                                 Teacher Notes




                                                                                                                                Mathsnet Exam
                                                                                                                                  Questions




                                                                                  Things to make you go hmmmmmm…….

                                                                                                                                  Produced for GlosMaths by S Lomax
                                                                                                       C4 (EDEXCEL)
                                                                                   ICT Resources                                                                                                    Success For All
                                                                                       including                               GlosMaths
Topic                                  Objectives                                                                                                                   Assessment                            and
                                                                              Bring on the Maths (BOTM)                        Resources
                                                                                Match Up Maths (MUM)                                                                                                other resources

                       Prior Knowledge:
                        Plot graphs of linear, quadratic, cubic functions, the reciprocal function y = 1/x, x ≠ 0, the exponential function y = kx for integer values of x and simple positive values of k, the trigonometrical
                         functions, using a spreadsheet of graph plotter as well as pencil and paper; recognise the characteristic shapes of all these functions (C1)
                       Solution of simultaneous equations. Analytical solution by substitution (C1)
 Coordinate Geometry




                       Cartesian and parametric equations of                   *BOTM*                                                                                    On Target                        A14
                       curves and conversion between the two                   Cartesian or parametric                                                                                                 EXPLORING
                       forms.                                                  Points on parametrics                                                                                                  EQUATIONS IN
                                                                               Parametric pictures                                                                                                  PARAMETRIC FORM
                                                                                                                                                                True, Never, Sometimes;
                                                                                                                                                                     Teacher Notes                           RISP 27

                                                                                                                                                                                                             RISP 29

                                                                                                                                                                     Mathsnet Exam
                                                                                                                                                                       Questions                           NRich
                                                                                                                                                                                                     Folium of Descartes




                                                                                 Things to make you go hmmmmmm…….




                                                                                                                                                                        Produced for GlosMaths by S Lomax
                                                                                               C4 (EDEXCEL)
                                                                                 ICT Resources                                                Success For All
                                                                                     including          GlosMaths
Topic                                   Objectives                                                                     Assessment                   and
                                                                            Bring on the Maths (BOTM)   Resources
                                                                              Match Up Maths (MUM)                                            other resources

                        Prior Knowledge:
                         Binomial expansion of (1+x)n for a positive integer n (C2)

                                                   n
                         The notations n! and (     ) (C2)
 Sequences and Series




                                                   r

                         Multiplying fractions and integers


                         Binomial series for any rational n.                 *BOTM*                                       On Target                RISP 19
                                                                             Valid expansions
                                                                             Rational powers
                                                                             Binomial with a twist                  True, Never, Sometimes;        RISP 22
                                                                             Partial binomials                           Teacher Notes

                                                                                                                                                    NRich
                                                                                                                        Mathsnet Exam           Discrete Trends
                                                                                                                          Questions




                                                                               Things to make you go hmmmmmm…….




                                                                                                                          Produced for GlosMaths by S Lomax
                                                                                           C4 (EDEXCEL)
                                                                         ICT Resources                                                          Success For All
                                                                             including                    GlosMaths
Topic                             Objectives                                                                             Assessment                   and
                                                                    Bring on the Maths (BOTM)             Resources
                                                                      Match Up Maths (MUM)                                                      other resources


                   Prior Knowledge:
                    Cartesian and parametric equations of curves and conversion between the two forms.
                    y = ax and its graph (C2)
                    Indefinite integration as the reverse of differentiation (C1)
                    Integration of xn (C1)
                   Differentiation of simple functions defined        *BOTM*                                                On Target                 NRich
                   implicitly or parametrically.                      Implicit functions                                                            Squareness
                                                                      Implicit differentiation                                                  Folium of Descartes
 Differentiation




                                                                      Parametric differentiation
                                                                      Parametric areas
                                                                      Areas with a twist

                   Exponential growth and decay                                                                       True, Never, Sometimes;
                                                                                                                           Teacher Notes




                   Formation of simple differential equations         *BOTM*                                                                         RISP 28
                                                                      Differential equations
                                                                                                                          Mathsnet Exam              RISP 30
                                                                                                                            Questions
                                                                                                                                                      NRich
                                                                                                                                                 Integral Equation




                                                                        Things to make you go hmmmmmm…….




                                                                                                                            Produced for GlosMaths by S Lomax
                                                                                             C4 (EDEXCEL)
                                                                          ICT Resources                                                          Success For All
                                                                             including                     GlosMaths
Topic                          Objectives                                                                                        Assessment            and
                                                                    Bring on the Maths (BOTM)              Resources
                                                                      Match Up Maths (MUM)                                                       other resources

               Prior Knowledge:
                Indefinite integration as the reverse of differentiation (C1)
                Integration of xn (C1)
                Evaluation of definite integrals (C2)
                Interpretation of the definite integral as the area under a curve (C2)
                Approximation of area under a curve using the trapezium rule (C2)
                Differentiation of ex , lnx, sinx, cosx and tanx and their sums and differences (C3)
                Differentiation using the product rule, the quotient rule, the chain rule (C3)
 Integration




                               dy      dy
                The use of       = 1/    (C3)
                               dx      dx
                Simplification of rational expressions including factorising and cancelling (C3)
                Partial fractions (C4)
                Formation of simple differential equations (C4)
                Solve problems involving volumes of right prisms, cylinders, cones and spheres
                                 x    1                               *BOTM*                            Log cabin or beachhut?
               Integration of e ,       , sinx, cosx                  Standard functions                     Maths poetry          On Target
                                      x                               Logarithms
                                                                                                               E Jokes

                                                                                                           SIC is negative

                                                                                                           Find your buddy




                                                                                                                                  Produced for GlosMaths by S Lomax
                                                                        C4 (EDEXCEL)
                                                       ICT Resources                                                                            Success For All
                                                             including                 GlosMaths
Topic                Objectives                                                                                        Assessment                     and
                                                    Bring on the Maths (BOTM)          Resources
                                                      Match Up Maths (MUM)                                                                      other resources

        Simple cases of integration by               BOTM                                                   dx
                                                                                i) Where does y = ∫ x )
                                                                                                  f(           du
           i)      substitution                      Simple substitution                                    du
                                                     Definite substitution
                                                                                         come from?;
                                                     Harder substitution
                                                     Integrating tanx
        and                                          Integrating lnx
                                                                                    Unjumble with a twist;
                                                     Trigonometry
                                                                                       Teacher Notes
                                                     Definite Integration
              ii)   integration by parts.            Making decisions
                                                                                     ii) Unjumble cyclic;
                                                                                                                    Standard, substitution or
                                                                                        Teacher Notes
         These methods as the reverse process of                                                                     parts*; Teacher Notes
        the chain and product rules respectively.
                                                                                *Gotta be, could be, can’t be*;
                                                                                       Teacher Notes

                                                                                 Fifty ways to do an integral
                                                                                                                    True, Never, Sometimes;
                                                                                                                         Teacher Notes
        Simple cases of integration using partial    BOTM
        fractions                                    Harder Logarithms




        Evaluation of volume of revolution.          BOTM                            Deriving V = π ∫dx
                                                                                                    y2                                              RISP 25
                                                     Volumes
                                                     Parametric volumes                                                 Mathsnet Exam
                                                                                          *Trio*;
                                                                                       Teacher Notes                      Questions

                                                                                       Cone Unjumble;
                                                                                       Teacher Notes

                                                                                      Sphere Unjumble;
                                                                                       Teacher Notes




                                                                                                                          Produced for GlosMaths by S Lomax
                                                                    C4 (EDEXCEL)
                                                       ICT Resources                                                               Success For All
                                                             including                 GlosMaths
Topic                 Objectives                                                                                   Assessment            and
                                                    Bring on the Maths (BOTM)          Resources
                                                      Match Up Maths (MUM)                                                         other resources

        Analytical solution of simple first order                               *Differential equation buddies*;                         RISP 30
        differential equations with separable                                           Teacher Notes
        variables.                                                                                                                       NRich
                                                                                                                                      Out in Space
        Numerical integration of functions.                                                                                        Mechanical Integration




                                                     *Things to make you go hmmmmmm…….*




                                                                                                                    Produced for GlosMaths by S Lomax
                                                                                       C4 (EDEXCEL)
                                                                    ICT Resources                                                                                      Success For All
                                                                        including                             GlosMaths
Topic                      Objectives                                                                                                             Assessment                 and
                                                               Bring on the Maths (BOTM)                      Resources
                                                                 Match Up Maths (MUM)                                                                                  other resources

           Prior Knowledge:
            Understand and use vector notation;
            Calculate and represent graphically the sum of two vectors, the difference of two vectors and a scalar multiple of a vector;
            Calculate the resultant of two vectors;
            Understand and use the commutative and associative properties of vector addition;
            Solve simple geometrical problems in 2-D using vector methods
            Multiplication of integers
            Find the gradient of lines given by equations of the form y = mx + c (when values are given for m and c )
            Understand that the form y = mx + c represents a straight line and that m is the gradient of the line, and c is the value of the y intercept
            The sine and cosine rules
            Area of a triangle = ½absinC
           Vectors in 2 and 3 dimensions.                        BOTM                                            Vector Song                                                    NRich
                                                                 Basic skills                                                                          On Target       Article: Vectors – What
           Magnitude of a vector .                                                                              Quick History                                                 Are They?
 Vectors




                                                                 Position vectors
                                                                 A mixed bag
           Algebraic operations of vector addition,                                                               *Trio*;
           subtraction and multiplication by a scalar,                                                         Teacher Notes
           and their geometrical interpretations
                                                                                                        *Vector terminology loop*;
           Position vectors. The distance between                                                            Teacher Notes
           two points.
                                                                                                             *Vector intro loop*;
           The orthogonal unit vectors.                                                                        Teacher Notes

                                                                                                        *Position vector buddies*;
                                                                                                             Teacher Notes                    *Treasure Hunt (Easy)*
            The scalar product. Its use for                      *BOTM*                                   Deriving the formula;                                                 NRich
            calculating the angle between two lines.             Dot Product                                 Student version                    Treasure Hunt (Hard)   Article: Multiplication of
                                                                                                                                                                                Vectors
                                                                                                               World problem                                                   Cubestick
                                                                                                                                                                             Flexi Quads
                                                                                                                                                                              Tetra Perp




                                                                                                                                                      Produced for GlosMaths by S Lomax
                                                           C4 (EDEXCEL)
                                        ICT Resources                                                                 Success For All
                                              including              GlosMaths
Topic                Objectives                                                                Assessment                   and
                                     Bring on the Maths (BOTM)       Resources
                                       Match Up Maths (MUM)                                                           other resources

        Vector equations of lines.    BOTM                            Cartesian link                                      RISP 29
                                      Equations of lines
                                      Intersecting lines               *Unjumble*;          True, Never, Sometimes;
                                                                      Teacher Notes              Teacher Notes

                                                                  *Trio Vector Equation*;
                                                                      Teacher Notes

                                                                     *Trio Vector link
                                                                     with Cartesian*;
                                                                      Teacher Notes             Mathsnet Exam
                                                                                                  Questions
                                                                  *Trio Perpendicular and
                                                                    Intersecting lines*;
                                                                       Teacher Notes

                                      *Things to make you go hmmmmmm…….*




                                                                                                  Produced for GlosMaths by S Lomax
                                                                       C4 (EDEXCEL)
                                                          ICT Resources                                         Success For All
                                                                including          GlosMaths
Topic                    Objectives                                                            Assessment             and
                                                       Bring on the Maths (BOTM)   Resources
                                                         Match Up Maths (MUM)                                   other resources

 Formulae that students are expected to remember and that may not be included in formulae booklets.


 Integration

 Function                        Integral
                                 1
 cos kx                            sin k x + c
                                 k
                                   1
 sin kx                           cos k x + c
                                   k
                                 1 kx
 ekx                               e +c
                                 k
  1
                                 ln x + c, x  0
  x
  f  ( x)  g ( x)             f ( x) + g ( x) + c
  f  (g ( x)) g ( x)           f ( x) + g ( x) + c




 Vectors

   x   a
     
   y    b   xa  yb  zc
   z  c 
     




                                                                                                 Produced for GlosMaths by S Lomax

				
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