# 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

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
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

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