SlideShare una empresa de Scribd logo
1 de 16
Descargar para leer sin conexión
C4 Revision Notes
Binomial expansions
• General binomial expansion, for           :




• When the series is infinite, this is only valid if |x|<1

• (a+x)n should be written as
Partial fractions
• A proper algebraic fraction with a denominator which factorises can be
  decomposed into a sum of partial fractions. Following forms should be
  used:




• e.g.
• e.g.




• E.g
Trigonometry
Reciprocal trig functions:
•                  ;              ;



•                        ;

Compound-angle formulae
•
•
•
•

•

•
Double-angle formulae
•



•



•



•



•
The r, α formulae
•

•

•

•
Small-angle approximations

•

•

•


    Keep Θ in radians
Parametric Equations
• To draw a graph from parametric equations, plot the points on the curve
  given by different values of the parameter.
• Eliminate the parameter to give the cartesian equation of the curve.
• Parametric equations of circles:

    - Circle centre (0,0) and radius r




    - Circle centre (a,b) and radius r




•
Techniques for integration
Volumes of revolution
• About the x axis:




• About the y axis:




• Trapezium rule, with n strips of width h:




Note that this gives an overestimation of the area under the curve.
Vectors
• Magnitude-direction form:            (2 dimensions)
                                                          measured
                                                        anticlockwise
• Component form:                                           from
                                                         horizontal




• Position vector      is from origin to point P

• Vector

• ‘r’ denotes position vector of a general point
Vector equations
• Vector equation of the line through A with direction u is given by:



• Vector equation through points A and B is given by:




• Equation of line through            in direction       is given by:




                                               Cartesian form
               Vector form
Angle between two vectors
• The angle between a and b is given by




• Where

                              in two dimensions



                                      in three dimensions
• Cartesian equation of a plane perpendicular to             is:




• Equation of the plane through the point with position vector a, and
  perpendicular to n, is given by

                                 (r-a).n=0.
Differential equations
• A differential equation involves derivatives such as




• First-order differential equation involves only a first derivative

• Some first-order differential equations can be solved by separating the
  variables

• In a general solution you leave the constant of integration in the
  solution, and in a particular solution you use additional information to
  calculate the constant of integration.
Example

Más contenido relacionado

La actualidad más candente

Hermit curves &amp; beizer curves
Hermit curves &amp; beizer curvesHermit curves &amp; beizer curves
Hermit curves &amp; beizer curvesKKARUNKARTHIK
 
MATHS IN-CLASS ACTIVITY SLIDES
MATHS IN-CLASS ACTIVITY SLIDESMATHS IN-CLASS ACTIVITY SLIDES
MATHS IN-CLASS ACTIVITY SLIDESLillian June
 
Construction and locus revision card
Construction and locus   revision cardConstruction and locus   revision card
Construction and locus revision cardPuna Ripiye
 
Bezier Curve and Spline Curve
Bezier Curve and Spline CurveBezier Curve and Spline Curve
Bezier Curve and Spline CurveAsifShahariar1
 
Test yourself unit 3 foundation as
Test yourself unit 3 foundation asTest yourself unit 3 foundation as
Test yourself unit 3 foundation asMrJames Kcc
 
Maths quadrilateral presentation
Maths quadrilateral presentationMaths quadrilateral presentation
Maths quadrilateral presentationJian Leo
 
Maths (quadrilateral)
Maths (quadrilateral)Maths (quadrilateral)
Maths (quadrilateral)NingL96
 
Scalers and Vectors: By DBU-MESA
Scalers and Vectors: By DBU-MESAScalers and Vectors: By DBU-MESA
Scalers and Vectors: By DBU-MESAYitagesu Ethiopia
 
Vectors - A Basic Study
Vectors - A Basic StudyVectors - A Basic Study
Vectors - A Basic StudyPankaj Bhootra
 
Geometric construction
Geometric constructionGeometric construction
Geometric constructionAnju Soman
 
Bezeir curve na B spline Curve
Bezeir curve na B spline CurveBezeir curve na B spline Curve
Bezeir curve na B spline CurvePooja Dixit
 
Curve modeling bezier curves
Curve modeling bezier curvesCurve modeling bezier curves
Curve modeling bezier curvesjhansi1986
 
Area of polygons
Area of polygonsArea of polygons
Area of polygonsmstf mstf
 
Area of quadrilaterals
Area of quadrilateralsArea of quadrilaterals
Area of quadrilateralsNisha Neethu
 
Curve modeling-bezier-curves
Curve modeling-bezier-curvesCurve modeling-bezier-curves
Curve modeling-bezier-curvesMahmudul Hasan
 
5.13.1 Area of Circles, Sectors, and Quads
5.13.1 Area of Circles, Sectors, and Quads5.13.1 Area of Circles, Sectors, and Quads
5.13.1 Area of Circles, Sectors, and Quadssmiller5
 
Introduction to vectors
Introduction to vectorsIntroduction to vectors
Introduction to vectorshamcosine
 
Geom 1point2
Geom 1point2Geom 1point2
Geom 1point2herbison
 

La actualidad más candente (20)

Hermit curves &amp; beizer curves
Hermit curves &amp; beizer curvesHermit curves &amp; beizer curves
Hermit curves &amp; beizer curves
 
MATHS IN-CLASS ACTIVITY SLIDES
MATHS IN-CLASS ACTIVITY SLIDESMATHS IN-CLASS ACTIVITY SLIDES
MATHS IN-CLASS ACTIVITY SLIDES
 
Construction and locus revision card
Construction and locus   revision cardConstruction and locus   revision card
Construction and locus revision card
 
Bezier Curve and Spline Curve
Bezier Curve and Spline CurveBezier Curve and Spline Curve
Bezier Curve and Spline Curve
 
Test yourself unit 3 foundation as
Test yourself unit 3 foundation asTest yourself unit 3 foundation as
Test yourself unit 3 foundation as
 
Maths quadrilateral presentation
Maths quadrilateral presentationMaths quadrilateral presentation
Maths quadrilateral presentation
 
Maths (quadrilateral)
Maths (quadrilateral)Maths (quadrilateral)
Maths (quadrilateral)
 
Scalers and Vectors: By DBU-MESA
Scalers and Vectors: By DBU-MESAScalers and Vectors: By DBU-MESA
Scalers and Vectors: By DBU-MESA
 
Vectors - A Basic Study
Vectors - A Basic StudyVectors - A Basic Study
Vectors - A Basic Study
 
Geometric construction
Geometric constructionGeometric construction
Geometric construction
 
Bezeir curve na B spline Curve
Bezeir curve na B spline CurveBezeir curve na B spline Curve
Bezeir curve na B spline Curve
 
Curve modeling bezier curves
Curve modeling bezier curvesCurve modeling bezier curves
Curve modeling bezier curves
 
Area of polygons
Area of polygonsArea of polygons
Area of polygons
 
triangles
trianglestriangles
triangles
 
Geometry and measurement review
Geometry and measurement reviewGeometry and measurement review
Geometry and measurement review
 
Area of quadrilaterals
Area of quadrilateralsArea of quadrilaterals
Area of quadrilaterals
 
Curve modeling-bezier-curves
Curve modeling-bezier-curvesCurve modeling-bezier-curves
Curve modeling-bezier-curves
 
5.13.1 Area of Circles, Sectors, and Quads
5.13.1 Area of Circles, Sectors, and Quads5.13.1 Area of Circles, Sectors, and Quads
5.13.1 Area of Circles, Sectors, and Quads
 
Introduction to vectors
Introduction to vectorsIntroduction to vectors
Introduction to vectors
 
Geom 1point2
Geom 1point2Geom 1point2
Geom 1point2
 

Destacado

Destacado (20)

Core 4 Binomial Expansion 2
Core 4 Binomial Expansion 2Core 4 Binomial Expansion 2
Core 4 Binomial Expansion 2
 
C3+C4 Formulae Everything Edexcel
C3+C4 Formulae Everything EdexcelC3+C4 Formulae Everything Edexcel
C3+C4 Formulae Everything Edexcel
 
properties of invers trigonometric function
properties of invers trigonometric functionproperties of invers trigonometric function
properties of invers trigonometric function
 
Core 4 Binomial Expansion 1
Core 4 Binomial Expansion 1Core 4 Binomial Expansion 1
Core 4 Binomial Expansion 1
 
Maths c3 c4
Maths c3 c4Maths c3 c4
Maths c3 c4
 
Core 4 Differential Equations 1
Core 4 Differential Equations 1Core 4 Differential Equations 1
Core 4 Differential Equations 1
 
C2 june 2012
C2 june 2012C2 june 2012
C2 june 2012
 
Binomial expansion
Binomial expansionBinomial expansion
Binomial expansion
 
C4 Revision
C4 RevisionC4 Revision
C4 Revision
 
Aural test statistics solutions
Aural test statistics solutionsAural test statistics solutions
Aural test statistics solutions
 
Simltaneous equations
Simltaneous equationsSimltaneous equations
Simltaneous equations
 
Kinematics
KinematicsKinematics
Kinematics
 
C3 bronze 1
C3 bronze 1C3 bronze 1
C3 bronze 1
 
C4 2012 june
C4 2012 juneC4 2012 june
C4 2012 june
 
C4 January 2012 QP
C4 January 2012 QPC4 January 2012 QP
C4 January 2012 QP
 
Schoenburg- AREA OF STUDY 2
Schoenburg- AREA OF STUDY 2Schoenburg- AREA OF STUDY 2
Schoenburg- AREA OF STUDY 2
 
M1 January 2012 QP
M1 January 2012 QPM1 January 2012 QP
M1 January 2012 QP
 
C3 January 2012 QP
C3 January 2012 QPC3 January 2012 QP
C3 January 2012 QP
 
C3 2012 june
C3 2012 juneC3 2012 june
C3 2012 june
 
Dynamics (full chapter)
Dynamics (full chapter)Dynamics (full chapter)
Dynamics (full chapter)
 

Similar a C4 EDEXCEL HELP

4. Motion in a Plane 3.pptx.pptx
4. Motion in a Plane 3.pptx.pptx4. Motion in a Plane 3.pptx.pptx
4. Motion in a Plane 3.pptx.pptxbablivashisht
 
Chapter 3 motion in two d
Chapter 3 motion in two dChapter 3 motion in two d
Chapter 3 motion in two dChris Auld
 
Chapter 3 motion in two d 2
Chapter 3 motion in two d 2Chapter 3 motion in two d 2
Chapter 3 motion in two d 2Chris Auld
 
Spatial Data Modeling (Lecture#5)
Spatial Data Modeling (Lecture#5)Spatial Data Modeling (Lecture#5)
Spatial Data Modeling (Lecture#5)Sadia_Sheikh
 
GeometricTransformations.ppt
GeometricTransformations.pptGeometricTransformations.ppt
GeometricTransformations.pptDebjit Doira
 
UNIT 2-Geometric Modeling.pptx
UNIT 2-Geometric Modeling.pptxUNIT 2-Geometric Modeling.pptx
UNIT 2-Geometric Modeling.pptxdinesh babu
 
Electromagnetic fields: Review of vector algebra
Electromagnetic fields: Review of vector algebraElectromagnetic fields: Review of vector algebra
Electromagnetic fields: Review of vector algebraDr.SHANTHI K.G
 
Mathematics fundamentals
Mathematics fundamentalsMathematics fundamentals
Mathematics fundamentalsSardar Alam
 
Curves wire frame modelling
Curves wire frame modellingCurves wire frame modelling
Curves wire frame modellingjntuhcej
 
The principal screw of inertia
The principal screw of inertiaThe principal screw of inertia
The principal screw of inertiaWangdo Kim
 
REGRESSION METasdfghjklmjhgftrHODS1.pptx
REGRESSION METasdfghjklmjhgftrHODS1.pptxREGRESSION METasdfghjklmjhgftrHODS1.pptx
REGRESSION METasdfghjklmjhgftrHODS1.pptxcajativ595
 
Polygon Fill
Polygon FillPolygon Fill
Polygon Fillwahab13
 
Digital Differential Analyzer Line Drawing Algorithm
Digital Differential Analyzer Line Drawing AlgorithmDigital Differential Analyzer Line Drawing Algorithm
Digital Differential Analyzer Line Drawing AlgorithmKasun Ranga Wijeweera
 

Similar a C4 EDEXCEL HELP (20)

4. Motion in a Plane 3.pptx.pptx
4. Motion in a Plane 3.pptx.pptx4. Motion in a Plane 3.pptx.pptx
4. Motion in a Plane 3.pptx.pptx
 
Chapter 3 motion in two d
Chapter 3 motion in two dChapter 3 motion in two d
Chapter 3 motion in two d
 
Chapter 3 motion in two d 2
Chapter 3 motion in two d 2Chapter 3 motion in two d 2
Chapter 3 motion in two d 2
 
Spatial Data Modeling (Lecture#5)
Spatial Data Modeling (Lecture#5)Spatial Data Modeling (Lecture#5)
Spatial Data Modeling (Lecture#5)
 
curve one
curve onecurve one
curve one
 
GeometricTransformations.ppt
GeometricTransformations.pptGeometricTransformations.ppt
GeometricTransformations.ppt
 
UNIT 2-Geometric Modeling.pptx
UNIT 2-Geometric Modeling.pptxUNIT 2-Geometric Modeling.pptx
UNIT 2-Geometric Modeling.pptx
 
cg mod2.pdf
cg mod2.pdfcg mod2.pdf
cg mod2.pdf
 
Lines
LinesLines
Lines
 
Electromagnetic fields: Review of vector algebra
Electromagnetic fields: Review of vector algebraElectromagnetic fields: Review of vector algebra
Electromagnetic fields: Review of vector algebra
 
Introduction to the curves
Introduction to the curvesIntroduction to the curves
Introduction to the curves
 
Mathematics fundamentals
Mathematics fundamentalsMathematics fundamentals
Mathematics fundamentals
 
Report in determinants
Report in determinantsReport in determinants
Report in determinants
 
Ahmed
AhmedAhmed
Ahmed
 
Graph 1
Graph 1Graph 1
Graph 1
 
Curves wire frame modelling
Curves wire frame modellingCurves wire frame modelling
Curves wire frame modelling
 
The principal screw of inertia
The principal screw of inertiaThe principal screw of inertia
The principal screw of inertia
 
REGRESSION METasdfghjklmjhgftrHODS1.pptx
REGRESSION METasdfghjklmjhgftrHODS1.pptxREGRESSION METasdfghjklmjhgftrHODS1.pptx
REGRESSION METasdfghjklmjhgftrHODS1.pptx
 
Polygon Fill
Polygon FillPolygon Fill
Polygon Fill
 
Digital Differential Analyzer Line Drawing Algorithm
Digital Differential Analyzer Line Drawing AlgorithmDigital Differential Analyzer Line Drawing Algorithm
Digital Differential Analyzer Line Drawing Algorithm
 

Más de anicholls1234

Business revision- AQA
Business revision- AQABusiness revision- AQA
Business revision- AQAanicholls1234
 
Ratio analysis Accounting Help
Ratio analysis Accounting HelpRatio analysis Accounting Help
Ratio analysis Accounting Helpanicholls1234
 
Mechanics revision- A2 Edexcel
Mechanics revision- A2 EdexcelMechanics revision- A2 Edexcel
Mechanics revision- A2 Edexcelanicholls1234
 
Destructive plate boundaries
Destructive plate boundariesDestructive plate boundaries
Destructive plate boundariesanicholls1234
 
Out of Town Shopping Centres
Out of Town Shopping CentresOut of Town Shopping Centres
Out of Town Shopping Centresanicholls1234
 
Contemporary sustainability issues in urban areas
Contemporary sustainability issues in urban areasContemporary sustainability issues in urban areas
Contemporary sustainability issues in urban areasanicholls1234
 
Geography presentation-Tropical Rainforests
Geography presentation-Tropical RainforestsGeography presentation-Tropical Rainforests
Geography presentation-Tropical Rainforestsanicholls1234
 
Blues Revision- Everything you need to know
Blues Revision- Everything you need to knowBlues Revision- Everything you need to know
Blues Revision- Everything you need to knowanicholls1234
 
Rag desh recap- AQA/EDEXCEL
Rag desh recap- AQA/EDEXCELRag desh recap- AQA/EDEXCEL
Rag desh recap- AQA/EDEXCELanicholls1234
 
Minimalism- Everything you need to know!
Minimalism- Everything you need to know!Minimalism- Everything you need to know!
Minimalism- Everything you need to know!anicholls1234
 
Franz schubert powerpoint
Franz schubert powerpointFranz schubert powerpoint
Franz schubert powerpointanicholls1234
 
Britpop – gcse music
Britpop – gcse musicBritpop – gcse music
Britpop – gcse musicanicholls1234
 
Handel - And the glory of the lord from messiah
Handel - And the glory of the lord from messiahHandel - And the glory of the lord from messiah
Handel - And the glory of the lord from messiahanicholls1234
 
Growth in plants- Geography
Growth in plants- GeographyGrowth in plants- Geography
Growth in plants- Geographyanicholls1234
 
Haiti’s earthquake 2010
Haiti’s earthquake 2010Haiti’s earthquake 2010
Haiti’s earthquake 2010anicholls1234
 
Energy security- Geography
Energy security- GeographyEnergy security- Geography
Energy security- Geographyanicholls1234
 
Geography Revision Pack AQA/Edexcel
Geography Revision Pack AQA/EdexcelGeography Revision Pack AQA/Edexcel
Geography Revision Pack AQA/Edexcelanicholls1234
 
Mt St Helens Geography Case Study
Mt St Helens Geography Case StudyMt St Helens Geography Case Study
Mt St Helens Geography Case Studyanicholls1234
 

Más de anicholls1234 (20)

C1 june 2012
C1 june 2012C1 june 2012
C1 june 2012
 
M1 june 2012
M1 june 2012M1 june 2012
M1 june 2012
 
Business revision- AQA
Business revision- AQABusiness revision- AQA
Business revision- AQA
 
Ratio analysis Accounting Help
Ratio analysis Accounting HelpRatio analysis Accounting Help
Ratio analysis Accounting Help
 
Mechanics revision- A2 Edexcel
Mechanics revision- A2 EdexcelMechanics revision- A2 Edexcel
Mechanics revision- A2 Edexcel
 
Destructive plate boundaries
Destructive plate boundariesDestructive plate boundaries
Destructive plate boundaries
 
Out of Town Shopping Centres
Out of Town Shopping CentresOut of Town Shopping Centres
Out of Town Shopping Centres
 
Contemporary sustainability issues in urban areas
Contemporary sustainability issues in urban areasContemporary sustainability issues in urban areas
Contemporary sustainability issues in urban areas
 
Geography presentation-Tropical Rainforests
Geography presentation-Tropical RainforestsGeography presentation-Tropical Rainforests
Geography presentation-Tropical Rainforests
 
Blues Revision- Everything you need to know
Blues Revision- Everything you need to knowBlues Revision- Everything you need to know
Blues Revision- Everything you need to know
 
Rag desh recap- AQA/EDEXCEL
Rag desh recap- AQA/EDEXCELRag desh recap- AQA/EDEXCEL
Rag desh recap- AQA/EDEXCEL
 
Minimalism- Everything you need to know!
Minimalism- Everything you need to know!Minimalism- Everything you need to know!
Minimalism- Everything you need to know!
 
Franz schubert powerpoint
Franz schubert powerpointFranz schubert powerpoint
Franz schubert powerpoint
 
Britpop – gcse music
Britpop – gcse musicBritpop – gcse music
Britpop – gcse music
 
Handel - And the glory of the lord from messiah
Handel - And the glory of the lord from messiahHandel - And the glory of the lord from messiah
Handel - And the glory of the lord from messiah
 
Growth in plants- Geography
Growth in plants- GeographyGrowth in plants- Geography
Growth in plants- Geography
 
Haiti’s earthquake 2010
Haiti’s earthquake 2010Haiti’s earthquake 2010
Haiti’s earthquake 2010
 
Energy security- Geography
Energy security- GeographyEnergy security- Geography
Energy security- Geography
 
Geography Revision Pack AQA/Edexcel
Geography Revision Pack AQA/EdexcelGeography Revision Pack AQA/Edexcel
Geography Revision Pack AQA/Edexcel
 
Mt St Helens Geography Case Study
Mt St Helens Geography Case StudyMt St Helens Geography Case Study
Mt St Helens Geography Case Study
 

Último

AUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptxAUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptxiammrhaywood
 
How to Show Error_Warning Messages in Odoo 17
How to Show Error_Warning Messages in Odoo 17How to Show Error_Warning Messages in Odoo 17
How to Show Error_Warning Messages in Odoo 17Celine George
 
Human-AI Co-Creation of Worked Examples for Programming Classes
Human-AI Co-Creation of Worked Examples for Programming ClassesHuman-AI Co-Creation of Worked Examples for Programming Classes
Human-AI Co-Creation of Worked Examples for Programming ClassesMohammad Hassany
 
How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17Celine George
 
Diploma in Nursing Admission Test Question Solution 2023.pdf
Diploma in Nursing Admission Test Question Solution 2023.pdfDiploma in Nursing Admission Test Question Solution 2023.pdf
Diploma in Nursing Admission Test Question Solution 2023.pdfMohonDas
 
Clinical Pharmacy Introduction to Clinical Pharmacy, Concept of clinical pptx
Clinical Pharmacy  Introduction to Clinical Pharmacy, Concept of clinical pptxClinical Pharmacy  Introduction to Clinical Pharmacy, Concept of clinical pptx
Clinical Pharmacy Introduction to Clinical Pharmacy, Concept of clinical pptxraviapr7
 
UKCGE Parental Leave Discussion March 2024
UKCGE Parental Leave Discussion March 2024UKCGE Parental Leave Discussion March 2024
UKCGE Parental Leave Discussion March 2024UKCGE
 
How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17Celine George
 
Prescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptxPrescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptxraviapr7
 
The basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptxThe basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptxheathfieldcps1
 
How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17Celine George
 
Drug Information Services- DIC and Sources.
Drug Information Services- DIC and Sources.Drug Information Services- DIC and Sources.
Drug Information Services- DIC and Sources.raviapr7
 
What is the Future of QuickBooks DeskTop?
What is the Future of QuickBooks DeskTop?What is the Future of QuickBooks DeskTop?
What is the Future of QuickBooks DeskTop?TechSoup
 
3.21.24 The Origins of Black Power.pptx
3.21.24  The Origins of Black Power.pptx3.21.24  The Origins of Black Power.pptx
3.21.24 The Origins of Black Power.pptxmary850239
 
Patterns of Written Texts Across Disciplines.pptx
Patterns of Written Texts Across Disciplines.pptxPatterns of Written Texts Across Disciplines.pptx
Patterns of Written Texts Across Disciplines.pptxMYDA ANGELICA SUAN
 
Education and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptxEducation and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptxraviapr7
 
Ultra structure and life cycle of Plasmodium.pptx
Ultra structure and life cycle of Plasmodium.pptxUltra structure and life cycle of Plasmodium.pptx
Ultra structure and life cycle of Plasmodium.pptxDr. Asif Anas
 
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdfP4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdfYu Kanazawa / Osaka University
 
Philosophy of Education and Educational Philosophy
Philosophy of Education  and Educational PhilosophyPhilosophy of Education  and Educational Philosophy
Philosophy of Education and Educational PhilosophyShuvankar Madhu
 

Último (20)

AUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptxAUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptx
 
How to Show Error_Warning Messages in Odoo 17
How to Show Error_Warning Messages in Odoo 17How to Show Error_Warning Messages in Odoo 17
How to Show Error_Warning Messages in Odoo 17
 
Human-AI Co-Creation of Worked Examples for Programming Classes
Human-AI Co-Creation of Worked Examples for Programming ClassesHuman-AI Co-Creation of Worked Examples for Programming Classes
Human-AI Co-Creation of Worked Examples for Programming Classes
 
How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17
 
Prelims of Kant get Marx 2.0: a general politics quiz
Prelims of Kant get Marx 2.0: a general politics quizPrelims of Kant get Marx 2.0: a general politics quiz
Prelims of Kant get Marx 2.0: a general politics quiz
 
Diploma in Nursing Admission Test Question Solution 2023.pdf
Diploma in Nursing Admission Test Question Solution 2023.pdfDiploma in Nursing Admission Test Question Solution 2023.pdf
Diploma in Nursing Admission Test Question Solution 2023.pdf
 
Clinical Pharmacy Introduction to Clinical Pharmacy, Concept of clinical pptx
Clinical Pharmacy  Introduction to Clinical Pharmacy, Concept of clinical pptxClinical Pharmacy  Introduction to Clinical Pharmacy, Concept of clinical pptx
Clinical Pharmacy Introduction to Clinical Pharmacy, Concept of clinical pptx
 
UKCGE Parental Leave Discussion March 2024
UKCGE Parental Leave Discussion March 2024UKCGE Parental Leave Discussion March 2024
UKCGE Parental Leave Discussion March 2024
 
How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17
 
Prescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptxPrescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptx
 
The basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptxThe basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptx
 
How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17
 
Drug Information Services- DIC and Sources.
Drug Information Services- DIC and Sources.Drug Information Services- DIC and Sources.
Drug Information Services- DIC and Sources.
 
What is the Future of QuickBooks DeskTop?
What is the Future of QuickBooks DeskTop?What is the Future of QuickBooks DeskTop?
What is the Future of QuickBooks DeskTop?
 
3.21.24 The Origins of Black Power.pptx
3.21.24  The Origins of Black Power.pptx3.21.24  The Origins of Black Power.pptx
3.21.24 The Origins of Black Power.pptx
 
Patterns of Written Texts Across Disciplines.pptx
Patterns of Written Texts Across Disciplines.pptxPatterns of Written Texts Across Disciplines.pptx
Patterns of Written Texts Across Disciplines.pptx
 
Education and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptxEducation and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptx
 
Ultra structure and life cycle of Plasmodium.pptx
Ultra structure and life cycle of Plasmodium.pptxUltra structure and life cycle of Plasmodium.pptx
Ultra structure and life cycle of Plasmodium.pptx
 
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdfP4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
 
Philosophy of Education and Educational Philosophy
Philosophy of Education  and Educational PhilosophyPhilosophy of Education  and Educational Philosophy
Philosophy of Education and Educational Philosophy
 

C4 EDEXCEL HELP

  • 2. Binomial expansions • General binomial expansion, for : • When the series is infinite, this is only valid if |x|<1 • (a+x)n should be written as
  • 3. Partial fractions • A proper algebraic fraction with a denominator which factorises can be decomposed into a sum of partial fractions. Following forms should be used: • e.g.
  • 5. Trigonometry Reciprocal trig functions: • ; ; • ; Compound-angle formulae • • • • • •
  • 7. The r, α formulae • • • •
  • 9. Parametric Equations • To draw a graph from parametric equations, plot the points on the curve given by different values of the parameter. • Eliminate the parameter to give the cartesian equation of the curve. • Parametric equations of circles: - Circle centre (0,0) and radius r - Circle centre (a,b) and radius r •
  • 10. Techniques for integration Volumes of revolution • About the x axis: • About the y axis: • Trapezium rule, with n strips of width h: Note that this gives an overestimation of the area under the curve.
  • 11. Vectors • Magnitude-direction form: (2 dimensions) measured anticlockwise • Component form: from horizontal • Position vector is from origin to point P • Vector • ‘r’ denotes position vector of a general point
  • 12. Vector equations • Vector equation of the line through A with direction u is given by: • Vector equation through points A and B is given by: • Equation of line through in direction is given by: Cartesian form Vector form
  • 13. Angle between two vectors • The angle between a and b is given by • Where in two dimensions in three dimensions
  • 14. • Cartesian equation of a plane perpendicular to is: • Equation of the plane through the point with position vector a, and perpendicular to n, is given by (r-a).n=0.
  • 15. Differential equations • A differential equation involves derivatives such as • First-order differential equation involves only a first derivative • Some first-order differential equations can be solved by separating the variables • In a general solution you leave the constant of integration in the solution, and in a particular solution you use additional information to calculate the constant of integration.