Complete Pure Mathematics 2 & 3 for Cambridge International AS & A Level
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A termék adatai:
- Kiadás sorszáma 2
- Kiadó OUP Oxford
- Megjelenés dátuma 2018. július 12.
- ISBN 9780198425137
- Kötéstípus Kötés ismeretlen
- Terjedelem344 oldal
- Méret 246x190x16 mm
- Súly 691 g
- Nyelv angol 0
Kategóriák
Rövid leírás:
Providing complete syllabus support (9709), this stretching and practice-focused course builds the advanced skills needed for the latest Cambridge assessments and the transition to higher education. Engaging, real world examples make mathematics relevant to real life.
TöbbHosszú leírás:
Support achievement in the latest syllabus (9709), for examination from 2020, with a stretching, practice-driven approach that builds the advanced skills required for Cambridge exam success and progression to further study.
This new edition is fully aligned with the Pure Mathematics 2 & 3 part of the latest International AS & A Level syllabus, and contains a comprehensive mapping grid so you can be sure of complete support.
Get students ready for higher education with a focus on real world application. From parabolic reflectors to technology in sport, up-to-date, international examples show how mathematics is used in real life.
Students have plenty of opportunities to hone their skills with extensive graduated practice and thorough worked examples. Plus, give students realistic practice for their exams with exam-style questions covering every topic.
Answers are included in the back of the book with full step-by-step solutions for all exercises and exam-style questions available on the accompanying support site.
Tartalomjegyzék:
Syllabus matching grid
1 Algebra
The modulus function
Division of polynomials
The remainder theorem
The factor theorem
2 Logarithms and exponential functions
Continuous exponential growth and decay
The logarithmic function
ex and logarithms to base e
Equations and inequalities using logarithms
Using logarithms to reduce equations to linear form
3 Trigonometry
Secant, cosecant, and cotangent
Further trigonometric identities
Addition formulae
Double angle formulae
Expressing a sin ? + b cos ? in the form R sin(? ? a) or R cos(? ? a)
Review exercise A - Pure 2
Review exercise A - Pure 3
Maths in real-life: Predicting tidal behaviour
4 Differentiation
Differentiating the exponential function
Differentiating the natural logarithmic function
Differentiating products
Differentiating quotients
Differentiating sin x, cos x, and tan x
Implicit differentiation
Parametric differentiation
5 Integration
Integration of eax+b
Integration of 1 x + b
Integration of sin (ax + b), cos (ax + b), ec2 (ax + b)
Extending integration of trigonometric functions
Numerical integration using the trapezium rule
6 Numerical solution of equations
Finding approximate roots by change of sign or graphical methods
Finding roots using iterative relationships
Convergence behaviour of iterative functions
Review exercise B - Pure 2
Review exercise B - Pure 3
Maths in real-life: Nature of Mathematics
7 Further algebra
Partial fractions
Binomial expansions of the form (1 + x)n when n is not a positive integer
Binomial expansions of the form (a + x)n where n is not a positive integer
Binomial expansions and partial fractions
8 Further integration
Integration using partial fractions
Integration of f(x) f´(x)
Integration by parts
Integration using substitution
Review exercise C - Pure 3
9 Vectors
The equation of a straight line
Intersecting lines
The angle between two straight lines
The equation of a plane
Configurations of a line and a plane
Configurations of two planes
The distance from a point to a plane or line
10 Differential equations
Forming simple differential equations (DEs)
Solving first-order differential equations with separable variables
Finding particular solutions to differential equations
Modelling with differential equations
11 Complex numbers
Introducing complex numbers
Calculating with complex numbers
Solving equations involving complex numbers
Representing complex numbers geometrically
Polar form and exponential form
Loci in the Argand diagram
Review exercise D - Pure 3
Maths in real-life: Electrifying, magnetic and damp: how complex mathematics makes life simpler
Exam-style paper A - Pure 2
Exam-style paper B - Pure 2
Exam-style paper C - Pure 3
Exam-style paper D - Pure 3
Answers
Glossary of terms
Index
