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Full Description
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.
Contents
Syllabus matching grid
1 Algebra
1.1: The modulus function
1.2: Division of polynomials
1.3: The remainder theorem
1.4: The factor theorem
2 Logarithms and exponential functions
2.1: Continuous exponential growth and decay
2.2: The logarithmic function
2.3: ex and logarithms to base e
2.4: Equations and inequalities using logarithms
2.5: Using logarithms to reduce equations to linear form
3 Trigonometry
3.1: Secant, cosecant, and cotangent
3.2: Further trigonometric identities
3.3: Addition formulae
3.4: Double angle formulae
3.5: Expressing a sin *C + b cos *C in the form R sin(*C ± a) or R cos(*C ± a)
Review exercise A - Pure 2
Review exercise A - Pure 3
Maths in real-life: Predicting tidal behaviour
4 Differentiation
4.1: Differentiating the exponential function
4.2: Differentiating the natural logarithmic function
4.3: Differentiating products
4.4: Differentiating quotients
4.5: Differentiating sin x, cos x, and tan x
4.6: Implicit differentiation
4.7: Parametric differentiation
5 Integration
5.1: Integration of eax+b
5.2: Integration of 1 x + b
5.3: Integration of sin (ax + b), cos (ax + b), ec2 (ax + b)
5.4: Extending integration of trigonometric functions
5.5: Numerical integration using the trapezium rule
6 Numerical solution of equations
6.1: Finding approximate roots by change of sign or graphical methods
6.2: Finding roots using iterative relationships
6.3: 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
7.1: Partial fractions
7.2: Binomial expansions of the form (1 + x)n when n is not a positive integer
7.3: Binomial expansions of the form (a + x)n where n is not a positive integer
7.4: Binomial expansions and partial fractions
8 Further integration
8.1: Integration using partial fractions
8.2: Integration of f(x) f'(x)
8.3: Integration by parts
8.4: Integration using substitution
Review exercise C - Pure 3
9 Vectors
9.1: The equation of a straight line
9.2: Intersecting lines
9.3: The angle between two straight lines
9.4: The equation of a plane
9.5: Configurations of a line and a plane
9.6: Configurations of two planes
9.7: The distance from a point to a plane or line
10 Differential equations
10.1: Forming simple differential equations (DEs)
10.2: Solving first-order differential equations with separable variables
10.3: Finding particular solutions to differential equations
10.4: Modelling with differential equations
11 Complex numbers
11.1: Introducing complex numbers
11.2: Calculating with complex numbers
11.3: Solving equations involving complex numbers
11.4: Representing complex numbers geometrically
11.5: Polar form and exponential form
11.6: 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
