Cambridge International AS & A Level Further Mathematics Further Pure Mathematics 1

Description

Exam board: Cambridge Assessment International Education Level: A-level Subject: Mathematics First teaching: September 2018 First exams: Summer 2020 Endorsed by Cambridge Assessment International Education to provide full support for Paper 1 of the syllabus for examination from 2020. Take mathematical understanding to the next level with this accessible series, written by experienced authors, examiners and teachers. - Improve confidence as a mathematician with clear explanations, worked examples, diverse activities and engaging discussion points. - Advance problem-solving, interpretation and communication skills through a wealth of questions that promote higher-order thinking. - Prepare for further study or life beyond the classroom by applying mathematics to other subjects and modelling real-world situations. - Reinforce learning with opportunities for digital practice via links to the Mathematics in Education and Industry's (MEI) Integral platform in the eTextbooks.* *To have full access to the eTextbooks and Integral resources you must be subscribed to both Dynamic Learning and Integral. To trial our eTextbooks and/or subscribe to Dynamic Learning, visit: www.hoddereducation.co.uk/dynamic-learning; to view samples of the Integral resources and/or subscribe to Integral, visit integralmaths.org/international Please note that the Integral resources have not been through the Cambridge International endorsement process. Answers to exercise questions are on Cambridge Extras: www.hoddereducation.co.uk/cambridgeextras This book covers the syllabus content for Further Pure Mathematics 1, including roots of polynomial equations, rational functions and graphs, summation of series, matrices, polar coordinates, vectors and proof by induction. About the series: Four separate textbooks ensure full coverage of the latest Cambridge International AS & A Level Further Mathematics syllabus (9231). Student and Whiteboard eTextbook editions are also available. Further Pure Mathematics 1: Student Textbook (ISBN 9781510421783), Student eTextbook (ISBN 9781510422025), Whiteboard eTextbook (ISBN 9781510422032) Further Pure Mathematics 2: Student Textbook (ISBN 9781510421790), Student eTextbook (ISBN 9781510422063), Whiteboard eTextbook (ISBN 9781510422070) Further Mechanics: Student Textbook (ISBN 9781510421806), Student eTextbook (ISBN 9781510422100), Whiteboard eTextbook (ISBN 9781510422117) Further Probability & Statistics: Student Textbook (ISBN 9781510421813), Student eTextbook (ISBN 9781510422148), Whiteboard eTextbook (ISBN 9781510422155) Cover Book title Copyright Contents Introduction How to use this book The Cambridge International AS & A Level Further Mathematics 9231 syllabus 1 Matrices and transformations 1.1 Matrices 1.2 Multiplication of matrices 1.3 Transformations 1.4 Successive transformations 1.5 Invariance 2 Series and induction 2.1 Sequences and series 2.2 Using standard results 2.3 The method of differences 2.4 Proof by induction 2.5 Other proofs by induction 3 Roots of polynomials 3.1 Polynomials 3.2 Quadratic equations 3.3 Cubic equations 3.4 Quartic equations 4 Rational functions and graphs 4.1 Graphs of rational functions 4.2 How to sketch a graph of a rational function 4.3 Oblique asymptotes 4.4 Sketching curves related to y= f(x) 5 Polar coordinates 5.1 Polar coordinates 5.2 Sketching curves with polar equations 5.3 Finding the area enclosed by a polar curve 6 Matrices and their inverses 6.1 The determinant of a 2 × 2 matrix 6.2 The inverse of a matrix 6.3 Finding the inverse of a 3 × 3 matrix 7 Vectors 7.1 The vector equation of a plane 7.2 The intersection of a line and a plane 7.3 The distance of a point from a plane 7.4 The angle between a line and a plane 7.5 The intersection of two planes 7.6 The angle between two planes 7.7 The vector product 7.8 Finding distances Index A C D E F G H I L M N O P Q R S T U V Z