Mei online provide a selection of resources for students following their further pure 1 mathematics course. Edexcel pure mathematics 1 a minimum of blind calculation. Mei structured mathematics module summary sheets fp1, further concepts for advanced mathematics topic 1. Mei, 2005 further pure 1 complex numbers i given that. To multiply and divide complex numbers written in modulusargument form. Mei online resources provide this introduction to complex numbers for aqa fp1. To be able to divide one complex number by another complex number. Complex numbers mr bartons a level mathematics site. The further mathematics must include both fp1 and fp2. Complex numbers cannot be reduced to a single term, the real and imaginary parts remain separate. Decision 1 algorithms, graphs and networks, linear programming, critical path analysis and simulation. With and being real numbers and being the imaginary unit.
A short introduction to complex numbers written primarily for students aged 14 to 19. Tes global ltd is registered in england company no 02017289 with its registered office at 26 red lion square london wc1r 4hq. They have allowed us to solve an equation that doesnt have real roots, and on a broader scale they open up a whole new world of possibilities in mathematics. Mathematicians tend to abbreviate complex numbers by \z, and use subscripts such as z 1 or z 2 when multiple complex numbers are used. View the video index containing tutorials and worked solutions for fp1 mei further maths. Complex number operations lesson plans and activities project maths. Alevel mathematicsmeifp1complex numbers wikibooks, open. The topics are organised according to the old pre2010 fp1fp3 of edexcel a level, so you will have to pick and choose the topics you need for your course. Further pure mathematics 2 calculus, polar coordinates, complex numbers, power series, matrices, hyperbolic functions. Aqa fp1 complex numbers study plan, notes and exercises stem. For the love of physics walter lewin may 16, 2011 duration. Further concepts for advanced mathematics page 2 competence statements fp1, m1, m2, m4 mei. Complex numbers can be multiplied using the same techniques as used in algebra. Fp1 revision notes chapter 1 complex numbers if you have a silver calculator, it will divide and multiply complex numbers for you.
Argand diagram o know what is meant by the modulus of a complex number. This website and its content is subject to our terms and conditions. Mei mathematics in education and industry mei structured mathematics further concepts for advanced mathematics, fp1 practice paper fp1c additional materials. Mei july 2004 mei structured mathematics practice paper fp1a page 4 10 you are given the complex numbers 1232j and 4cosjsin. In fp1 you will asked to solve a cubic or quartic equation using your knowledge of complex numbers. Oxford cambridge and rsa thursday 14 may 2015 morning. A very few tried to transform a square or rectangle of area 3 but this method was very rarely successful. If finding roots of a cubic, and weve found the two complex roots, a nice little trick is that we. Mei mathematics in education and industry mei structured mathematics further concepts for advanced mathematics, fp1 practice paper fp1d additional materials. Mei fp1 curve sketching and inequalities fmsp revision videos. The locus l 2 consists of the points representing complex numbers z for which arg 1 2i 3 s z. Further pure 1 mei powerpoint presentations fp1 matrices lesson 1 fp1 transformations lesson 2 fp1 inverse matrices lesson 3 fp1 simultaneous equations lesson 4 fp1 complex numbers lesson 5 fp1 complex numbers lesson 6 fp1 sketching graphs lesson 7 fp1 inequalities lesson 8 fp1 identities and roots of equations lesson 9 fp1 roots of equations. So asymptote is axis 0 0 from above as and 0 from below as x xy x x x xx xy x x.
The group of roots you will find for a cubic are either three real roots, or one real root and a complex conjugate pair. Argand diagram is an easy way for candidates to avoid this error. These include thorough notes, a study plan, additional exercises, a multiple choice test and an extension piece of work. Thursday 14 may 2015 morning as gce mathematics mei 475501 further concepts for advanced mathematics fp1 printed answer book instructions to candidates these instructions are the same on the printed answer book and the question paper. The question paper will be found inside the printed answer book. Written for teachers, teach further maths is a suite of high quality, fully animated colour alevel further maths powerpoint presentations, consisting of over 3000 slides. In addition to the resources listed here, i highly recommend the activities provided by the further maths support networkmei school login required, which include topic notes, worksheets, activities and assessments. These mei online resources are suitable for use by students studying aqa further pure mathematics 1 fp1. Mei online resources for fp1 provide a selection of materials for the modulusargument form of complex numbers. Complex roots of polynomials with real coefficients always come in complex conjugates. The notes may be useful to a student without access to a teacher or a textbook. Ocr fp1 complex number practise teaching resources. Alevel mathematicsocrfp1complex numbers wikibooks, open. This is a short introduction to complex numbers written primarily for students aged from about 14 or 15 to 18 or 19.
You are advised that an answer may receive no marks unless you show sufficient detail of the working to indicate that a correct method is being used. This revision video, prepared by the further mathematics support programme wales, looks at the geometry of complex numbers. It covers mainly solving equations and loci as these are the sections my students tend to struggle on. File type icon file name description size revision time user.
Powered by create your own unique website with customizable templates. Written by a very experienced classroom practitioner, examiner and published maths author paul hunt, the presentations include demonstrations, proofs, worked examples, exercises, examstyle. In addition to the resources listed here, i highly recommend the activities provided by the further maths support network mei school login required, which include topic notes, worksheets, activities and assessments. The complex numbers z and w are represented by points a and b on an argand diagram. The number of marks is given in brackets at the end of each question or part question on the question paper. Ocr fp1 june 20 q2ii fp1 ocr series january 20 q8 fp1 ocr matrices january 20 q1 q1 core 1 c1 ocr may june 20 past paper exam practice as maths this channel is managed by up and coming uk maths teachers. Coloured diagrams can be obtained by seeing how quickly divergence occurs for each complex c. Aug 29, 2015 this website and its content is subject to our terms and conditions. Mei mathfurther math exams june 2014 alevel and gcse exam thread directory 2017 2017 unofficial markscheme list gcse and alevel ocr mei fp1 past paper help. A complex number is something that has both real and imaginary parts. Adding the two together is as simple as adding the real parts in this case.
While jeanrobert argand 1768 1822 is generally credited with the discovery in 1806, the argand diagram also known as the argand plane was actually described by c. Ocr fp1 not mei 19th may 2017 edexcel alevel further pure 2 25th june 2019 exam discussion fp1 todayyyy a level maths self study show 10 more further maths as. Mei july 2004 mei structured mathematics practice paper fp1b mark scheme page 4 qu answer mark comment section b 8 i x 1 b1 1 ii 2 2 421 when, 1 88 0 for large. You can also use the following rule to simplify powers of i. Answer bookletpaper graph paper mei examination formulae and tables mf12. To understand what is meant by modulusargument form.
Complex numbers are numbers that consist of a real number and an imaginary number. Describe the locus of points in the argand diagram representing the complex numbers z for which za 3. Answer bookletpaper graph paper mei examination formulae and tables mf12 time 1 hour 30 minutes instructions. Dec 12, 2014 this revision video, prepared by the further mathematics support programme wales, looks at the geometry of complex numbers for the wjec further maths module fp1. Fp1 mei further maths video tutorials from examsolutions. Detailed notes covering the number system, adding subtracting and multiplying complex numbers, complex conjugates, equations with complex roots, equating real and imaginary parts and crucial points to learn are included, together with study plans for both heinemann and oxford textbooks. Here are further pure 1 questions from past maths alevel papers separated by topic. This is a collection of revision questions for ocr fp1 adapted from aqa papers fp1 and fp2.
You can multiply complex numbers and simplify powers of i. Modulesunits s c h e d u l e further pure mathematics 1. If finding roots of a cubic, and weve found the two complex roots, a nice little trick is that we can think about the constant term in the expansion to get the last real root without requiring algebraic division. Matrices, complex numbers, graphs and inequalities, algebra and proof by induction. Given that 1 2i is a complex solution of f x 0, a write down the other complex solution of fx 0, 1. They do form a logical progression, in that no topic depends on a topic further down the list. Or possibly to a teacher looking for a quick source. Mar 30, 2015 for the love of physics walter lewin may 16, 2011 duration. Oct 07, 2014 further pure 1 mei powerpoint presentations fp1 matrices lesson 1 fp1 transformations lesson 2 fp1 inverse matrices lesson 3 fp1 simultaneous equations lesson 4 fp1 complex numbers lesson 5 fp1 complex numbers lesson 6 fp1 sketching graphs lesson 7 fp1 inequalities lesson 8 fp1 identities and roots of equations lesson 9 fp1 roots of equations.