Theorem 251 suppose that r t is a vector valued function and. Examsolutions youtube video stuart the examsolutions guy 20200227t15. Unit fp2 further pure mathematics fp2 a2 2 series what students need to learn. If you see some unexpected behavior, you may want to use a supported browser instead. Complex numbers are numbers that consist of a real number and an imaginary number.
Written by a very experienced classroom practitioner, examiner and published maths author paul hunt, the presentations include demonstrations, proofs, worked examples, exercises, examstyle. A complex number z is represented by the point p in the argand diagram. Competence statements complex numbers modulus argument form. Further pure 2 fp2 complex numbers 4 converting to exponential form further maths a level by ukmathsteacher. Further complex numbers edexcel further pure mathematics 2 fp2. Mark scheme results summer 2010 pearson qualifications. For any complex number, going round an entire circle i. Jun 24, 2010 a complex number z is represented by the point p in the argand diagram. Given further that a and b satisfy the above equation, determine an equation for the. To build on and extend students knowledge of pure mathematics and associated techniques. Further pure 2 key skills checklist how confident are you with each topic.
Gce further pure mathematics fp2 6668 summer 2010 question number scheme marks 6a imaginary axis rez 3 real axis vertical straight line through 3 on real axis b1 b1 2 b these are points where line x 3 meets the circle centre 3, 4 with radius 5. Mei structured mathematics module summary sheets fp2, further methods for advanced mathematics version b. Edexcel further pure mathematics 2 fp2 edexcel igcse further pure maths. The locus of the points represented by the complex number. Pure further mathematics 2 revision notes november 2014 2 fp2 nov 2014 sdb further pure 2 1 inequalities. Fp2 oct 2016 sdb 9 nth roots of a complex number the technique is the same for finding nth roots of any complex number. Further complex numbers further complex numbers pearson. As we saw in the introduction, complex numbers can act as variables in quadratics just like any other number. Alevel core pure further maths paper 1 and 2 questions organised by topic for edexcel. Click here for recent fp2 exam questions on this topic click here for worked answers to all recent fp2 exam questions on this topic work covered in last. 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.
Alevel edexcel core pure further maths exam questions by. Further pure mathematics fp2 issue 1 september 2009. Aug 21, 2016 fp2 further complex numbers click here for pdf booklet for mobius transformations lessons 20167 version. Exercise on exp and ln functions, ninth page in the booklet with 41 on bottom right corner of photocopy 2. Complex numbers tutorial for a level further maths fp1. You can express a complex number in the form z rcos. Further pure 2 fp2 complex number loci 2 perpendicular bisector edexcel. Know what is meant by the modulus of a complex number, and calculate it using pythagoras theorem. 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. Candidates sitting fp2 may also require those formulae listed under further pure mathematics fp1 and core mathematics c1c4.
Most of the lessons teaching was done during the 10 questions. Complex numbers of the form x 0 0 x are scalar matrices and are called. Kinematics,centre of mass, kinetic and potential energy, momentum and. Complex number operations lesson plans and activities project maths. Using complex numbers to represent regions on an argand diagram. General discussion further pure 1 4 maths 2015 all exam boards further maths help fp2 complex numbers transformations further pure 2 or mechancis 1 hardest fp2 3 questions edexcel module choice fm how hard is fp3. Sample chapter from oxford a level mathematics for edexcel. Paper references edexcel gce pearson qualifications. Fp2 pure further mathematics 2 revision notes november.
Fp2j1 understand the polar modulusargument form of a complex number, and the definition of modulus, argument. A level further mathematics core pure mathematics practice papers 15. We are working hard on a new platform for setting, building and monitoring homework. Sometimes a quadratic has no real roots and can only be solved by using complex numbers. Fp2 pure further mathematics 2 revision notes november 2014. The value r is the modulus of the complex number, its distance from the origin 0,0 the argument is the angle the complex number makes with the positive x. Fp2 june 2014 question 4a fp2 june 2012 question 3.
Study materials for the complex numbers topic in the fp2 module for alevel further maths. The meaning of conjugate, modulus, argument, real part, imaginary part and equality of complex numbers should be known. This is a collection of revision questions for ocr fp1 adapted from aqa papers fp1 and fp2. It covers mainly solving equations and loci as these are the sections my students tend to struggle on. Make sure that you understand why this is the case, both algebraically using the sum of a geometric series and geometrically using vector addition. Dfm is a huge bank of free educational resources for teaching mathematics, with full sets of slides, worksheets, games and assessments that span year 7 to further maths and enrichment resources with a maths challengeolympiad focus. Mfp2 gce mathematics unit further pure 2 5366, 5370, 6366. Fp2 june 2011 question 7a loci in the complex plane. The technique is the same for finding n th roots of any complex number. You can express a complex number z with modulus r and. In spite of this it turns out to be very useful to assume that there is a number ifor which one has. Further complex numbers edexcel fp2 the maths centre. 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. Edexcel has a weird further maths syllabus general discussion further pure 1 4 maths 2015 all exam boards fp2 complex numbers transformations fp2 of s2 fp2 compared to a2 maths fp2 aqa hardest topic in fp2.
Ocr fp1 complex number practise teaching resources. Complex numbers edexcel further pure mathematics 1 fp1 what students need to learn. Edexcel igcse further pure mathematics 4pm1 e learning video. Write down a complex number, z, in modulusargument form as either zrcos. Inequalities, series, further complex numbers, first and second order differential equations, maclaurin and taylor series and polor coordinates. Two complex numbers are equal to each other if and only if their real parts are equal and their imaginary parts are equal, i. The locus l 2 consists of the points representing complex numbers z for which arg 1 2i 3 s z. With and being real numbers and being the imaginary unit. Really useful for anyone teaching the edexcel fp2 course especially if you are new to it. A level further maths 2017 old a level websites stuff. Pure further mathematics 2 revision notes studywise. Fp2 further complex numbers click here for pdf booklet for mobius transformations lessons 20167 version.
Complex numbers r a g express a complex number in the form rcos. Mfp2 gce mathematics unit further pure 2 5366, 5370, 6366, 6370. Exercise 3a, eleventh page in the booklet with 23 on bottom right corner of photocopy 3. A quick quiz to recap on the first bit of work we had done on complex numbers and then get them to figure out what we were doing next. Exam questions further complex numbers examsolutions.
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