The general point on the parabola y2 4ax has coordinates at at2,2. Fp2 tutorials stuart the examsolutions guy 20181107t15. Suitable for use with all asa level maths andor further maths students. In fp2 youll need to know how to use the inverse trigonometric functions for differentiation and integration. Mei mathematics in education and industry mei structured mathematics further methods for advanced mathematics, fp2 practice paper fp2b additional materials. The straight line l is a tangent to the curve parallel to the initial line, touching the curve at the points p and q. Videos designed for the site by steve blades, retired youtuber and owner of to assist learning in. Further pure 2 fp2 polar coordinates 4 sketching polar cuvers fm. Figure 1 shows the curves given by the polar equations r 2. Converting the equation of a polar curve to cartesian form. This channel is managed by up and coming uk maths teachers. Or if anyone has the answer to question 3iv on the polar coordinates chapter assessment for fp2, that would be great. Jun 08, 2016 a find the polar coordinates of p and the polar coordinates of q.
Ill start by showing you the functions, what their graphs look like, and how to use them in calculus. There is a simple geogebra file that goes with the further complex numbers ppt, but youll have to edit the hyperlink. Fp2 tutorials stuart the examsolutions guy 20180508t08. Converting the equation of a polar curve to cartesian form converting the. Angles are generally expressed in radians anticlockwise from the x axis. These study materials are based on the edexcel and mei specifications for further pure mathematics 2.
We will look at polar coordinates for points in the xyplane, using the origin 0. A curve has polar equation where k is a constant with i use your graphical calculator to obtain sketches of the curve in the three cases 5. Converting the equation of a cartesian curve to polar form. In this unit we explain how to convert from cartesian co ordinates to polar co ordinates, and back again. Converting between cartesian and polar coordinates. In this section we will discuss how to the area enclosed by a polar curve. We will also discuss finding the area between two polar curves. Section a 54 marks answer all the questions 1 a a curve has polar equation for where a and k are positive constants. Chapter 11 conics and polar coordinates 158 figure 11. The equations are easily deduced from the standard polar triangle.
Accessible from school or college and home at any time. Further pure 2 fp2 polar coordinates 1 introduction and cartesian. Centre number candidate number edexcel gce further pure. Polar coordinates polar coordinates are given as points with r.
The main point of the video is finding the angle which can often cause problems. Mathematics mei thursday 15 may 2008 m34 sixth form. Converting cartesian coordinates to polar coordinates. Hence show that the cartesian equation of the curve is y x2 1. Jun 04, 2014 powerpoints and worksheets good as unit tests for the entire fp2 course, in a similar style to my other alevel stuff. Mei 4756 further methods for advanced mathematics fp2 question paper instructions to candidates these instructions are the same on the printed answer book and the question paper.
Powerpoints and worksheets good as unit tests for the entire fp2 course, in a similar style to my other alevel stuff. I am studying ocr mei fp2, and i just cannot get my head around polar coordinates, they continue to frustrate and confuse me. Fp2 tangents in polar coordinates the student room. Further pure mathematics fp2 a minimum of blind calculation. Made for the edexcel pearson books but can probably be adapted for other courses. Converting polar coordinates to cartesian coordinates. Mei mathematics in education and industry mei structured mathematics further methods for advanced mathematics, fp2 practice paper fp2 b additional materials. Competence statements polar coordinates polar co ordinates in two dimensions. In your mind take this curve in your hand and put it in the polar system, y will be the r that is the distance from the pole and x will be the angle, so imagine the curve stretched out as fanshape along an arc so that the zero y values will be in the pole distance is 0 at 0 and \pi.
The point p on the rectangular hyperbola xyc 2 has coordinates, c cp p a. Designed for the edexcel spec but applicable to aqa, ocr,mei and wjec. In polar co ordinates any point can be described in terms of its distance and direction from a fixed point o. The finite region r, shown shaded in the figure above. Fp2 chapter 7 polar coordinates teaching resources. The figure above shows a curve c with polar equation r2 2cos2. Integral for the aqa, edexcel, mei, ocr and cambridge international specifications are integrated with hodder educations student etextbooks and whiteboard etextbooks for asa level mathematics. Polar coordinates mctypolar20091 the x,y co ordinates of a point in the plane are called its cartesian co ordinates. Tes global ltd is registered in england company no 02017289 with its registered office at 26 red lion square london wc1r 4hq. Alevel mathematicsmeifp2polar coordinates wikibooks. X is a continuous random variable with probability density function pdf fx. Instead of using these rectangular coordinates, we can use a coordinate system to circular. Leave blank 24 p48860a02428 do not write in this area do not write in this area do not write in this area 8. Ocr a level h645 and as level h635 further mathematics b mei.
Fp2p1 understand the meaning of polar co ordinates r. Mei maths m1 chapter assessment solutions alevel maths aqa s2. The finite region r, is bounded by the two curves and is shown shaded in the figure. I now run over three examples where you have to convert polar coordinates to cartesian coordinates.
Further pure 2 fp2 polar coordinates 1 introduction and. Polar coordinates, parametric equations whitman college. Converting polar coordinates to cartesian coordinates stuart the examsolutions guy 20200227t20. For instance, the point 1,1 in cartesian coordinates, would translate to v2. Effort to wait until tomorrow to check with my teacher. For example, i was trying to do this past paper question here. Polar coordinates are an alternative system which can describe position of a point. Further methods for advanced mathematics, fp2 specification ref. There is, however, a lot of crossover with other boards. Mei further methods for advanced mathematics fp2 ocr. Further pure 2 fp2 polar coordinates 4 sketching polar cuvers fm edexcel ocr mei.
Markov chains mei multivariable calculus mei vectors mei m1. 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. Answer bookletpaper graph paper mei examination formulae and tables mf2 time 1 hour 30 minutes instructions. The regions we look at in this section tend although not always to be shaped vaguely like a piece of pie or pizza and we are looking for the area of the region from the outer boundary defined by the polar equation and the originpole.
I would encourage you to look at or even try these examples in the video where you are asked to convert the cartesian coordinates to polar coordinates. The part that confuses me is for 3pi4 polar coordinates. Show that any point on the parabola is equidistant from the point a, 0 and the line x. If you got the question right first time, well done. Show, by considering its cartesian equation, that the curve is a circle. The area element in polar coordinates in polar coordinates the area element is given by da r dr d. Alevel mathematicsocrfp2polar coordinates wikibooks. Area bounded by a loop converting cartesian coordinates to polar form. Aug 29, 2015 this website and its content is subject to our terms and conditions. Fp2 edexcel further maths video tutorials examsolutions. We would like to be able to compute slopes and areas for these curves using polar coordinates. I have published pages for the calculus, hyperbolic functions, and further matrices topics specifically to help students doing mei fp2. It is advisable to check the official fp2 edexcel specification in case of changes. There are some aspects of polar coordinates that are tricky.
The part that confuses me is for 3pi4 aug 30, 20 further pure 2 fp2 polar coordinates 6 more integration aqa, mei and ocr. Tailored to each of the aqa, edexcel, ocr, mei, wjec. But there is another way to specify the position of a point, and that is to use polar co ordinates r. Standard integrals involving inverse trigonometric functions. The question paper will be found in the centre of the printed answer book. Section a 54 marks answer all the questions 1 a a curve has polar equation for where a is a positive constant. Fp2 mei further maths video tutorials from examsolutions. Further pure 2 fp2 polar coordinates 4 sketching polar cuvers fm edexcel ocr mei aqa. Converting polar coordinates to cartesian coordinates i now run over three examples where you have to convert polar coordinates to cartesian coordinates. Further pure 2 fp2 complex numbers 1 cartesian, polar and exponential form edexcel.
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