Easter Work (Dr Brennan-Rhode's lockdown work guide)



Woodhouse Further Maths DepartmentLower Sixth self-reflection sheet & remote work planPrior to your one to one meeting with your maths & further maths teacher, you should fill out the following questions. You should attend the meeting with this questionnaire ready to share!How confident are you feeling with each topic studied since lockdown began? Which ones do you really need to work on?TopicTotally confidentNeeds some workThis is a priority!SeriesRoots of polynomialsVolume of revolutionMatricesLinear transformationsProof by inductionVectorThinking about the year in general, especially considering MA1/2, are there any other topics that really need your attention this summer?What resources will you use to complete this revision?Think carefully about all the text book mixed exercise questions and integral resources. How much have you completed so far?What work are you going to focus on over the summer and bring with you in September?Below, majority of them is Dr Brennan-Rhode's lockdown work guide. You can use this to give yourself an idea of the amount of work you might need to do if you need to catch up on any specific topics.Chapter-3 Series (Dr Brennan-Rhode's lockdown work guide)Instructions Read the Guide to remote learning (attached) if you haven’t alreadyWatch Series Part 1 video Ex 3A, page 46 of Core Pure 1. Q 2, 4, 5, 9, 10, 14Watch Series Part 2 video Ex 3B, page 49 of Core Pure 1. Q 2a,b, 4, 7, 10, 11Complete the section test (attached) without looking at the answers. Then mark it.Chapter-4 Roots of polynomials (Dr Brennan-Rhode's lockdown work guide)Week-1Watch my two videos:Ex 4A page 56 - Q2, 7, 10Ex 4B page 58 - Q 2, 3, 8, 11Ex 4C page 60 - Q 5, 8, 10, 13Alternative approach – Can you just teach it to yourself – I attach a sheet of questions that could motivate you to teach this part yourself. If you struggle with that, watch the videosWeek-2Watch my video on identities: Ex 4D Page 63 Q 2, 4, 5, 6, 10, 11, 14Watch my video on transformations of roots: Ex 4E Page Ex 4E Page 66, Q 3, 4, 7, 8 and mixed exercise questions.Extension question: How many total roots will a polynomial (with integer coefficients) with the below roots have? Why?x= -5, x=7 and x=3+2iChapter-5 Volume of revolution (Dr Brennan-Rhode's lockdown work guide)Week-1Watch Henry Rudd-Clarke’s videos on Volumes of revolutions: questions from Ex 5A on page 73. Q 3, 4, 6, 7, 8, 9Have a go at the challenge as well.Week-2Content is easy on this chapter, but the questions are hard! Pay close attention!Watch Henry Rudd-Clarke’s second video on Volumes of revolutions: Complete questions from Ex 5B on page 77. Q 2, 4, 7Complete questions from Ex 5C on page 81. Q 2, 3, 6, 7Complete questions from Ex 5D on page 84. Q 4, 7Have a go at the challenge as well.Chapter-6 Matrices (Mr Kadir’s lockdown work guide) these following videos and complete textbook questions6A question 13 to 18.Introduction & The size of a matrix C1-01 Matrices: Introducing Matrices C1-02 Matrices: Special Matrices C1-03 Matrices: Adding and Subtracting Matrices C1-04 Matrices: Multiplying a Matrix by a Scalar C1-05 Matrices: Associativity & Commutativity 6B question 6, 9, 10, 17, 18 & 19.C1-06 Matrices: Multiplying Matrices C1-08 Matrices: Proving Matrix Multiplication is not Commutative 6C question: 4, 5, 6, 8 & 14 Singular and Non-Singular Matrices C5-01 Determinants: Introducing Determinants C5-02 Determinants: Determinants of 2x2 Matrices C5-07 Determinants: Determinants of 3x3 Matrices Determinants of a matrix using a calculator 6D question: 2, 5, 10 & 13 C6-03 Inverse Matrices: Finding the Inverse of a 2x2 Matrix C6-08 Inverse Matrices: Inverse of a Product of Matrices Inverse Matrices: Singular Matrix Problem question: 1, 3, 6 & 8C6-10 Inverse Matrices: Finding the Inverse of a 3x3 Matrix Inverse Matrices: 3x3 Transformed Triangle Problem a calculator to find inverse of a 3x3 matrix question: 1, 3 & 5(please watch all nine videos, this topic is quite important)1.C7-04 Simultaneous Equations: Three Equations Simultaneous Equations: 3x3 Matrix Geometrical Interpretation: Two Dimensions Geometrical Interpretation: Three Planes Geometrical Interpretation: Example 1 Geometrical Interpretation: Example 2 Geometrical Interpretation: Example 3 Geometrical Interpretation: Example 4 Geometrical Interpretation: Example 5 all the questions from the mixed exercise.HW Matrices topic assessmentsHW Systems of equationsChapter-7 Linear transformations (Mr Kadir’s lockdown work guide)7A question: 2, 4, 6, 8 & 10 C3-01 Matrices: Introducing Matrices as Transformations C3-02 Matrices: Transforming Coordinates C3-03 Matrices: Stretches and Enlargements Full list of videos: question: 2, 4, 6, 8 & 10 C3-06 Matrices: Reflections C3-09 Matrices: Examples of Finding a Rotation Matrix C3-10 Matrices: Describing a Rotation Matrix 7C question: 4, 6, 8, 10 & 12C3-03 Matrices: Stretches and Enlargements question: 4b(i), 6, 8, 10 & 12C3-12 Matrices: Successive Transformations Matrices: Successive Transformations Problems question: 2, 4, 6, 7C3-17 3D Matrices: Reflection in the Plane x=0 3D Matrices: Rotation of 90 degrees anticlockwise about the x-axis 3D Matrices: Successive Transformations Problem question: 2, 4, 6, 8, 10 & 12C5-06 Determinants: Negative Determinants and Orientation Inverse Matrices: 2x2 Transformed Triangle Problem exercise: please complete textbook questions: 2, 4, 6, 8, 10 & 12HW Linear Transformations Topic assessmentChapter-8 Proof by induction (Dr Brennan-Rhode's lockdown work guide)Watch video by Henry Rudd-Clarke on proof by induction: all of Ex 8A. This is really important. It takes a bit of getting used to.Submit a clear photo of your answer to the attached exam questions. It must be perfect with a perfect conclusion.Reminder: the conclusion is: We have shown true for n=1.When assumed true for n=k, we have shown true for n=k+1Therefore true for all integers n≥1 Complete Exercise 8B and 8C watching the videos by Henry Rudd-ClarkeVideo on 8B on 8C Vector (Mr Kadir’s lockdown work guide)Please complete the following textbook questions:Ex 9(a) Q-4, 7, 13 & 15Ex 9(b) Q-2, 4 & 6Ex 9(c) Q-2, 8 & 12Ex 9(d) Q-4, 5, 7, 8, 10 & 14 Ex 9(e) Q-3, 6, 8 & 11Ex 9(f) Q-2, 4, 7, 98 & 11Complete all the questions from the mixed exercise.Work outside further core -1 (Dr Brennan-Rhode's lockdown work guide)Complete both of these Madasmaths papers. One is Pure maths (year 1 and 2) and one is Mechanics and Stats. Complete it all before checking the worked solutions.Revision part 1: I would like you to complete at least five online lessons or homeworks from MyMaths.Reminder – login with:Username: woodhousecollPassword: dobson(you do not need an individual login, although you do have one sent to you by Mr. Kadir) just click that you are doing them for practiseRecommendation:Maths – Pure – Functions - FunctionsMaths – Pure – Differentiation -Differentiation parametric functionsMaths – Pure – Integration – Integration reviewStatistics – Hypothesis Testing – Hypothesis Testing 1,2, or 3Mechanics – Forces and Newton’s Laws – Dynamic FrictionRevision Part 2:Choose some videos from the AMSP’s collection of videos and watch them. Take notes.Please then tell me which MyMaths lessons and AMSP videos you did/watched (write on a piece of paper or in a word document and attach to this assignment along with your notes).Please do let me know feedback on the MyMaths and AMSP videos. Were they useful?Easter Work (Dr Brennan-Rhode's lockdown work guide)I want you to investigate something mathematical and tell me about it.I decided to do it to have a go myself, and I am going to share it with you. It is attached (video - Buffon's Needle) - have a watch (it's only a couple of minutes long). can present it using:a poster,a Powerpoint, a video, Geogebra DesmosA physical object (origami)Or just a well written story in Word!something else!As long as it is mathsy, interesting and well-presented I don't care. You can replicate a result you have seen, as long as you understand it and explain it in your own words. You could even just explain something I already showed you.Here are some ideas of where to look for inspiration:On YouTube: Numberphile, 3blue1brown, Matt Parker, Veritasium, VSauceOn Twitter: Tamas Gorbe, Rob Eastaway, John Burn-MurdochSome topic ideas:The maths of the current pandemicA weird proof of PythagorasA surprising place that pi or complex numbers appearwhy eπ163 is (nearly) a whole number?The key here is for you to just be interested in maths for a bit. Don't stress too much. You can do some other maths revision you wanted to catch up on too, I will leave this up to you. ................
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