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Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2011"

Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2011"

A Further Maths "past paper" for Pure Core 1 on the new syllabus on Edexcel (2017). This is a "past paper" that takes questions from the June 2011 exam session, and adds in a few other questions from the textbook that are new to the syllabus this year. Great for preparing students for summer exams. All with solutions given.
samfletch18
Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2012"

Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2012"

A Further Maths "past paper" for Pure Core 1 on the new syllabus on Edexcel (2017). This is a "past paper" that takes questions from the June 2012 exam session, and adds in a few other questions from the textbook that are new to the syllabus this year. Great for preparing students for summer exams. All with solutions given.
samfletch18
40 slide Powerpoint Advanced Higher Maths Complex Numbers Argand Diagrams Worked Solutions

40 slide Powerpoint Advanced Higher Maths Complex Numbers Argand Diagrams Worked Solutions

40 slide Powerpoint for Advanced Higher Maths Unit 2: Complex Numbers. There is a brief revision of the basics of Complex numbers followed by a series of questions. The 24 questions (many of them multi-part) require the construction of Argand Diagrams, use of the quadratic formula, polynomial long division, and simultaneous equations. There are fully worked solutions (including diagrams) for complex number topics relating to: Equating Real and Imaginary Parts; Finding square, cube, fourth, fifth and sixth roots of complex numbers (including unity) and plotting them on an Argand diagram; Verifying and finding roots of complex number polynomials; Expanding and simplifying complex numbers using the Binomial Theorem and De Moivre’s Theorem; Interpreting geometrically loci in the complex plane; Conversions between polar and rectangular forms; Complex Conjugates; Exponential Form; Trigonometric identities, substitutions and simplification. The questions are grouped in approximate order of difficulty and to match the usual order of progress through this topic. *Animated workings come up line by line on mouse clicks.*
biggles1230
Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2013"

Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2013"

A Further Maths "past paper" for Pure Core 1 on the new syllabus on Edexcel (2017). This is a "past paper" that takes questions from the June 2013 exam session, and adds in a few other questions from the textbook that are new to the syllabus this year. Great for preparing students for summer exams. All with solutions given.
samfletch18
Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2014"

Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2014"

A Further Maths "past paper" for Pure Core 1 on the new syllabus on Edexcel (2017). This is a "past paper" that takes questions from the June 2014 exam session, and adds in a few other questions from the textbook that are new to the syllabus this year. Great for preparing students for summer exams. All with solutions given.
samfletch18
Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2015"

Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2015"

A Further Maths "past paper" for Pure Core 1 on the new syllabus on Edexcel (2017). This is a "past paper" that takes questions from the June 2015 exam session, and adds in a few other questions from the textbook that are new to the syllabus this year. Great for preparing students for summer exams. All with solutions given.
samfletch18
Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2016"

Pure Core 1 (Further Maths - Edexcel) "Past Paper June 2016"

A Further Maths "past paper" for Pure Core 1 on the new syllabus on Edexcel (2017). This is a "past paper" that takes questions from the June 2016 exam session, and adds in a few other questions from the textbook that are new to the syllabus this year. Great for preparing students for summer exams. All with solutions given.
samfletch18
Complex numbers - polar form, calculations and geometrical applications

Complex numbers - polar form, calculations and geometrical applications

The first resource introduces the technique for writing a complex number z=a+bi in (trigonometric) polar form, r(cos (theta)+ i sin(theta)), there are few examples of converting from one form into the other (to do as a class), and then an exercise of 30 questions for students to do. The next section introduces the exponential polar form re^(i theta), a few examples of converting from one form into the other (to do as a class), and then an exercise of questions for students to do. The exercise includes questions that get students to consider what z* and -z look like in both polar forms, as well as investigating multiplying and dividing complex numbers in polar form. Answers to the exercises are included. The second resource begins with a reminder of how to multiply/divide complex numbers in polar form, followed by an exercise of questions to practise. The remaining 3 pages cover the geometrical effect of multiplying, with several examples for students to learn from. Fully worked solutions are included. The final resource focuses on examination-style questions that consider the geometric effect of multiplying by a complex number in polar form. Fully worked solutions are included.
langy74
Complex numbers

Complex numbers

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1, which is called an imaginary number because there is no real number that satisfies this equation. For the complex number a + bi, a is called the real part, and b is called the imaginary part. This lesson is suitable for the AS and A level pupils and is written in a pupil friendly manner in order to help the students easily master the topic and go on to solve all of the relevant questions with ease and confidence.
nouchinjohn
Finding roots and real factors of z^n+k=0

Finding roots and real factors of z^n+k=0

The first resource guides your class through the process of using the real and complex roots of z^n+k=0 to write down its real factors. The introduction includes the important result about the sum of conjugates and then uses equations of the form z^n=1 or z^n=-1 to establish that there is always an even number of complex roots, which can be put into conjugate pairs. It is then shown how each conjugate pair of roots produces a real quadratic factor, while each real root produces a real linear factor. To practise all this there is an exercise with 7 questions for students to complete. Solutions to all the examples and the exercise are included. The second resource contains an exercise with further examination-style questions on this topic. This could be used as additional practice in class or as a homework/test. Answers are provided.
langy74
IB Maths HL - Topic 1 Algebra - Notes

IB Maths HL - Topic 1 Algebra - Notes

Handwritten notes that I made for my HL students on Topic 1 of Algebra in the IB. It includes: 1.1 - Sequences & Series 1.2 - Exponents and Logs 1.3 - Binomial Expansion & Permutations/Combinations 1.4 - Proof by Induction 1.5 - Complex Numbers 1.6 - Complex (Polar Form) 1.7 - De Moivre's Theorem/Euler's Theorem 1.8 - Complex Conjugate Roots of Polynomials 1.9 - Solving Systems of Equations with 3 variables
jwmcrobert