FSMQ Additional Mathematics. FSMQ Additional Mathematics. FSMQ Additional Mathematics. FSMQ Additional Mathematics. FSMQ Additional Mathematics

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1 the Further Mathematics network Additional Maths (MEI Conference) 5 th July 2007 University of Reading Hello, my name is Tim And you are I have just completed my first year teaching Additional Maths to students from three different schools, through the Further Mathematics Network Lessons took place at the University of Warwick on Thursdays after school, 4pm-5.30pm I come from a University background and taught alongside someone with a school background. This worked well How many students did we have? At first we had getting on for thirty! They all seemed to enjoy the lessons, but sadly a lot dropped off (reasons: perhaps after school, too hard, largely though problems with schools arranging taxis) We finished with about twelve Why did students join our classes? NOT everyone joined our classes to sit the exam Even people who weren t too confident for the Additional Mathematics exam still recognised that the lessons had improved their confidence in GCSE no end, and had prepared them brilliantly for A Level Our success story was a student who was keen but not one of the best in the class. Over the course of the year he became a top student in his GCSE lessons. The school now wants to send 10+ students to Additional Mathematics next year One student even used Additional Mathematics to improve his confidence in his Core A Level Mathematics (and the improvements have been very noticeable) Homeworks/Independent Study? All students had access to the Online Resources Homework was set though some of the students weren t very motivated for independent study. It was hard to push this when they were doing this as an extra subject (I ll be harder next year!) We could cover the course content across the year but only just! Please ask me any questions at any stage of this hour or afterwards! This is a Conference so we ve got to have a few funnies 1

2 What is Additional Maths? The content of Additional Maths Extension to GCSE mathematics Aimed at able year 11 students Level 3 qualification 4 strands of Pure Maths each followed by an application 1. Algebra The binomial distribution 2. Co-ordinate geometry Linear programming 3. Trigonometry 3D Trigonometry 4. Calculus Kinematics Models of delivery Complete GCSE Maths in year 10 or by January of year 11, then study Add Maths Study alongside GCSE Maths in year 11 (or across Years 10 and 11) Whole group Selected students from a group It is preferable if the decision to enter the students for the exam is delayed for as long as possible Resources Textbook Online resources Past papers Handwritten solutions and Powerpoint solutions Professional Development 2-day CPD courses Day 1: introduction to the big ideas in Add Maths In-between: consolidation based on web-resources and textbook Day 2: teaching approaches, student misconceptions and extension work Useful URLs The Further Mathematics Network: Online resources: Past papers and CPD information Specification see 2

3 UCAS tariff points FSMQ A level AS level 120 A 100 B 80 C 60 D A 50 B 40 E C 30 D A 20 E B 17 C 13 D 10 E 7 Performance table points Grade Points A 45 B 40 C 35 D 30 E 25 Additional Mathematics Statistics candidates A B C D E % 44.50% 58.00% 67.40% 76.40% This is a Conference so we ve got to have a few funnies % % % % % % % % % % % % % % % the Further Mathematics network the Further Mathematics network Additional Maths Revision Day 11 th June 2007 University of Warwick Welcome! 3

4 Outline of Topics 1. Algebra I - Review 2. Algebra II - Techniques 3. Algebra III - Polynomials 4. Algebra IV - Applications 5. Co-ordinate Geometry I 6. Co-ordinate geometry II Applications 7. Trigonometry I 8. Trigonometry II Applications 9. Calculus I differentiation 10. Calculus II Integration 11. Calculus III Applications to Kinematics Algebra I - Review I. Linear Expressions II. Solving Linear Equations III. Changing the subject of an equation IV. Quadratic expressions V. Solving a quadratic equation that factorises VI. VII. Completing the square Simultaneous equations Question 1 Algebra II - Techniques I. Linear Inequalities II. Solving quadratic inequalities III. Simplifying algebraic fractions IV. Solving equations involving fractions V. Simplifying expressions containing square roots Question 5 Question 6 4

5 Question 13 Algebra III - Polynomials I. Operations with polynomials II. The factor theorem III. The remainder theorem Question 9 Question 9 Question 2 Question 10 5

6 Algebra IV - Applications I. The binomial expansion II. The binomial distribution Question 6 Question 6 Question 11 Question 5 Question 12 6

7 Question 9 Co-ordinate geometry I I. Co-ordinates II. The gradient of a line III. Parallel and perpendicular lines IV. The distance between two points V. The midpoint of a line joining two points VI. The equation of a straight line VII. Drawing a line given its equation VIII. Finding the equation of a line IX. The intersection of two lines X. The circle Question 10 Question 7 Question 7 Question 1 7

8 Question 4 Question 12 Co-ordinate geometry II - Applications I. Inequalities II. Using inequalities for problem solving III. Linear Programming Question 8 Question 5 Question 11 8

9 Question 11 Trigonometry I I. Using trigonometry in right-angled triangles II. Trigonometric functions for angles of any size III. The sine and cosine graphs IV. The tangent graph V. Solution of equations using graphs of trigonometric functions VI. Identities involving sin θ, cos θ, and tan θ VII. Using trigonemetric identities to solve equations VIII. The sine rule IX. The cosine rule X. Using the sine and cosine rule together Question 12 Question 4 Question 4 Question 3 9

10 Question 5 Question 9 Question 7 Question 3 Question 8 Question 2 10

11 Question 14 (Part One) Question 14 (Part Two) Trigonometry II- Applications I. Working in three dimensions II. Lines and planes in three dimensions Question 3 Question 8 Question 13 (Part One) 11

12 Question 13 (Part Two) Calculus I - Differentiation I. The gradient of a curve II. Finding the gradient of a curve III. Differentiation using standard results IV. Tangents and normals V. Stationary points Question 1 Question 2 Question 4 Question 10 12

13 Question 14 (Part One) Question 14 (Part Two) Calculus II - Integration I. Reversing differentiation II. Definite integrals III. The area between two curves Question 1 Question 3 Question 6 dy 13

14 Question 7 Question 2 Question 11 (Part One) Question 11 (Part Two) Question 13 (Part One) Question 13 (Part Two) 14

15 Calculus III Applications to kinematics I. Motion in a straight line II. The constant acceleration formulae III. Motion with variable acceleration: the general case IV. Finding displacement from velocity and velocity from acceleration Question 10 Question 8 Question 12 Question 14 Question 13 15

16 The End This is a Conference so we ve got to have a few funnies Here s looking at you kids Reminder to me Show Bob Francis Powerpoint exam solutions!! This is a Conference so we ve got to have a few funnies 16