Extension 1 Content List

Transcription

1 Extension 1 Content List Revision doesn t just happen you have to plan it! 2014 v2 enzuber 2014

2 30 minute revision sessions Step 1: Get ready Sit somewhere quiet. Get your books, pens, papers and calculator. Turn off your mobile phone, your internet. Choose a specific revision topic. Start the clock! Step 2: What can you recall? (5 minutes) Before you look at your notes, try to remember the key idea. Try to write a summary without looking at your note : write a few sentences, draw diagrams, give examples. Step 3: Review the content (5 minutes) Review your notes, look at the text books. Update your revision note if necessary. Step 4: DO a practice question (or three) (15 minutes) Do an easier and a harder question check your answers. Step 5: Reflect and update your plan (5 minutes) Ask yourself: What did I learn? What do I still need to work on? Update your revision note to reflect your learning. Decide if you want to do another 30 minutes on this topic. If so, allocate a time to return to the topic : use one of your catch-up dates, or mark an empty time period. Stop after 30 minutes. Colour two sunflower seeds. Give yourself an immediate reward for doing 30 minutes revision. This work is licensed Creative Commons CC-BY-NC-SA. You are free to share, copy, or modify this work for non-commercial purposes so long as you: (i) Attribute the source : enzuber (ii) Share all derived works under a similar CC license. Revision Checklist Extension1 v This resource is designed for teachers and senior high school students. enzuber@gmail.com exzuberant.blogspot.com For my students: please use our class edmodo not . Cover photo: Astrolabe by Andrés David Aparicio Alonso CC-BY-NC-2.0

3 2U topics extended into X1 Mathematics Extension 1 1 Equations: inequations with unknowns in the denom. 2e 5 6 Plane Geometry: circle geometry Trig Ratios: 3D, compound angles; t-transform; auxiliary angle; the general solution Linear functions: internal/external division into a ratio; angles between two lines. 7 Series: induction 9b Locus of the parabola : parametrics; properties of the parabola; locus problems 10 Geometry of the derivative: sketching rational functions 11 Integration: integration by substitution 13 Trigonometric functions: integrating sin 2 x, cos 2 x. 14 Applications to the physical world: exp. growth and decay difference from a constant; equations of motion in terms of x; simple harmonic motion; projectile motion X1 topics 15 Inverse Functions and Inverse Trigonometric Functions 16 Polynomials 17 Binomial Theorem 18 Permutations and Combinations

4 Remember: This course assumes you know everything in the 2 Unit course! Go back and revise anything you didn t fully understand. 1c Equations 0115 Solve inequations with unknowns in the denominator. 2e Circle Geometry 0220 Terminology: parts of the circle. Segment and a sector Problems involving angles at the centre compared to angles at the circumference Problems involving angles in the same segment Problems involving equal chords, chords equidistant from the centre, product of intercepts of two chords Problems involving cyclic quadrilaterals Problems involving tangents and radii, equal tangents from an external point, circles tangential to each other. Problems involving tangents and angles in alternate segment. Problems involving tangent and secant from external point. Image: CC-BY-NC Thomas Hawk.

5 05 Trigonometric Ratios D problems Compound angle formulae Double angle formulae t-transformation Auxiliary angle transformation The general solution. 06 Linear Functions and Lines 0602 Dividing an interval in the ratio m:n (internal and external) Angle between two intersecting lines. 7e Series: Induction 0705 Proof by mathematical induction - proving a formula Proof by mathematical induction - proving divisibility Proof by mathematical induction - proving inequalities.

6 09b Locus of the Parabola 0914 Parametric representations of curves - conversion between parametric and Cartesian form Parametric representation of the parabola Equations of the chord of a parabola and properties of the focal chord. Equations of tangents to the parabola (parametric and Cartesian) Equation of the chord of contact Special properties of the parabola (reflection property, focal chords and their tangents) Locus problems involving parabolas. 10 Geometry of the Derivative 1007 Curve sketching of rational polynomials. 11 Integration 1110 Integration by substitution: indefinite integrals Integration by substitution: definite integrals. Photo by Kevin Dooley CC-BY-2.0

7 13 Trigonometric Functions 1310 Integration of sin 2 x and cos 2 x. 14 Applications of Calculus to the Physical World 1402 Related rates of change problems Exponential growth and decay - difference from a constant dp/dt = k(p-a) Distance given v(x) - integration with respect to x Velocity given a(x) - integration with respect to x Simple harmonic motion concepts & problems Projectile motion concepts & problems.

8 15E Inverse Functions Finding inverse relations algebraically (swap x and y) and graphically (reflection in y=x). Definition and properties of monotonic functions and their inverses Restriction of the domain to make inverse functions Definitions and graphs of the inverse trigonometric functions Transformations of inverse trigonometric functions Four special properties of the inverse trigonometric functions. Differentiating and integrating the inverse trigonometric functions.

9 16E Polynomials 1601 Polynomials definitions and concepts Algebraic properties of polynomials Polynomial long division Polynomial division transform P(x) = D(x)Q(x) + R(x) Using the remainder theorem to find values of unknown coefficients. Using the factor theorem to find zeros of a polynomial. Equating coefficients of congruent polynomials to find values of unknown coefficients Sum and product of roots Numerical methods for finding roots: halving the interval. Numerical methods for finding roots: Newton's method.

10 17E Binomial Theorem 1701 Expansion of a + b n using the binomial theorem Proving Pascal's triangle identities Finding the greater coefficient or greater term in a binomial expansion Proving identities on the binomial coefficients. 18E Permutations and Combinations 1801 The Fundamental Counting Principle Permutations - counting ordered selections - with and without repetition Permutations - counting with identical elements Combinations - counting unordered selections Applications of permutations and combinations to probability Arrangements in a circle Binomial probability.

11 One sunflower seed = 15 minutes of revision Design: enzuber Original concept: Peter Garside Photo: CC-BY-NC Fir0002/Flagstaffotos

12 One sunflower seed = 15 minutes of revision Design: enzuber Original concept: Peter Garside Photo: CC-BY-NC Fir0002/Flagstaffotos