Extension 1 Content List

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

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. http://creativecommons.org/licenses/by-nc-sa/3.0/ 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 v2014.1 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 email. Cover photo: Astrolabe by Andrés David Aparicio Alonso CC-BY-NC-2.0 http://www.flickr.com/photos/adapar/2562290656/

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

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. 0221 Problems involving angles at the centre compared to angles at the circumference. 0222 Problems involving angles in the same segment. 0223 Problems involving equal chords, chords equidistant from the centre, product of intercepts of two chords. 0224 Problems involving cyclic quadrilaterals. 0225 0226 0227 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. http://www.flickr.com/photos/thomashawk/156398361/

05 Trigonometric Ratios 0505 3D problems. 0510 Compound angle formulae. 0511 Double angle formulae. 0512 t-transformation. 0513 Auxiliary angle transformation. 0514 The general solution. 06 Linear Functions and Lines 0602 Dividing an interval in the ratio m:n (internal and external). 0607 Angle between two intersecting lines. 7e Series: Induction 0705 Proof by mathematical induction - proving a formula. 0706 Proof by mathematical induction - proving divisibility. 0707 Proof by mathematical induction - proving inequalities.

09b Locus of the Parabola 0914 Parametric representations of curves - conversion between parametric and Cartesian form. 0915 Parametric representation of the parabola. 0916 0917 Equations of the chord of a parabola and properties of the focal chord. Equations of tangents to the parabola (parametric and Cartesian). 0918 Equation of the chord of contact. 0919 Special properties of the parabola (reflection property, focal chords and their tangents). 0920 Locus problems involving parabolas. 10 Geometry of the Derivative 1007 Curve sketching of rational polynomials. 11 Integration 1110 Integration by substitution: indefinite integrals. 1111 Integration by substitution: definite integrals. Photo by Kevin Dooley http://www.flickr.com/photos/pagedooley/1918813544/ CC-BY-2.0

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. 1404 Exponential growth and decay - difference from a constant dp/dt = k(p-a). 1407 Distance given v(x) - integration with respect to x. 1408 Velocity given a(x) - integration with respect to x. 1409 Simple harmonic motion concepts & problems. 1410 Projectile motion concepts & problems.

15E Inverse Functions 1501 1502 Finding inverse relations algebraically (swap x and y) and graphically (reflection in y=x). Definition and properties of monotonic functions and their inverses. 1503 Restriction of the domain to make inverse functions. 1504 Definitions and graphs of the inverse trigonometric functions. 1505 Transformations of inverse trigonometric functions. 1506 1507 Four special properties of the inverse trigonometric functions. Differentiating and integrating the inverse trigonometric functions.

16E Polynomials 1601 Polynomials definitions and concepts. 1602 Algebraic properties of polynomials. 1603 Polynomial long division. 1604 Polynomial division transform P(x) = D(x)Q(x) + R(x) 1605 1606 1607 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. 1608 Sum and product of roots. 1609 1610 Numerical methods for finding roots: halving the interval. Numerical methods for finding roots: Newton's method.

17E Binomial Theorem 1701 Expansion of a + b n using the binomial theorem. 1702 Proving Pascal's triangle identities. 1703 Finding the greater coefficient or greater term in a binomial expansion. 1704 Proving identities on the binomial coefficients. 18E Permutations and Combinations 1801 The Fundamental Counting Principle. 1802 Permutations - counting ordered selections - with and without repetition. 1803 Permutations - counting with identical elements. 1804 Combinations - counting unordered selections. 1805 Applications of permutations and combinations to probability. 1806 Arrangements in a circle. 1807 Binomial probability.

One sunflower seed = 15 minutes of revision Design: enzuber 2012. Original concept: Peter Garside Photo: CC-BY-NC Fir0002/Flagstaffotos

One sunflower seed = 15 minutes of revision Design: enzuber 2012. Original concept: Peter Garside Photo: CC-BY-NC Fir0002/Flagstaffotos