Revision doesn’t just happen – you have to

plan it!

Extension 1 Content List

enzuber 2014

2014 v2

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.

Cover photo: Astrolabe by Andrés David Aparicio Alonso CC-BY-NC-2.0 http://www.flickr.com/photos/adapar/2562290656/

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.

This work is licensed Creative Commons CC-BY-NC-SA. http://creativecommons.org/licenses/by-nc-sa/3.0/

Mathematics Extension 1

2U topics extended into X1

1 Equations: inequations with unknowns in the denom.

2e Plane Geometry: circle geometry

5 Trig Ratios: 3D, compound angles; t-transform; auxiliary angle; the general solution

6 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 sin2 𝑥 , cos2 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

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 Problems involving tangents and radii, equal tangents from an external point, circles tangential to each other.

0226 Problems involving tangents and angles in alternate segment.

0227 Problems involving tangent and secant from external point.

Image: CC-BY-NC Thomas Hawk. http://www.flickr.com/photos/thomashawk/156398361/

Remember: This course assumes you know everything in the 2 Unit course! Go back and revise anything you didn’t fully understand.

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 Equations of the chord of a parabola and properties of the focal chord.

0917 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.

Photo by Kevin Dooley http://www.flickr.com/photos/pagedooley/1918813544/ CC-BY-2.0

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.

13 Trigonometric Functions

1310 Integration of sin2 𝑥 and cos2 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 Finding inverse relations algebraically (swap x and y) and graphically (reflection in y=x).

1502 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 Four special properties of the inverse trigonometric functions.

1507 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 Using the remainder theorem to find values of unknown coefficients.

1606 Using the factor theorem to find zeros of a polynomial.

1607 Equating coefficients of congruent polynomials to find values of unknown coefficients.

1608 Sum and product of roots.

1609 Numerical methods for finding roots: halving the interval.

1610 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