Year 13 Pure Mathematics Syllabus 2006 - 2007 Textbook: Understanding Pure Mathematics. These notes should be read in conjunction with the C3 and C4 specifications, which include further detail on what is required for each topic. Specimen papers for the new units are available as are copies of the Cambridge textbooks which have been written specifically for OCR. References are made in the notes to use of IT. There are many places, in addition to those specifically mentioned where IT can be usefully employed. Also, the OHP graphic is particularly useful for graphing demonstrations and calculus work. AVM has some good ideas for the Casio. Please place copies of successful worksheets into the file. There are a large number of good worksheets available in the file in W13. C3 unit will be taken by all A Level 62 candidates in Jan 2007. |
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The following work was covered with the vast majority of the 6.1 students in June/July 2006. |
| Trigonometry | p118-123 | P2(4) – Trigonometry; Compound angle, Double angle. 1 + tan2 x = sec2 x , etc. asinx + bcosx also covered. | Sec, cosec and cot were introduced in Section 4. Proof of simple identities and solution of equations within a given interval. There is an IT sheet that works well, investigating the various trig identities. |
| Differentiation | p317-334 | Chain Rule(including integration), Product and Quotient Rules. Differentiation of simple functions defined implicitly. | Finding the equations of tangents and normals to curves given implicitly is required. |
NEW WORK FOR SEPTEMBER 2006 |
1 | Functions | p29 –45 p274-288 Cambridge OCR Core 3/4 pages 16-38 Modulus p113-128 | C3 – Functions; Composition and inverse functions; Graphs of functions and their inverses; Sketching curves; Modulus function; Simple transformations and combinations. | Simple odd and even functions. Domain and Range etc. Extra work needed on graphs of . The transformations . There is a worksheet that investigates transformations of trig functions using the IT centre or a graphic calculator. |
2 | Exponentials and Logs(ln) | Cambridge C3/4 P39-53 | C3- Understand the properties of exponential and Log functions and their graphs, including their relationship as inverse functions. Exponential growth and decay. | Laws of Logs covered in yr 12. This work not in Sadler and Thorning. |
3 | Differentiation of exp and logs | P477-488 Cambridge p65-89 | C3 Differentiate and ln x and integrate and . Together with constant multiples, sums and differences. | Work to include functions such as and . is not in text. |
4 | Volumes of revolution | p305-307 Cambridge p173-181 | C3 – Integration; Evaluation of volume of revolution about one of the coordinate axes | Include, for example the region between rotated about the x axis. |
5 | Numeriacal Methods | OCR p135-149 Or P530-532 +535 P182-191 or P525-527 | C3 - Locate root by sign change and/or graph. Iterative sequences Integration by Simpson’s Rule | Not Newton Raphson Trapezium Rule covered in C2 |
6 | Further Differentiation | P322-324 OCR p155-161 | C3 – Connected rates of change | Note |
C4 STARTS HERE |
1 | Calculus with Trig Functions | P367-374 OCR p203-223 | Differentiation of Trig Functions Integration of trig functions | Differentiation of sine,cosine and tan, and extend to cosec, sec and cot. Differentiation of inverse trig functions is not required. |
2 | Further Binomial | P228-231 OCR P275-283 | Binomial Expansion of for any rational index. | |
3 | Partial Fractions | P451-456 OCR P289-313 | Partial Fractions | Denominators to include (ax + b)(cx + d)(ex + f) and (ax + b)(cx + d)2 . The fraction may be ‘top heavy’. Application to integration, differentiation and series expansion (see Binomial Expansion).Method of differences in FP1 To include expansion of rational functions by decomposition into Partial Fractions. |
4 | Integration | P496-509, but not t subs OCR P224-240 Do not do inverse trig* as a full topic. But p233 OCR book qu.3 needed. | Integration by substitution and parts Integration using partial fractions and trig identities. | Substitution given except in the simplest cases. No integration of inverse trig functions. Revise volumes of revolution using harder functions. *NB:- Could be given the substitution to use for an inverse trig integration type question. |
5 | Parameters Revision of Implicit | P325-328 P334 OCR p241-253 OCR p328-345 | Parametric to Cartesian type questions. Finding Areas using parametric equations Work done at end of 61. | Curve sketching to be done. Not in Sadler and Thorning. Curve sketching to be done. |
6 | Differential equations. | P509-516 OCR p314-327 | Formation of simple diff equations First Order Differential Equations-solution by separating the variables. | Practice needed on Newton’s Law of Cooling type questions General and particular solutions. |
7 | Vectors | p47-62 p65-70 p409-413 p415-422 OCR p266 eg 4.6.5 OCR p254-274 P346-361 | 2 and 3 dimensionsMagnitude Position Vectors Distance between 2 points and distance of a point from a line. Vector and Cartesian equations of a Line including conversion between the two types. Scalar Product; its use for calculation of the angle between 2 lines. Determine if lines are parallel, intersect or skew. | AB = b - a Both 2 and 3 dimension needed a.b = 0 Þ a is perp to b or a or b = 0 Area of triangle and parallelogram needed. |
