Order | Topic | UPM Reference | Specification reference | Notes |
1 | Algebraic Manipulation | p5 – 10 p131 - 133 | C1 Polynomials (a) C2 Algebra (b): algebraic division C1 Indices and Surds (b and c) C1 Indices (a) | Division of a cubic (at most) by a linear poly. Easy surds were covered in Pre Sixth Form Algebra booklet. |
2 | Quadratics | p10-12 p141 – 149 p152 - 156 | C1 Polynomials (b to f) C1 Coordinate Geometry and Graphs (h) C1 Polynomials (d) Linear and Quadratic inequalities C2 Algebra (a); Factor theorem and Remainder Theorem. | Completing the square. Use of the Discriminant (the word itself needs to be understood !) Identities: equating coefficients, eg. a(x+b)2 + c = 3x2 + 2x + 1 Proof of the quadratic formula may be required. Disguised quadratics eg x + 2 + 1/x =0, x4 – 3x2 + 2 = 0. Solution of quadratic inequalities Simultaneous equations – one linear, one quadratic |
3 | Trigonometry | P16 - 21 | C2 Trigonometry (a and b) | Sine and cosine rules. Area of triangle using 0.5absinC. |
4 | Coordinate Geometry | P 72 – 82 + Ex 3F No 1,2,5,7 and 8 p 87 – 89 p94 - 97 | C1 Coordinate Geometry and Graphs (a,b,c,d and g) | Very easy; do not spend too long on this as much of it is revision of GCSE work. |
5 | Differentiation | p255-269 p272-273 | C1 Differentiation (a – d) | Knowledge of Chain Rule is not required. Ability to differentiate, e.g. (2x + 5)(x – 1) and . This is a good opportunity to do some investigative work in the IT centre Use of second order derivative to establish nature of stationary points. Application to curve sketching. Use of . Finding tangents and normals. Rates of change, increasing and decreasing functions are all needed but ‘small changes’ is not needed. |
6 | Graphs and Circles | p 275 – 279 (281 Ex 11A No 1,2 and 5) p 284(11.3) – p287 Ex 11C No 1 – 5 P 385 – 389 Ex 16C No 1 – 12 | C1 Coordinate Geometry and Graphs (h,i,e and f) | Modulus not needed Sketch y = kxn, y = kx½ , y = product of 2 or 3 linear factors. Transformations involving translations, reflections and stretches. Intersecting circles is not on the syllabus, but it does give good opportunities to practise Algebra and Coord Geometry. Revise Simultaneous Equations, one linear and one quadratic. |
7 | Trigonometry Graphs and Radians | p101 – 109 p 124 - 127 | C2 Trigonometry (c,d and e) | Degrees to radians conversion, etc. The formulae s = rθ and A = ½r2θ. Radian measure, arc length and area of sectors. Ex 4G is good here. Leave the solving of Trig equations until later (eg example 32 and Ex 4g No 13) |
| End of C1 specification |
8 | Sequences and Series | P220 example 15 and Ex 8c No 1,2,4,5and 6. P208-217 P222-228 | Sequences and Series C2 (a-f) Use of Σ summation Arithmetic and Geometric Progressions Binomial expansion of for a positive integer n. | Iterative relationships, eg un = n2 and un+1 = 2un, should be revision of GCSE. Nothing in UPM on this topic. Questions in OCR book. Need to know Σr = 0.5n(n+1). The notations . The proof of Binomial Theorem may be too hard for some sets. |
9 | Trigonometry | P100 example 2 and p104 No3 P110-118 | Trigonometry C2(f-h) | Exact values of tan30, etc Include sec, cosec and cot as it means there is no restriction on the exercise questions (but not graphs of sec, etc) |
10 | Integration | P293 – 305 P314 Ex12F No1-4 and 6 P524 + Ex 21A (P526) No 1,2,3,7a,8a(NB radians) | Integration C2 (a-e) Definite and indefinite integrals of rational powers of x (index not = 1) Trapezium Rule | To include the area between 2 curves. Solving eg d2y = 30x with initial conditions. d2x Also infinite limits may be included (nothing in UPM on this). Questions may be asked on whether the estimate is an over- or under-estimate. |
11 | Logs and Indices | P136 – 141, inc Ex 5c No1--7,11,14,16,18,19, 20a,b,c 21a,c,d. P156 Ex 5H No 1,4,5,6,8,(9) | Algebra C2 (c-e) | Sketch y=ax for different a>0. Rules of logs (excluding change of base) and using logs to solve equation ax = bx-2 and similar. Some of these are quite tricky . |
