CORE MATHEMATICS 2 SCHEME OF WORK 2005-2006:
C2 UNIT: ≈ 40 Lessons (the course should be completed by Easter, leaving time for consolidation and past paper practice after Easter). A specimen paper is available and another one is at the back of the C2 staff copy. Otherwise, old papers under topic headings are needed.
The text used is Heinemann P1 (new edition). Other sources referenced include Heinemann C2 (staff copy), Introducing Pure Mathematics (Smedley & Wiseman) (MAC & JLW have old edition, PJW, SAM and ACD new). Also remember to make use of the Heinemann “A-Level Exambank” CD-Rom containing past paper questions under topic headings (see MC for a copy). Homework of approximately 1 hour duration should be given after each lesson, including revision, past paper and review exercise questions whenever possible. Encourage pupils to use the likes of the website “AS Guru”.
The formulae that candidates are expected to know are indicated in the appropriate sections in this scheme. Other formulae can be found in the booklet Mathematical Formulae including Statistical Formulae and Tables – please allow pupils to familiarise themselves with this document as early as possible within the course (new version for 2005 onwards).
In order to assist pupils’ learning, give short timed tests as lesson starters, using examination style questions, as early on in the course as possible.
It is assumed that pupils have a good knowledge of C1 material and its formulae. Exam is 1½hr, approx 9 questions, with (QCA) calculators permitted.
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Time |
Specification |
Notes |
Page and Exercise |
Other Sources |
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• Trigonometry: The sine and cosine rules, and the area of a triangle in the form ½absineC Radian measure Arc length and sector area (radian form) Sine, cosine and tangent functions. Knowledge and use of tanθ ≡ sinθ / cosθ and sin²θ + cos²θ = 1 (learn) Solutions of simple trigonometric equations in a given interval |
A=½absineC and a/sine A=b/sineB = c/sineC not in booklet, but a²=b²+c²-2bc cosA is. NB Include surd form for functions of 30º, 45º & 60º Use of s = rθ and A = ½r²θ for a circle Discuss symmetry, amplitude and periodicity of these graphs and use this to determine the sin, cos or tan of any magnitude. e.g. y = 3sinx, y = sin(x + π/6), y = 3sin2x e.g. sin(x – π/2) = ¾ for 0<x<2π c cos(x + 30º) = ½ for –180º<x<180º tan2x = 1 for 90º<x<270º 6cos²xº + sinxº - 5 = 0 for 0<x<360 sin²(x + π/6) = ½ for –π<x<π |
Ex8E p244 Ex 2A p50 Ex2B p67 Ex2C p73 |
Ex2B p61(p64) Ex2D p70(p74) Ex14A p347q3— (ex15A p354)q3-- |
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• Differentiation: Applications of differentiation to maxima and minima and stationery points: this will include curve sketching and optimisation problems. Increasing and decreasing functions |
The notation f’’(x) may be used. |
Ex5B p147 |
Ex6C p181(p180) |
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CoordinateGeometry in the x-y plane: Coordinate geometry of the circle using the equation of the circle in the form (x-a)²+(y-b)²=r² Knowledge of these properties:
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Be able to find the radius and coordinates of the centre of the circle given its equation and vice versa |
Ex3A p69(P3 text) |
Ex8Ap224 (p223_ |
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Algebra and Functions: Simple algebraic division Factor theorem, including extending to factorise cubic expressions such as x³+3x²-4 and 6x³+11x²-x-6 The remainder theorem: determine the remainder when the polynomial f(x) is divided by (ax+b) |
Only division by x+a or x-a will be required If f(x)=0 when x=a, then x-a is a factor of f(x) Understanding of terms “quotient” and “remainder” |
Ex1F p26 Ex1G p29 Ex1B p18 P3 text |
Ex4C p127(p131) Ex4B p124(p129) |
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• Sequences and Series: The sum of a finite geometric series The sum to infinity of a convergent geometric series, including the use of r <1 Binomial Expansion of (1+x) n for positive integer n. The notation n! and (n r) |
The general term and sum to n terms are required. Proof of the sum formula is needed . U n =ar n-1 , S n =a(1-r n )/1-r and S ∞ =a/1-r for r <1 in booklet (but learn!) Expansion of (ax+b) n may be required |
Ex4C p123 Ex 4D p126(select appropriate questions) Ex3B,3C,3D p41 |
Ex9D p250(p249) Ex9E p257q1-9(p256) Ex 9E q10----- (p256) Ex10A p267(p266) |
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Integration: Evaluation of definite integrals Interpretation of a definite integral as the area under a curve. Approximation of the area under a curve using the trapezium rule |
Evaluation of areas enclosed by curves and given lines. E.g. find the area bounded by the curve y=6x-x² and the line y=2x E.g. Evaluate the area under √ (2x-1) between x=0 and x=1 using the values of √ (2x-1) at x=0, 0.25, 0.5, 0.75 and 1. |
Ex6B p161 q2--- Ex6C p167 Ex7C p140 P2text |
Ex7B p205 q1,2 Ex 7Bp205 q3— (p204) Ex20B p487q1-6 (Ex21C p501 q1-6) |
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• Exponentials and logarithms: y=a x and its graph Logarithms: definition and laws (not in formula booklet) Solutions of equations of the form a x =b |
log a a ≡ 1 and log a 1 ≡ 0 log a xy ≡ log a x + log a y loga(x/y) ≡ log a x - log a y log a x k ≡ klog a x extending to log a (1/x)=-log a x Candidates may use the change of base formula |
Ex5A.B,C,D p104 P2 text |
Ex17C p414(Ex18C p420) |
For information: movement from P1 to C2:
Factor theorem (and remainder theorem (previously P3))
Algebraic division
Radians, arc length and sector area
Sine, cosine and tangent functions: their graphs, symmetry and periodicity; Trig identities and equations
Geometric series
Increasing and decreasing functions, optimisation problems, stationery points
Definite integrals and areas
The circle (from P3)
Sine, cosine and area formulae (previously background knowledge)
Omissions from C2, previously in P2:
Algebraic fractions (now C3)
Functions (now C3)
Recurrence relations (now C1)
Further trig e.g. sec θ , double and half angle etc. (now C3)
Exponentials and natural logs (now C3)
Differentiation of e x , lnx (now C3) and integration of these (now C4)
Volumes of revolution (now C4)
Location of roots and iteration (now C3) and further numerical integration (now C4)