SPECIFICATION CONTENTS FOR CORE 4
SPANNING THE SECOND HALF OF YEAR 13
TERM CONTENT
YEAR 13
More Algebra
SPRING TERM Series
(2nd Half) Curve sketching
Further differentiation
Integration
More Integration
SUMMER TERM Differential equations
Vector Geometry
Revision & Past Papers
Page 1
MATHEMATICS SCHEME OF WORK FOR Text: : Pearson Longman (There are also linked - Syllabus 1992-99)
Exercises from PURE Authors: G Mannall
DEPARTMENT A-LEVEL MODULE C4 ‘A2 Core for Edexcel’ MATHEMATICS 1-4 and M Kenwood.
(ISBN: 0 582 84236 0)
CHAPT. TOPIC TIME OBJECTIVES SPECIFICATION NOTES METHODOLOGY OTHER ASSESSMENT
(wks) (C4 Specification) RESOURCES
Ch. More Algebra 2 Algebraic Division. Revision of the Remainder Revise the factorisation
Ex.1E
1&8 [C3 Course] Theorems applied to techniques used in C1/2. (P2 Book)
polynomials with real Cover algebraic division as
coefficients and their real a preparation for certain Ex 1B
factorisation. (C2) types of partial fractions (P. 8)
questions, where the
degree of the numerator is
Partial Fractions. Denominators will be linear equal (or higher) than the
or quadratic. To include denominator. Ex.1D
denominators such as :- (P2 Book)
(ax + b)(cx + d)(ex + f) or
2
(ax + b)(cx + d) or Ex. 8A
2
(ax + b)(cx + dx + e) Check some of the (P. 186)
answers by multiplying out.
Candidates may require
partial fractions for use in
simplifying for integration
and/or differentiation.
Ch. 9 Series 2 Binomial Expansion (C2 Revision) Extend ideas to form the Ex.5B
Ex.5C
Expansion of (1 + x)n Start by multiplying out Binomial Theorem. Show (P2 Book)
for a positive binomial terms and relate how the Binomial
integer n. to coefficients of Pascal’s coefficients can be Old P3 Book
(Revision of C2) Triangle. expressed in terms of nCr . Ex 2C
(Link with Stats.) (Link with Stats.)
Ex 9A
Also the Binomial Theorem Also show how Partial
decomposition of Expansion of (1 + x)n for (P. 197)
Fractions can break
rational functions into rational values of n and expressions down before
partial fractions may -1 x 1 using the Binomial Theorem to
be required The notation n! and n expand them.
r
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CHAPT. TOPIC TIME OBJECTIVES SPECIFICATION NOTES METHODOLOGY OTHER ASSESSMENT
(wks) (C4 Specification) RESOURCES
Ch. 11 Curve 2 Cartesian and Questions may be set Make good use of Ex.10B
‘Omnigraph’ and graphical (P2 Book)
Sketching parametric equations involving tangents, normals
of curves. or areas under curves calculators.
(where x and y may be 1) Cartesian Equations
expressed parametrically
Revise y = mx + c Ex 11A & C
2
y = ax + bx + c (P. 229)
as either an algebraic or 3 2
y = ax + bx + cx + d
trigonometric function) [Selection]
Revise turning points,
Candidates may be inflexions etc.
expected to sketch the Look at y = f(x) / g(x)
curve. Questions involving Pay attention to g(x) = 0 to
oblique asymptotes will not give vertical asymptotes, etc.
be set. Investigate behaviour as x
becomes large/small.
Show examples of modulus
graphs and how 1 / f(x) is
related to f(x).
3) Parametric Equations Ex.10C
Converting from Parametric to (P2 Book)
Cartesian by eliminating ‘t’.
Plotting parametric equations
by tabulation.
Ex 11A & C
Discuss the appropriate (P 229)
ranges needed for ‘t’. [Selection]
Outline differences between
Circle and Ellipse equations in
both systems.
Equations could be of the
2 2 2
Equation of a circle. form (x-a) + (y-b) = r Begin by looking at centre Old P4 Book
(Not on Specification, and the origin and apply
but a useful extension x2 + y2 + 2gx + 2fy + c = 0 Pythagoras to a general Ex. 1A
topic) point (x,y)
Explain and link two forms 2
Hence x + y = r
2 2
and work out how to find Link with parametric form
the origin and radius given
r cos θ , r sin θ.
the equation (and v.v)
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CHAPT. TOPIC TIME OBJECTIVES SPECIFICATION NOTES METHODOLOGY OTHER ASSESSMENT
(wks) (C4 Specification) RESOURCES
Ch. 11 Further 1 Differentiation of Define parametric Ex.8E
(selection)
Differentiation functions defined equations and show how (P2 Book)
parametrically. ‘Omnigraph’ and graphical
calculators can be used to
plot in this mode. Ex 11B
Revise dy/dx = dy/dt .
(P.235)
dt/dx (gives gradient, ’m’
of the curve)
Hence apply previous Ex.8E
Differentiation of topic’s work to find (selection)
inverse functions : tangents & normals of (P2 Book)
dy/dx = 1 / (dx/dy) parametric equations. Ex 11C
(P. 237)
[Selection]
Ch. 12 Integration 1 Integration as a Examples to include solids Revise AS techniques for OU Video is
process to find formed by revolving about x areas under curves and an excellent
areas under curves and y-axis. (Restrict examples extend ideas to volumes. resource. It
Ex 12A
and Volumes of to polynomials) Consider elemental discs shows 3D (P. 254)
revolution. rather than rectangular models of
strips. various
volumes of
revolution.
Integration of To include the integrals of Revise and draw up a Ex.9A
Ex.9B
standard functions. ex and 1/x table of standard (P2 Book)
derivatives done so far.
By considering integration Ex 12B
as the inverse operation
(P. 259)
to differentiation, create a
table of standard
integrals. Ex 12C
(P. 267)
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Ch. More 2-3 a) Simple Questions may be set which Give plenty of examples Ex.9C
showing a range of Ex.9D
12 & 13 Integration techniques of require more than one Ex.9E
integration to application of integration by substitutions. Include square (P2 Book)
root types, and trigonometric
include parts.
questions.
decomposition, Substitutions will be given Use partial fractions to break Ex 12D
linear and non-linear except in the easiest of cases. down an expression and (P. 274)
substitutions, and show that solutions usually
simple integration Ex 12E
involve logs (ln). (Also
by parts. demonstrate the method of (P. 284)
expressing the constant as ln
K to give a neat solution)
b) Integrals of To include using integrals of Derive the ‘by parts’ formula Ex 13A
trigonometric say, tan x and cot x, by using by considering the d/dx(UV)
rule. (P. 298)
functions and logarithm recognition from
products using the integrating the related fraction. Show a ‘by parts’ example Ex 13B
where the integrand ‘loops (P. 305)
‘By Parts’ method. Examples may include areas back.’
and volumes. x
(say, e cosx ) Ex 13C
Use (P. 314)
Extend ideas to finding ‘Omnigraph’ to
Integrating parametric show Ex 13D
volumes using
c) Parametric equations by using parametric
Equations ∫ y (dx/dt) dt to find areas. ∫ ∏y 2
(dx/dt) dt. Compare curves help
(P. 323)
with Cartesian formulae and ‘see’ the areas
Chain Rule. and volumes.
Application of the trapezium rule
d) Numerical to functions covered in C3 and Ex 13E
integration of C4. Use of increasing number of
trapezia to improve accuracy and
(P. 328)
functions. estimate error will be required.
Questions will not require more
than three iterations.
Revision of 1 Different methods of INTEGRATION
integration. Selection from Review TEST
Integration Exercise on Integration.
Ex 13F
(P. 329)
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CHAPT. TOPIC TIME OBJECTIVES SPECIFICATION NOTES METHODOLOGY OTHER ASSESSMENT
(wks) (C4 Specification) RESOURCES
Ch. 9. Differential 2
Ex.3C (decay/growth)
10 & 14 Equations Formation of simple Only first order equations in Use exponential growth Also M2
differential which the variables are and decay as illustration. syllabus uses Ex 10B
Equations. separated. Link with biology and this method to (P. 213)
physics. solve [Rates of
Kinematics Change]
Cover ‘Connected Rates of and SHM &
Solution of simple Change.’ Stress the importance of problems. Ex 10C
differential the constant of (P. 220)
equations by E.g. Rate of change of integration and the initial (Decay /
analytical means. surface area of a sphere. conditions stated in the Growth)
Revise the ‘Chain Rule.’ problem. Ex.9G
(P2 Book)
Ex 14 A–C
(P. 344)
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CHAPT. TOPIC TIME OBJECTIVES SPECIFICATION NOTES METHODOLOGY OTHER ASSESSMENT
(wks) (C4 Specification) RESOURCES
Ch. 15 11. Vector 2-3 Cartesian Co- To include the distance This is a natural extension of Ex.7E
(P2 Book)
Geometry. ordinates in 3 between two points. the formula covered in C1/2,
(New) dimensions. but we have an additional
term
Ex 15A
2
(z2 – z1) . (P. 365)
Vectors in 2 and 3 Magnitude of a vector.
dimensions. Vector (Link with Mechanics) Definition of a unit vector in
(Old P3 book)
addition, direction of a Ex 6A
subtraction and Definition of orthogonal unit Ex 6B
multiplication by a vectors i, j, k.
scalar. Geometric Ex 15B
diagrams.(GCSE) Position vectors. OB - OA = AB = b - a (P. 370)
Show on ‘vector walk’
diagram. (GCSE) (Old P3 book)
Ex 6C
Vector Equations Forms to include Illustrate as ‘jump & run’
of lines r = a + tb Show similarities with Ex 15D
y = mx + c. (a is location & b (P. 380)
r = c + t(d - c) is gradient vector)
The Scalar (dot) a.b = a1b1 + a2b2 + a3b3 Use the scalar product to Ex 15C
product. prove that two vectors are (P. 374)
Cos AOB = a.b / a b perpendicular if a.b = 0
to find the angle between
two lines.
Revision 1 Past papers from C4 Selected
Specifications. Use bank of questions from
TEST
Review
papers in Subjects folder via Exercises at the (Past C4 Paper)
Interactive whiteboard. end of each
GENERAL 2-3 Also, www.mathsnet.net chapter / section
REVISION Be familiar with contents of Lots of ‘timed’
Formula Booklet supplied by PAST EXAM papers.
EDEXCEL. PAPERS
Page 7
C4 – Formulae
This appendix lists formulae that candidates are expected to remember and that may
not be included in formulae booklets.
Integration
function integral
1
cos kx sin k x + c
k
1
sin kx cos k x + c
k
1 kx
ekx e +c
k
1
ln x + c, x 0
x
f ( x) g ( x) f ( x) + g ( x) + c
f (g ( x)) g ( x) f ( g ( x)) + c
Vectors
x a
y b xa yb zc
z c
Notes:-
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