Work Covered After As Exams in Year 12

For examination in June of Year 13

Duration of course: approximately 17 weeks plus revision time (After AS examinations in Year 12 and Autumn Term in Year 13)

WORK COVERED AFTER AS EXAMS IN YEAR 12

TRIGONOMETRY (5 lessons)

Topic / Syllabus / Resources / ICT / Lessons
Trigonometric graphs / Knowledge of arcsin, arcos and arctan and their relationships to sine, cosine and tangent
Knowledge of secant, cosecant and cotangent
Properties of sinx, cosx, tanx, secx, cosecx and cotx – domain, range, symmetries, periodicity, shapes of graphs.
Knowledge and use of sec2x=1+tan2x and cosec2x=1+cot2x / Worksheets (see C3 folder)
A2 Core for OCR
Ch 2 A & B / Autograph / 3
ASSESSMENT

ALGEBRA AND FUNCTIONS (5 lessons)

Topic / Content / Text
A2 Core for OCR / ICT / Number of lessons
Functions / Identify the range of a given function in simple cases, and find the composition of two given functions;
Determine whether or not a given function is one-one, and find the inverse of a one-one function in simple cases;
Illustrate in graphical terms the relation between a one-one function and its inverse.
Even and odd functions / Ex 1A, 1B, 1C / Autograph for graph sketching / 5
Assessment

EXPONENTIAL FUNCTIONS (3 lessons)

Topic / Content / Text
A2 Core for OCR / ICT / Number of lessons
Exponential function and natural logarithm / Introduction to the properties and graphs of y = exand y = ln(x). Solving equations involving exand ln.To include the graph of y=eax+b+c. Solution of the equations of the form eax+b=p and ln(ax+b)=q is expected. / Ex 3A
Ex 3B / Autograph / 3
Assessment

WORK FOR AUTUMN TERM IN YEAR 13

DIFFERENTIATION (9 lessons)

Topic / Content / Text
A2 Core for OCR / ICT / Number of lessons
Differentiation / Differentiating expressions of the form (f(x))n, where f(x) is a polynomial. ) use of chain rule to differentiate powers of brackets (such as or ) Applications to TPs, tangents and normals. / Ex 4A Worksheets (see C3 folder) / 2
Use of the relationship . / Ex 4A
Differentiating y = exand y = ln(x).
Use of chain rule to differentiate y = ef(x) and y = ln(f(x)). Applications of differentiation. / Ex 4B
Ex 4C / 3
Exponential growth and decay. / Ex 4D / 1
Connected rates of change. / Ex 4E / 1
Product rule and quotient rule with applications.
product rule (to differentiate functions like
quotient rule (to differentiate functions like ). / Ex 4F / 2
Product rule and quotient rule with applications.
product rule (to differentiate functions like
quotient rule (to differentiate functions like ). / Ex 4F / 2
Assessment
TRIGONOMETRY (6 lessons)
Topic / Content / Text
A2 Core for OCR / ICT / Number of lessons
Trigonometrical identities and equations. / Knowledge and use of formulae for sin(A±B), cos(A±B), and tan(A±B), knowledge of the t(tan1/2x) formulae will not be required
Knowledge and use of double angle formulae (sin 2A, cos 2A & tan 2A)
Knowledge and use of expressions for acosx+bsinx in the equivalent forms of rcos(x±a) or rsin(x±a), candidates should be able to solve equations such as acosx+bcosx=c in a given interval, and to prove simple identities such as cosxcos2x+sinxsin2x=cosx / Ex 2C
Ex 2D
Ex 2F / 6
Assessment

NUMERICAL METHODS (4 lessons)

Topic / Content / Text
A2 Core for OCR / ICT / Number of lessons
Numerical methods / Recognising that a change in sign indicates a solution. Finding roots using decimal search. / Ex 6A / Autograph to plot graphs. / 1
Iteration methods for equation solving.Solution of equations by use of iterative procedures for which leads will be given. Knowledge of conditions of convergence not required but candidates should understand that an iteration may not converge. / Ex 6B / 2
Numerical integration – Simpon’s rule. / Ex 6C / 1
Assessment

Half term

INTEGRATION (6 lessons)

Topic / Content / Text
A2 Core for OCR / ICT / Number of lessons
Integration / Integrating expressions of the form (ax + b)n , eax + b and ln(ax+b) by inspection. Candidates should recognise integrals of the form ∫f’(x)/f(x) dx = lnf(x)+c. se to find areas. Integrate expressions involving linear substitution. / Ex 5B, Ex 5C, Ex 5D / 4
Solids of revolution (rotations about x and y axes). / Ex 5A, Ex 5B, Ex 5C, Ex 5D / 2
Assessment

ALGEBRA AND FUNCTIONS (5 lessons)

Topic / Content / Text
A2 Core for OCR / ICT / Number of lessons
Functions / Sketching graphs of functions involving the modulus function.
Solve equations involving the modulus function. / Ex 1D, 1E / Autograph for graph sketching / 3
Transformation of graphs.Combinations of the transformations y=f(x) as represented by y=af(x), y=f(x)+a, y=f(x+a), y=f(ax). Candidates should be able to sketch the graph of eg, y=2f(3x), y=f(-x)+1, given the graph of y=f(x) or the graph of, eg y=3+sin2x, y=-cos(x+π/4).
The graph of y=af(x+b) will be required. / Ex 1F / 2
Assessment

PROOF (2 lessons)

Topic / Content / Text
A2 Core for OCR / ICT / Number of lessons
Proof / Methods of proof (including counter example and contradiction). / Ex 7A, 7B, 7C / Autograph to plot graphs. / 2

FORMAL ASSESSMENT WEEK – Core 3 paper.

Core 4

DIFFERENTIATION (4 or 5 lessons)

Topic / Syllabus / Resources / ICT / Lessons
Trigonometric differentiation / Use the derivatives of sin x , cos x and tan x , together with sums, differences and constant multiples – use results in conjunction with the chain, product and quotient rules to differentiate more complex functions. Applications to tangents and TPs. / A2 Core Chapter 10 / for illustrating gradients of sin and cos. / 2/3
Implicit differentiation / Find and use the first derivative of a function which is defined implicitly – apply to finding gradients of curves, tangents, normals and TPs. / A2 Core Chapter 10 / Omnigraph/ Autograph for drawing implicit functions. / 2
Assessment

PARAMETRIC CURVES AND DIFFERENTIATION (3 lessons)

Topic / Syllabus / Resources / ICT / Lessons
Parametric equations / Understand the use of a pair of parametric equations to define a curve, and use a given parametric representation of a curve in simple cases.
Convert the equation of a curve between parametric and cartesian forms. / A2 Core Chapter 11 / Graphing software for plotting parametric curves. / 1
Find and use the first derivative of a function which is defined parametrically. Apply to finding equations of tangents/ normals and TPs. / A2 Core Chapter 11 / Graphing software for plotting parametric curves / 2
Assessment

CHRISTMAS HOLIDAY

BINOMIAL EXPANSIONS (2 or 3 lessons)

Topic / Syllabus / Resources / ICT / Lessons
Binomial expansion / Use the expansion of (1x)n, where n and x 1 (finding a general term is not included, but adapting the standard series to expand, e.g. (2 - 3x)n is included). / A2 Core Chapter 9 / 2 or 3
Assessment

INTEGRATION (10 lessons)

Topic / Syllabus / Resources / ICT / Lessons
Method of substitution. / Use the method of integration by recognition and by substitution to evaluate definite and indefinite integrals. / A2 Core Chapter 12 / 3
Integration of rational functions. / Integrate rational functions by means of decomposition into partial fractions / A2 Core Chapter 12 / 2
Integration of trigonometric functions. / Extend the idea of ‘reverse differentiation’ to include the integration of trigonometric functions (e.g. cos x and
sec2 2x );
Use trigonometric relations (such as double angle formulae) in order to facilitate the integration of functions such as cos2x / A2 Core Chapter 13 / 3
By parts / Recognise when an integrand can usefully be regarded as a product, and use integration by parts to integrate, for example, xsin 2x , x2 ex , ln x. / A2 Core Chapter 13 / 2
Assessment

ALGEBRA AND FUNCTIONS (4 lessons)

Topic / Syllabus / Resources / ICT / Lessons
Partial fractions and dividing polynomials / Recap of algebraic fractions from GCSE – simplifying, adding, subtracting, multiplying and dividing.
Divide a polynomial by a linear or quadratic polynomial, and identify the quotient and remainder.
Write rational functions in partial fractions in cases where the denominator has distinct and repeated factors and where the degree of the numerator is less than that of the denominator. / A2 Core Chapter 8 / 4

TRIAL EXAMINATIONS & HALF TERM

FIRST ORDER DIFFERENTIAL EQUATIONS (3 lessons)

Topic / Syllabus / Resources / ICT / Lessons
Differential equations / Modelling a situation as a differential equation.
Separate the variables in order to find the general solution of a 1st order differential equation. Use initial conditions to evaluate constants. / A2 Core Chapter 14 / 3
Assessment

VECTORS (5/6 lessons)

Topic / Syllabus / Resources / ICT / Lessons
Vectors / Carry out addition and subtraction of vectors and multiplication of a vector by a scalar, and interpret these operations in geometrical terms.Calculate the magnitude of a vector, and identify the magnitude of a displacement vector as being the distance between the points A and B. / A2 Core Chapter 15 / 2
Scalar product / Calculate the scalar product of two vectors and use the
scalar product to determine the angle between two directions and to solve problems concerning perpendicularity of vectors / A2 Core Chapter 15 / 1
Vector equation of a line. / Understand the significance of all the symbols used when the equation of a straight line is expressed in the form ratb;
Determine whether two lines are parallel, intersect or are skew;
Find the angle between two lines, and the point of intersection of two lines when it exists. / A2 Core Chapter 15 / 2 or 3
Assessment

EASTER HOLIDAYS

REVISION & PAST PAPERS

Notes on the scheme of work

ASSESSMENTS

Students should complete an assessment test at the end of each unit of work. These assessments can be completed in class or set as a homework exercise.

LESSON RESOURCES

Lesson activities are stored in the module folder.

USEFUL WEBSITES

(for interactive learning resources)

worksheets)