Ch.

Title

Description

Notes

Duration

Key Skills

1

Algebra

Rules of indices

Manipulation of surds and rationalise denominator

Processing polynomials (+, -, x)

Factorising polynomials

Quadratic functions and their graphs

Completing the square

Solving quadratics (factors, formula, comp. square)

Simultaneous equations (quadratic + linear)

Solving linear + quadratic equations

8 Exercises

1.5: Identities; 1.6: Algebraic divison; 1.7:Factor theorem is not required

10 lessons

3

Coordinate

Geometry

Equation of a straight line

Parallel and perpendicular lines

2 Exercises

could simply use

y=mx+c

3.5 Midpoint is not required

4 Lessons

Using y=mx+c can be easier for weaker students to use

4

Sequences and Series

Sequences including those defined by an nth term

Arithmetic series – nth term and sum

2 Exercises

T_n=a+(n-1)d

S_n=ⁿ/₂[2a+(n-1)d]

4.4 and 4.5 not required

4 Lessons

Proof of  sum formulae for the arithmetic should be known

Ch.

Title

Description

Notes

Duration

Key Skills

5

Differentiation

Gradient of a graph – numerical approach

General approach to rates of change

General formula for ^dy/_dx when y = xⁿ

Second derivatives

Turning points

Tangents and normals to curves

Application of differentiation to gradients, tangents and normals

2 Exercises

Notation that

^dy/_dx = f’(x)

m₁ x m₂ = -1

5.5: Increasing functions 5.9: practical problems

not required

5 Lessons

6

Integration

Integration as inverse to differentiation

Integration of xⁿ where n Î rational nos. n ¹ -1

Solution of differential equation ^dy/_dx = f(x)

1 Exercise

A = ò f(x) dx

6.5: Definite integrals

6.6 Area under curve not required

2 Lessons

PLEASE NOTE THAT CALCULATORS ARE NOT ALLOWED FOR THIS COURSE

There are a selection of workseets available in the maths dept. for each section although please select appropriate questions

No.

Title

Description

Resource/Notes

Duration

Key Skills

1

Algebra

Simple algebraic division and identities

Factor Theorem

Remainder Theorem

P1 book Ch 1 Pg 14  30

(3 Exercises)

6 lessons

2

Coordinate

Geometry

Equation of a circle

Use the properties: angle in semicircle is right angles

Perpendicular bisector

Perpindicularity of radius and tangent

P3 Ch 3

(2 Exercises)

4 lessons

3

Sequences and Series

Geometric series – nth term and sum

Sum to infinity of a geometric series

Binomial expansion and Pascal’s triangle

Factorial notation and nCr

P1 Ch 4 Pg 114 – 127( 2 Exercises)

T_n=ar ^n-1

S_n=a(1-rⁿ)/(1-r)

S¥ =^a/_1-r

P2 Ch 3 Pg 39 - 49

(3 Exercises)

10 lessons

Proof of  sum formulae for the geometric should be known

Expansion of

4

Trigonometry

Radian measure

Length of an arc

Area of a sector

The 3 basic trig. fuctions of any angle (ASTC)

Graphs of sin, cos, tan

Trig. identities

Solving simple trig. equations in a given interval

P1 Ch 2 (3 Exercises)

s = rq

A = ¹/₂r²q

Tan = ^Sin/_Cos

Sin²q + Cos²q = 1

6 lessons

Convert degrees to radians and vice versa. Some students will prefer to solve trig. equations in degree mode then convert later.

No.

Title

Description

Notes

Duration

Key Skills

5

Exponentials and logarithms

and its graph

Laws of logarithms

Solving equations of the form

P2 Ch5

( 4 Exercises)

May use the change of base formula

a= b, solve by taking logs on both sides.

8 lessons

6

Differentiation

Increasing and decreasing functions

Application of differentiation to maxima and minima and stationary points

P1 Ch 5 Pg 138 – 151

(1 Exercise)

2 lessons

7

Integration

Boundary conditions and definite integrals

Finding area of region bounded by curve and lines

Numerical integration: the trapezium rule

P1 Ch 6 Pg 160 – 171

(2 Exercises)

P2 Ch7 Pg 137-141

(1 Exercise)

6 lessons

There are a selection of workseets available in the maths dept. for each section although please select appropriate questions

Title

Topics

Time

Notes/HW suggestions

Algebra

Partial fractions

Remainder theorem and the factor theorem

The binomial series (1+x), n

1 lesson

1 lesson

1lesson

Negative and fractional indices

Range of values for which the expansion is valid

Differentiation

Differentiating composite functions using the chain rule

Product and quotient rule

Connected rates of change

Differentiating trigonometric functions

Differentiating functions given implicitly and parametrically

1 lesson

1 lesson

1 lesson

2 lessons

1 lesson

Coordinate geometry

Cartesian equation of the circle

Equations and properties of tangents to a circle

Sketching curves given by Cartesian equations

Sketching curves given by parametric equations

Curves with trigonometric parametric equations

1 lesson

1 lesson

1 lesson

1 lesson

1 lesson

Omnigraph

Review exercise 1

Integration

Integrating standard trigonometric functions

Integration using identities

Integration using substitutions

Integration by parts

Systematic approach to integration using the above methods

Areas of regions and volumes of solids of revolution

Exponential growth and decay: forming and solving differential equations

1 lesson

1 lesson

1 lesson

2 lessons

2 lessons

2 lessons

2 lessons

Learn cos 2A identities and

secx = 1 + tanx

Identification of log function and numerator is derivative of denominator

Vectors

Some definitions: directed line segment, displacement vector, modulus of a vector, equality of vectors, zero vector and the negative vector.

More definitions and operations on vectors: unit vector, scalar multiplication of a vector, parallel vectors, adding vectors, commutative law, associative law, subtracting vectors and non parallel vectors

Position vectors, Cartesian components of a vector in 2 and 3 dimensions, Cartesian coordinates in 3 dimensions, distance between two points

Scalar or dot product of two vectors, scalar product in terms of Cartesian coordinates, projection of a vector on to another vector

Vector equation of a straight line, deriving Cartesian equations of straight line from a vector equation

1 lesson

2 lessons

2 lessons

1 lesson

1 lesson

Review exercise 2