AQA Core 2

 

13.1 Algebra and functions

Laws of indices for all rational exponents

Knowledge of the effect of simple transformations on the graph y = f(x) as represented by

y = af(x)         y = f(x) +a

y = f(x + a)      y = f(ax)

Expected to use the terms reflection, translation and stretch in the x or y direction in their descriptions of these transformation

Eg y = sin 2x       y= cos(x + 30°)

     Y = 2 x+3        y = 2 –x

Descriptions involving combinations of more than one transformation will not be tested.

13.2 Sequences and Series

Sequences , including those given by a formula for the nth term

Position to term formulae

Sequences generated by a simple relation of the form x n+1 = f(xn)

Iterative formulae

To include their use in finding of a limit L as n à ¥ by putting L = f(L)

 

Arithmetic series, including the formula for the sum of the first n natural numbers

To include the å notation for sums of series

 

The sum of a finite geometric series

The sum to infinity of a convergent

( -1<r<1 ) geometric series

Should be familiar with the notation êr ê < 1 in this context

The binomial expansion of ( a + b)n for positive integer n

Should be familiar with the notation n ! and [n]

                                                                      r

Use of Pascal’s triangle or formulae to expand

( a + b)n will be accepted

The binomial expansion ( 1 + x ) n for positive integer n

13.3 Trigonometry

The sine and cosine rules

The area of a triangle in the form  ½ab sin C

Degree and radian measure

Sector arc length and area

Knowledge of the formulae l = rθ

                                    Area = ½ r2 θ

Sine, cosine and tangent functions

Their graphs, symmetries and periodicity Concepts of odd and even functions are not required

Knowledge and use of

Tan θ = Sin θ          sin2 θ + cos2 θ = 1

             Cos θ

Solution of simple trigonometric equations in a given interval of degrees or radians

Max level of difficulty ;

Sin 2θ = - 0.4

Sin (θ - 20°) = 0.2

2Sin θ – cos θ = 0

2 sin2 θ + 5 cos θ = 4

13.4 Exponentials and logarithms

y = ax and its graph

Using the laws of indices where appropriate

Logarithms and the laws of logarithms

loga x + logay = loga (xy)

logax – logay = loga (x/y)

klog ax = loga (xk)

 

The equivalence of

y = ax and x = logay

The solution of equations of the form

                                                   ax = b

Use of a calculator logarithm function to base 10 ( or base e) to solve for example 3 2x =2

13.5 Differentiation

Differentiation of xn, where n is a rational number, and related sums and differences

Eg x 3/2 + 3    including terms which

               X2                                                  

Can be expressed as a single power such as xÖ x

Applications to techniques included in Core 1

13.6 Integration

Integration of xn , n is a rational number and n ≠ -1

also related sums and differences Expressions such as  x 3/2 + 2x -1/2

Or x + 2 = x ½ + 2x – 1//2

       Öx

 

Approximation of the area under a curve using the trapezium rule

The term ‘ordinate’ will be used.

To include a graphical determination of whether the rule over- or under- estimates the area and improvement of an estimate by increasing the number of steps.