 # Calculus Externals

## General

Comments from the Chief Marker regarding the 2012 papers:

Above all else the defining characteristics of successful candidates were good algebraic skills.

There was also a noticeable correlation between the ability of students to present their thoughts in a clear, logical manner and the attainment of grades above Achieved.

As usual the ability to differentiate (or integrate) alone was not sufficient to pass the differentiation (or integration) standards. Algebraic manipulation of expressions into forms appropriate for differentiating or integrating is vital. It is also essential in solving a problem once the differentiation or integration step has been carried out.

With regard to lack of algebra, the marker mentioned specifically that problems with using brackets, negatives, fractions, logs and surds prevented students from reaching Achieved, even when they could do the calculus.

Notation Page

A page to help with some of the notation that will be used during the year.

Formula Sheet

The formula sheet that will be issued in the exams to students.

## Algebra of Complex Numbers

Complex Numbers on Graphics Calculators

Brief notes on how to get complex numbers on your graphics calculator.

### Questions

Worksheets for various types of question likely to be seen in the Complex Number paper.

Practice 1     Practice 2     Practice 3

Solving equations and inequations

Practice 1     Practice 2     Practice 3

Finding the missing coefficient in cubics

Practice 1     Practice 2     Practice 3

Quadratic formula and completing the sqaure

Practice 1     Practice 2     Practice 3

Practice 4     Practice 5     Practice 6

Complex number questions, the first three concentrating on rectangular form, the next three on polar form.

### Basic Skills

Practice at basic skills, which you will need in the other topics, as well as Algebra.

Practice 1     Practice 2     Practice 3

Logs and exponential equations

Practice 1     Practice 2     Practice 3

Powers

Practice 1     Practice 2     Practice 3

Fractions

Practice 1     Practice 2     Practice 3

Expanding

Practice 1     Practice 2     Practice 3

Factorising

Practice 1     Practice 2     Practice 3

Surds

## Differentiation

Practice 1     Practice 2     Practice 3

Practice at mixed differentiation, mostly harder Achieved, but a few Merit.

Practice 1     Practice 2     Practice 3

Practice sketching gradient functions from functions and vice versa. Also finding where second differentials equal zero.

## Integration

Flip cards for Integration

The first page gives simple examples of the main techniques. The next pages put those in more disguised situations and adds some Merit techniques.

They are intended to be folded over and glued, but putting them twice through a printer to print on the back of each page, preferably on light card, works too.

Practice 1     Practice 2     Practice 3

Practice at finding intergrals, focusing on getting the correct numerical correction factor. Mostly harder Achieved, but a few Merit.