Immediately below this paragraph is a table
with links to the exam questions and answers for all the externals way back to 2013.
Focus on the exams for the last three years. Recognise the type of question e.g This is
a question about..... Know how you are going to set out your working when answering each type of question.
We use the Nulake maths revision book. This external standard is worth 6 credits.
READ the question, all of it. There will be useful information
ANSWER the question. If it asks for the equation of a curve, then give the equation, not just the
integral. If it asks for the co-ordinates of a point, give the y-value as well as the x-value
Integration is anti-differentation. You find the integral of a power of a function by
raising the power by 1
dividing by the new power
dividing by the derivative of the composite part of the function
so the integral of (2x+1)^5 is (2x+1)^6/6*2 + c
With an indefinite integral don't forget the "+ c"
When there is a square root symbol, you will convert this to an exponent before you integrate
dividing by a fraction is the same as multiplying by the reciprocal of the fraction.
For example dividing by 3/2 is the same as multiplying by 2/3
if 'y' is proportional to 'x' then y = kx for some constant 'k'
if 'y' is inversely proportional to 'x' then y = k/x for some constant 'k'
Kinematic Equations are covered on pages 209-213 of the Nulake Year 13 Calculus Workbook
Velocity is the antiderivative (integral) of acceleration
distance (or displacement) is the antiderivative (integral) of velocity
You will probably have to work out what 'c' is at least once. This wll require you to
subsitute some information given to you in the question into the integral
So, Question 1c from the 2021 exam
Integration of Quotients (rational functions)
First type - the fraction is an improper fraction
This is covered on pages 178-182 of the Nulake Year 13 Calculus Workbook
The trick here is to treat the quotient as an improper fraction and seperate it into a
whole number and a proper fraction
Question 3c from the 2022 exam
Second type - the numerator is the derivative of the denominator
The trick here is to realise that this is the derivative of a natural logarithm
This is covered on pages 183-185 of the Nulake Year 13 Calculus Workbook
Question 3d from the 2023 exam
Integration of products of trigonometric functions
This is covered on pages 186-188 of the Nulake Year 13 Calculus Workbook
You need to use the formula sheet to convert the product to a sum
The formulae are on the back page. The one you want is probably going to
be a double angle formula or a product formula
For this exam make sure your calculator is set to 'radian' mode
Question 2c from the 2021 exam
Exponential and Log functions
Exponential functions are covered on pages 171-172 of the Nulake Year 13 Calculus Workbook
Log functions are covered on pages 176-177 of the Nulake Year 13 Calculus Workbook
the exponential function never goes below zero
the log function is undefined for a negative value of x
the exponential function is its own derivative and integral
Integration of differential equations with variable separated
This is covered on pages 233-234 of the Nulake Year 13 Calculus Workbook
In these dy/dx depends on both 'x' and 'y'. You will have to find the function ( y = ....)
use algebra to get all the 'y' and dy on one side and the functions of 'x' and the dx on the other
integrate both sides, put "+ c" on the 'x' side
you will be given some condition that lets you calculate 'c'
Question 2c from the 2022 exam
Trapezium Rule
The Trapezium Rule is covered on pages 216-219 of the Nulake Year 13 Calculus Workbook
make sure you can use the formula in your formula sheet
The answer to the question below is 8.92
2022 exam, Q3b
Simpson's Rule
Simpson's Rule is covered on pages 220-223 of the Nulake Year 13 Calculus Workbook
Make sure you can use the formula in the formula sheet.
