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 Walker 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
derivative or slope of the gradient line. If it asks for the co-ordinates of a point, give the y-value as well as the x-value
The derivative of a curve/function at a point is the slope of the tangent line to the curve at that point. The derivative
is sometimes called the 'rate of change'.
When there is a square root symbol, you will convert this to an exponent before you differentiate
An interval can be described as -2 < x ≤ 1 OR (-2, 1]
Product Rule, Quotient Rule, Composite functions
You guys all know how to use these rules. Well done
First, write the rule down
Then, write down f = .... and g = ...
Underneath these write f' = .... and g' = ...
Then substitute f, g, f', and g' into the formula
remember to multiply by the derivative of the composite part of the function (if there is a composite part)
The chain rule is covered on pages 30-37 of Walker, together with exponential functions,
log functions and trig functions
The product rule is covered on pages 40-44 of Walker
The quotient rule is covered on pages 45-47 of Walker
Questions 1a and 2a from the 2022 exam
Maxima, Minima, Points of Inflection
Stationary points are covered on pages 61-72 of Walker
the derivative is zero at stationary points
if the second derivative is positive the point is a minimum
if the second derivative is zero the point is a point of inflection
if the second derivative is negative the point is a maximum
Question 1b from the 2022 exam
Equation of a normal
Tangents and normals are covered on pages 51-60 of Walker.
The slope of the tangent times the slope of the normal = -1
Question 1c from the 2022 exam
Kinematic Equations
Kinematics are covered on pages 86-89 of Walker.
The derivative of distance is velocity, v(t) = ds/dt
The derivative of velocity is acceleration, a(t) = dv/dt
When an object is stationary its velocity is zero
Question 2c from the 2022 exam
Optimisation Problems
Question 3e from the 2022 exam
Related Rates of Change
Related Rates of Change are covered on pages 73-85 of Walker.
In these problems you are asked to find, say, dh/dt, and you are given a related rate of change
such as dV/dt, and a formula connecting 'V' and 'h'
The technique is to write dh/dt as dh/dV times dV/dt, and to remember that dh/dV is just the reciprocal
of dV/dh
Question 3c from the 2022 exam
Derivatives of parametric functions
Parametric functions are covered on pages 48-50 of Walker.
Both 'x' and 'y' are expressed as functions of 't'
calculate dy/dt and dx/dt
then dy/dx = dy/dt times dt/dx
Question 1d from the 2022 exam
Properties of Graphs
These are covered on pages 16-27 of Walker.
A curve is continuous if it can be drawn without lifting the pen from the paper
A curve is smooth if just one tangent can be drawn at every point on the curve
A curve is differentiable at a point if is continuous and smooth at that point
The limit exists at a point if the curve approaches the same value from both sides of the
point
A curve is concave in an interval if it has an upright cup shape (curves inward)
A curve is convex in an interval if it has an upside down cup shape (curves outward)
