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.
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]
the derivative as the gradient of a curve
Q3a from the 2023 exam
(ii) Find the coordinates of another point on the curve that has the same gradient as in part (i).
Q1a from the 2023 exam
Q3b from the 2023 exam
(i) What is the rate of increase of followers on day 5?
stationary points and the 2nd derivative test
Q3b(ii) from the 2023 exam
(ii) What is the maximum number of followers the social media account has during the first
90 days?
the equation of the tangent to a curve at a point
Q2b from the 2023 exam
sketching the gradient function
Q3b(iii) from the 2023 exam
(iii) How many days during the first 90 days does the social media account lose followers?
Use calculus methods to justify your answer.
Q1c from the 2023 exam
Q2a from the 2023 exam
antiderivatives (integration)
Q1b from the 2023 exam
Find the function whose gradient function is f'(x) = 4x3 - 6x2 - 4x
, and which passes through
the point (2,–5).
optimisation
Q1d from the 2023 exam
kinematics
Q2c from the 2023 exam
(ii) Using calculus methods, show that the distance the car travels between the time the driver
applies the brakes, and the car coming to a complete stop, is approximately 154 m.
(iii) A car with new brake pads is capable of deceleration of 2.5 m s–2. However, as a car’s
brakes age, they become less effective at slowing down the car.
If an older car’s brakes were only able to allow for a deceleration of 2.1 m s–2, what is the
highest speed in which the car should be travelling so that it is able to come to a complete
stop in the same distance (approx. 154 m) as the new car described in part (ii).
