TopicFurther Maths
Calculus · SS2–SS3
Applications of differentiation
Using derivatives: gradients, tangents, maximum and minimum points, and rates of change.
- Before this
- Differentiation
Learn
- 1Stationary points and optimisationFind and classify stationary points, find where a function is increasing or decreasing, sketch a curve, solve 'largest' and 'smallest' problems by writing the quantity in one letter first, and find the greatest height of a thrown object.Done25 min
- 2Tangents, rates of change and small changesTangents and normals, including curves in x and y; connected rates of change with the chain rule; and approximate percentage changes.Done18 min
Flashcards
8 cards: the rules, facts and methods to know by heart, with the diagrams from the lessons. They come back until you know them.
Practise
Answer applications of differentiation questions one at a time. You'll know straight away whether you're right, with hints and the working step by step.
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Past questions (27)
From 2008–2023: 26 WAEC, 1 NECO. Theory questions first, then objective, newest first.
Theory (23)
- WAEC 2022 · Paper 2 · Q10A solid rectangular block has a base which measures by . The height of the block is and its volume …
- WAEC 2022 · Paper 2 · Q15Two particles, and , of masses and respectively moved in opposite directions. moved with a velocity …
- WAEC 2019 · Paper 2 · Q15Given that , and , find …
- WAEC 2018 · Paper 2 · Q10Find the equation of the normal to the curve at the point .
- WAEC 2018 · Paper 2 · Q8A body is thrown vertically upwards. Its height metres at time seconds is given by . Find:
- WAEC 2018 · Paper 2 · Q9The radius of a sphere increased by . Find the percentage increase in the volume.
- WAEC 2017 · Paper 2 · Q3Given that , and , express in terms of …
- WAEC 2017 · Paper 2 · Q10If , find at .
- WAEC 2017 · Paper 2 · Q9Simplify and leave the answer in terms of .
- WAEC 2016 · Paper 2 · Q11Without using mathematical tables or a calculator, solve .
- WAEC 2016 · Paper 2 · Q7A ball is thrown vertically upwards from ground level and its height after seconds is . Find, correct to one decimal …
- WAEC 2014 · Paper 2 · Q11If , and , , find .
- WAEC 2014 · Paper 2 · Q4Find the equation of the tangent to the curve when .
- WAEC 2013 · Paper 2 · Q12Find the maximum and minimum points of the curve .
- WAEC 2013 · Paper 2 · Q18The displacement, metres, of a particle from a fixed point at time seconds is given by . On a graph sheet, draw …
- WAEC 2013 · Paper 2 · Q2Calculate the gradient of the curve at the point .
- WAEC 2013 · Paper 2 · Q3A side of a rectangle is three times the other. If the perimeter increases by , find the percentage increase in the area of the rectangle.
- WAEC 2013 · Paper 2 · Q9Find the:
- WAEC 2011 · Paper 2 · Q10The gradient of a curve is given by . Find the equation of the curve if the point lies on it.
- WAEC 2010 · Paper 2 · Q3Find the equation of the tangent to the curve at the point where the tangent makes an angle of with the positive …
- WAEC 2009 · Paper 2 · Q10Using the same axes, sketch the curves and .
- WAEC 2009 · Paper 2 · Q10An exponential sequence is given by Find an expression for the th term;
- WAEC 2008 · Paper 2 · Q10The equation of a circle is , where is a constant. If the radius of the circle is , find the value …
Objective (4)
- NECO 2023 · Paper 1 · Q23Find the minimum value of .
- WAEC 2023 · Paper 1 · Q28Find the equation of the normal to the curve at point .
- WAEC 2020 · Paper 1 · Q29In what interval is the function increasing?
- WAEC 2020 · Paper 1 · Q33The variables and are such that . Calculate the corresponding change in when changes from 2.00 to 2.05.