3 self-marking IGCSE and Additional Maths practice questions on Classifying stationary points, written specifically for Cambridge IGCSE Additional Maths (0606), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Single and Extended tier. Instant marking with full worked solutions on every question.
A few of the 3 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 13 marksGrade 8
A curve has a stationary point at x=3, where dx2d2y=6x−20
What are the common mistakes in Classifying stationary points?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Assumes every stationary point is a maximum or minimum, not recognising a point of inflection where the gradient does not change sign
Not every stationary point is a maximum or minimum - since (x−2)2 is never negative, the gradient is positive (or zero) on BOTH sides of x=2, meaning it never actually changes sign, so this is neither a maximum nor a minimum.
Reverses the sign convention for the second derivative test, classifying a maximum as a minimum or vice versa
Quick answers about Classifying stationary points
How many Classifying stationary points practice questions are there?
There are 3 self-marking IGCSE and Additional Maths Maths questions on Classifying stationary points, written for Cambridge IGCSE Additional Maths (0606), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Single and Extended tier. Each one is marked instantly and has a full worked solution.
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(a) State whether this stationary point is a maximum or a minimum. [1]
(b) Give a reason for your answer. [2]
Show the worked solution
At x=3: dx2d2y=6(3)−20=18−20=−2.
Since dx2d2y<0, the stationary point is a maximum.
Question 23 marksGrade 8
A curve has dxdy=(x−2)2 everywhere, giving a stationary point at x=2.
(a) State the nature of this stationary point. [1]
(b) Give a reason for your answer. [2]
Show the worked solution
(x−2)2≥0 for every real x, so dxdy≥0
Question 38 marksGrade 9
Consider the curve y=x3−3x2−9x+5. Find the coordinates of the two stationary points, and use the second derivative test to determine the nature of each.
(a) Coordinates of the first stationary point. [2]
(b) Nature of the first stationary point. [1]
(c) Coordinates of the second stationary point. [2]
(d) Nature of the second stationary point. [1]
A NEGATIVE second derivative means the gradient is decreasing through the point, which is characteristic of a MAXIMUM, not a minimum - the rule is: dx2d2y>0 for a minimum, dx2d2y<0 for a maximum.
Pairs an x-value from one solution with the y-value calculated for a different solution, instead of keeping each coordinate matched to the point it belongs to
Each x-value gives its OWN y-value from the original curve equation - x=−1 gives y=10 and x=3 gives y=−22; don't pair an x-value from one point with the y-value from the other.
on both sides of
x=2
- the gradient does not change sign.
Since the first derivative test relies on a sign CHANGE to identify a maximum or minimum, and none occurs here, this stationary point is neither a maximum nor a minimum.