Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

TopicSkillDifficulty

14 questions

SA-9709-P1-DF4-G013 marksL1 FoundationCalculatorStationary points

Find the coordinates of the stationary point of

y=x^2-6x+1

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SA-9709-P1-DF4-Q011 markL1 FoundationCalculatorStationary points

At a stationary point of a curve,

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SA-9709-P1-DF-Q031 markL1 FoundationCalculatorNature

At a stationary point,

\dfrac{d^2y}{dx^2}>0

. The point is

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SA-9709-P1-DF-0085 marksL2 StandardCalculatorStationary points

Find the

x

-coordinates of the stationary points of

y=x^3-6x^2+9x+2

, and the

y

-coordinates of the maximum and minimum points.

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SA-9709-P1-DF-0123 marksL2 StandardCalculatorIncreasing/decreasing

The function

f(x)=x^3-12x

is decreasing for

a<x<b

. Find

a

and

b

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SA-9709-P1-DF4-0013 marksL2 StandardCalculatorIncreasing/decreasing

f(x)=2x^3+3x^2-12x

is decreasing for

a<x<b

. Find

a

and

b

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SA-9709-P1-DF4-0023 marksL2 StandardCalculatorStationary points

Find the

x

-coordinates of the stationary points of

y=2x^3-9x^2+12x

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SA-9709-P1-DF4-0032 marksL2 StandardCalculatorNature

y=x^3-12x

has a stationary point at

x=2

. Using the second derivative, this point is

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SA-9709-P1-DF-0133 marksL3 ExamCalculatorIncreasing/decreasing

It is given that

f(x)=(2x-1)^3+6x

. Show that

f

is an increasing function by finding the least value of

f'(x)

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SA-9709-P1-DF-0145 marksL3 ExamCalculatorStationary points

The curve

y=2x^3-3x^2-12x+5

has two stationary points. Find the

y

-coordinate of the maximum point and of the minimum point.

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SA-9709-P1-DF4-0043 marksL3 ExamCalculatorStationary points

Find the coordinates of the stationary point of

y=x+\dfrac4x

for

x>0

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SA-9709-P1-DF4-0053 marksL3 ExamCalculatorNature

y=x^4-2x^2

has three stationary points. Find the

x

-coordinate of the one that is a maximum.

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SA-9709-P1-DF4-0074 marksL3 ExamCalculatorNature

y=x^3-3x^2+4

has a maximum point and a minimum point. Find the

y

-coordinate of each.

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SA-9709-P1-DF4-0064 marksL5 ExtensionCalculatorIncreasing/decreasing

Find the least value of

k

for which

f(x)=x^3+3x^2+kx

is an increasing function for all

x

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