Practise questions · Salam Academy

SA-9709-P1-DF5-G013 marksL1 FoundationCalculatorRates

The radius of a circle increases at

2

cm s⁻¹. Find the rate at which the area is increasing when the radius is

3

cm. Give an exact answer.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF5-Q011 markL1 FoundationCalculatorRates

If

V

depends on

r

and

r

changes with time

t

, then

\dfrac{dV}{dt}

equals

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF-0103 marksL2 StandardCalculatorRates

The radius of a circle is increasing at

0.5

cm s⁻¹. Find the rate at which the area is increasing when the radius is

4

cm. Give an exact answer.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF5-0013 marksL2 StandardCalculatorRates

The side of a cube increases at

0.1

cm s⁻¹. Find the rate at which the volume is increasing when the side is

5

cm.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF5-0023 marksL2 StandardCalculatorRates

The radius of a sphere increases at

0.2

cm s⁻¹. Find the rate at which the surface area

S=4\pi r^2

is increasing when

r=10

. Give an exact answer.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF5-0044 marksL2 StandardCalculatorOptimisation

60

m of fencing forms three sides of a rectangular pen; a wall forms the fourth side. Find the maximum possible area.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF5-0071 markL2 StandardCalculatorOptimisation

For

A=60x-2x^2

,

\dfrac{d^2A}{dx^2}=-4

. At

x=15

,

A

is

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF-0095 marksL3 ExamCalculatorOptimisation

An open box is made from a square sheet of side

12

cm by cutting a square of side

x

cm from each corner and folding up the sides. Find the value of

x

that maximises the volume, and the maximum volume.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF-0113 marksL3 ExamCalculatorRates

The volume of a sphere is increasing at

20

cm³ s⁻¹. Find the rate at which the radius is increasing when the radius is

5

cm. Give an exact answer.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF5-0033 marksL3 ExamCalculatorRates

A quantity

V=x^3+2x

is increasing at

6

units per second. Find the rate at which

x

is increasing when

x=1

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF5-0055 marksL3 ExamCalculatorModelling

A closed box has a square base of side

x

cm and a volume of

1000

cm³. Show that its surface area is

S=2x^2+\dfrac{4000}{x}

, and find the least possible surface area.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF5-0063 marksL3 ExamCalculatorOptimisation

The profit

P

(in $1000s) from selling

x

thousand items is

P=12x-x^3+5

, for

x>0

. Find the maximum profit.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF-0174 marksL4 ChallengingCalculatorRates

Water is poured into a container at

8

cm³ s⁻¹. When the depth of water is

h

cm, the volume is

V=\dfrac{\pi h^3}{3}

cm³. Find the rate at which the depth is increasing when

h=2

. Give an exact answer.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF5-0084 marksL4 ChallengingCalculatorRates

Water is poured at

5

cm³ s⁻¹ into an inverted cone. When the depth is

h

cm, the volume is

V=\dfrac{\pi h^3}{12}

cm³. Find the rate at which the depth is increasing when

h=10

. Give an exact answer.

Salam Academy Original Practice · Proposed mark scheme

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