Practise questions | Salam Academy

SA-9709-P1-DF-0042 marksL2 StandardCalculatorRoots and fractions

Differentiate

\sqrt{4x+1}

with respect to

x

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF-0063 marksL2 StandardCalculatorTangents and normals

Find the equation of the tangent to the curve

y=x^3-3x+4

at the point

(2,6)

. Give your answer in the form

y=mx+c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF-0074 marksL2 StandardCalculatorTangents and normals

Find the equation of the normal to the curve

y=2x^2-3x+1

at the point where

x=2

.

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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-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.

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SA-9709-P1-DF1-0022 marksL2 StandardCalculatorChords to tangents

P

is the point

(3,9)

on

y=x^2

and

Q

is the point

(3+h,\ (3+h)^2)

. The gradient of

PQ

simplifies to

a+h

. Find

a

, and hence state the gradient of the curve at

P

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF1-0042 marksL2 StandardCalculatorPower rule

Find

\dfrac{dy}{dx}

when

y=(x+3)(x-2)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF2-0022 marksL2 StandardCalculatorChain rule

Differentiate

(x^2+3)^4

with respect to

x

.

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SA-9709-P1-DF3-0023 marksL2 StandardCalculatorTangents and normals

Find the equation of the normal to

y=x^2

at the point

(2,4)

, in the form

y=mx+c

.

Salam Academy Original Practice · Proposed mark scheme

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-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-FN1-0013 marksL2 StandardCalculatorRange of quadratics

f(x)=x^2+4x+9

,

x\in\mathbb{R}

. By completing the square, find the least value of

f(x)

, and hence state the range of

f

as

f(x)\ge k

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN1-0062 marksL2 StandardCalculatorDomain

The largest possible domain of

f(x)=\sqrt{5-2x}

is

x\le k

. Find

k

.

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SA-9709-P1-FN2-0022 marksL2 StandardCalculatorExpressions

f(x)=2x+3

and

g(x)=x^2-1

. Find an expression for

fg(x)

.

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SA-9709-P1-FN2-0053 marksL2 StandardCalculatorExpressions

f(x)=2x+3

and

g(x)=x^2-1

. Solve

fg(x)=19

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN3-0013 marksL2 StandardCalculatorFind the inverse

f(x)=\dfrac{4}{x-2}

for

x>2

. Find

f^{-1}(x)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN3-0042 marksL2 StandardCalculatorOne-one

f(x)=x^2-4x+7

for

x\ge k

. Find the least value of

k

for which

f

is one-one.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN4-0012 marksL2 StandardCalculatorIntersections

f(x)=2x+3

. Find the

x

-coordinate of the point where the graphs of

y=f(x)

and

y=f^{-1}(x)

meet.

Salam Academy Original Practice · Proposed mark scheme

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