Practise

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2730 questions · page 33 of 137 · choose a topic above to narrow them down

SA-9709-P3-DE4-G013 marksL1 FoundationCalculatorIn context

A colony of bacteria grows according to

\dfrac{dN}{dt}=0.1N

, with

N=50

when

t=0

(

t

in hours). Find the exact value of

N

when

t=10

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE-G014 marksL1 FoundationCalculatorSeparating variables

Solve the differential equation

\dfrac{dy}{dx}=2xy

, given that

y=3

when

x=0

. Give

y

in terms of

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DF-0022 marksL1 FoundationCalculatorStandard derivatives

Differentiate

\tan2x

with respect to

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DF-0042 marksL1 FoundationCalculatorProduct rule

Find

\dfrac{dy}{dx}

when

y=x\ln x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DF-0113 marksL1 FoundationCalculatorParametric

A curve is given by

x=t^2

y=2t

. Find the gradient of the curve at the point where

t=3

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-I31-0011 markL1 FoundationCalculatorStandard integrals

Find

\displaystyle\int e^{-3x}\,dx

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-I32-0031 markL1 FoundationCalculatorSquares

Find

\displaystyle\int\left(1+\tan^2x\right)dx

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-I33-0012 marksL1 FoundationCalculatorExact integrals

Find the exact value of

\displaystyle\int_1^e\frac2x\,dx

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-I34-G013 marksL1 FoundationCalculatorTrapezium rule

Use the trapezium rule with

2

strips to estimate

\displaystyle\int_0^2x^2\,dx

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-I35-G013 marksL1 FoundationCalculatorRecognising

Use the substitution

u=x^2+1

to find

\displaystyle\int2x(x^2+1)^4\,dx

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-I36-G013 marksL1 FoundationCalculatorBy parts

Find

\displaystyle\int xe^{2x}\,dx

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-IN-0012 marksL1 FoundationCalculatorStandard integrals

Find

\displaystyle\int\cos3x\,dx

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-LE-0012 marksL1 FoundationCalculatoraˣ = b

Solve

3^x=20

, giving

x

correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-LE-0052 marksL1 FoundationCalculatorLog equations

Solve

\ln(x+3)=2

, giving the exact value of

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-LE-0082 marksL1 FoundationCalculatorDefinition

Find the exact value of

\log_3 81+\log_3\tfrac19

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-LE1-0011 markL1 FoundationCalculatorDefinition

Find the value of

\log_5\dfrac{1}{25}

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-LE1-0031 markL1 FoundationCalculatorLog laws

\lg12=\lg3+k\lg2

. Find

k

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-LE1-G012 marksL1 FoundationCalculatorDefinition

Find the values of

\log_2 32

and

\log_{10}1000

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-LE2-0012 marksL1 FoundationCalculatorGraphs

For

y=e^x+2

, state the equation of the asymptote,

y=c

, and the

y

-intercept.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-LE2-G012 marksL1 FoundationCalculatorGraphs

State the

y

-intercept of

y=3e^x

and the

x

-intercept of

y=\ln x

Salam Academy Original Practice · Proposed mark scheme