Practise questions | Salam Academy

SA-9702-WA1-0052 marksL2 StandardCalculatorIntensity

A

60

W point source emits waves equally in all directions. Calculate the intensity at a distance of

2.0

m.

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SA-9702-WA2-0052 marksL2 StandardCalculatorDoppler effect

An

800

Hz siren moves away from a stationary listener at

30

m s⁻¹. Calculate the frequency heard. (

v=340

m s⁻¹)

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SA-9702-WE1-0022 marksL2 StandardCalculatorPower & efficiency

A car travels at a constant

25

m s⁻¹ against total resistive forces of

2000

N. Calculate the useful power output of the engine, in kW.

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SA-9702-WE1-0042 marksL2 StandardCalculatorPower & efficiency

An

80

kg person climbs

3.0

m of stairs in

4.0

s. Calculate the useful power developed. (

g=9.81

m s⁻²)

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SA-9702-WE2-0032 marksL2 StandardCalculatorKE & GPE

An object falls from rest through

3.2

m with negligible air resistance. Calculate its speed.

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SA-9702-WE2-0051 markL2 StandardCalculatorKE & GPE

The formula

\Delta E_p=mg\Delta h

is derived by considering

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SA-9709-P1-CG-0024 marksL2 StandardCalculatorGradients

A

is

(-2,\,3)

and

B

is

(4,\,7)

. Find the equation of the perpendicular bisector of

AB

, in the form

y=mx+c

.

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SA-9709-P1-CG-0133 marksL2 StandardCalculatorGradients

Find the equation of the line through

(5,\,1)

that is parallel to

2x-5y=3

, in the form

y=mx+c

.

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SA-9709-P1-CG1-0032 marksL2 StandardCalculatorGradient & midpoint

M(3,5)

is the midpoint of

AB

, where

A

is

(1,2)

. Find the coordinates of

B

.

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SA-9709-P1-CG2-0033 marksL2 StandardCalculatorGradients

Find the equation of the line through

(4,1)

perpendicular to

2x+3y=6

, in the form

y=mx+c

.

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SA-9709-P1-CG3-0013 marksL2 StandardCalculatorExpanded form

Find the centre and radius of the circle

x^2+y^2-6x+2y-15=0

.

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SA-9709-P1-CG3-0033 marksL2 StandardCalculatorProperties

A(-1,2)

and

B(5,10)

are the ends of a diameter of a circle. Find the centre and the radius.

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SA-9709-P1-CG4-0014 marksL2 StandardCalculatorIntersections

Find the

x

-coordinates of the points where the line

y=x+1

meets the circle

x^2+y^2=13

.

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SA-9709-P1-CG4-0022 marksL2 StandardCalculatorIntersections

Substituting the line

y=2x+10

into the circle

x^2+y^2=20

gives

x^2+8x+16=0

. The line

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SA-9709-P1-CG4-G013 marksL2 StandardCalculatorTangents

P(4,3)

lies on the circle

x^2+y^2=25

. The tangent at

P

is

y=mx+c

. Find

m

and

c

.

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SA-9709-P1-CM2-0012 marksL2 StandardCalculatorSector area

A sector has radius

6

cm and angle

\dfrac{5\pi}{6}

. Find the exact arc length and the exact area.

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SA-9709-P1-CM2-0022 marksL2 StandardCalculatorArc length

A sector of radius

9

cm has angle

40^\circ

. Find the exact arc length.

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SA-9709-P1-CM3-0012 marksL2 StandardCalculatorChords

A chord

AB

of a circle of radius

5

cm subtends an angle of

\dfrac{2\pi}{3}

at the centre. Find the exact length of

AB

.

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SA-9709-P1-CM3-G013 marksL2 StandardCalculatorSegments

A chord

AB

of a circle with centre

O

and radius

4

cm has

\angle AOB=\dfrac{\pi}{2}

. Find, exactly, the area of the sector

OAB

, the area of triangle

OAB

and the area of the minor segment.

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SA-9709-P1-DF-0032 marksL2 StandardCalculatorChain rule

Differentiate

(2x-5)^4

with respect to

x

.

Salam Academy Original Practice · Proposed mark scheme

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