8/10/2019 Basic Geomatry 70 Min Test

1/32

Math Basic Geometry Evaluation Test : 70 Marks 70 Mins

Q1.

*

CDEF is a straight line.AB is parallel to CF.DE = AE.

Work out the size of the angle markedx.

You must give reasons for your answer.

(Total or Question is ! marks"

Q#.

Jon has a flower garden in the shape of a circle.The diameter of the garden is 5 metres.

Jon wants to put fencing around the edge of the garden.The fencing costs 1.! per metre.

Work out the total cost of the fencing.

..

............................................................................................................................................

(Total or Question is $ marks"

8/10/2019 Basic Geomatry 70 Min Test

2/32

Q$.

OAB is a sector of a circle" centre O.The radius of the circle is 15 cm.The angle of the sector is #!$.

%alculate the area of sector OAB.&ive your answer correct to # significant figures.

. . . . . . . . . . . . . . . . . . . . . cm'

(Total or Question is # marks"

Q!.

(ere is a solid prism.

Work out the volume of the prism.

. . . . . . . . . . . . . . . . . .cm#

(Total or Question is $ marks"

8/10/2019 Basic Geomatry 70 Min Test

3/32

Q%.

) frustrum is made *y removing a small cone from a similar large cone.

The height of the small cone is '! cm.The height of the large cone is +! cm.The diameter of the *ase of the large cone is #! cm.

Work out the volume of the frustrum.

&ive your answer correct to # significant figures.

. . . . . . . . . . . . . . . . . . . . . . . .cm#

(Total or Question is ! marks"

Q&.

The diagram shows the plan of a playground.

8/10/2019 Basic Geomatry 70 Min Test

4/32

,ill is going to cover the playground with tarmac.-t costs '.5 to cover each s/uare metre with tarmac.

Work out the total cost of the tarmac ,ill needs.

..............................................................................................................................................

(Total or Question is ! marks"

8/10/2019 Basic Geomatry 70 Min Test

5/32

Q7.

0umeet has a pond in the shape of a prism.

The pond is completely full of water.0umeet wants to empty the pond so he can clean it.

0umeet uses a pump to empty the pond.

The volume of water in the pond decreases at a constant rate.The level of the water in the pond goes down *y '! cm in the first #! minutes.

Work out how much more time 0umeet has to wait for the pump to empty the pond completely.

..............................................................................................................................................

(Total or Question is & marks"

Q'.

ABC" PQR andAQD are straight lines.ABC is parallel to PQR.

)ngle BAQ = #5$

8/10/2019 Basic Geomatry 70 Min Test

6/32

)ngle BQA 2!$

Work out the size of the angle markedx.&ive reasons for each stage of your working.

x . . . . . . . . . . . . . . . . . . . . . . $

(Total or Question is ! marks"

8/10/2019 Basic Geomatry 70 Min Test

7/32

Q.

ABCD is a s/uare with a side length of +xM is the midpoint of DC.N is the point onAD where ND x

BMN is a right3angled triangle.

4ind an epression" in terms ofx" for the area of triangle BMN.

&ive your epression in its simplest form.

..............................................................................................................................................

(Total or Question is ! marks"

Q10.) circle has a diameter of 1+! cm.

Work out the circumference of the circle.&ive your answer correct to # significant figures.

........................................................... cm

(Total or Question is # marks"

8/10/2019 Basic Geomatry 70 Min Test

8/32

8/10/2019 Basic Geomatry 70 Min Test

9/32

8/10/2019 Basic Geomatry 70 Min Test

10/32

Q1#.ABCis an isosceles triangle.

Work out the area of the triangle.&ive your answer correct to # significant figures.

........................................................... cm'

(Total or Question is ! marks"

8/10/2019 Basic Geomatry 70 Min Test

11/32

Q1$.

(ere is a triangular prism.

Work out the volume of this triangular prism.

...........................................................

(Total or Question is ! marks"

8/10/2019 Basic Geomatry 70 Min Test

12/32

Q1!.6

AOCand BODare diameters of a circle" centre O.

7rove that triangleABDand triangle DCAare congruent.

(Total or Question is $ marks"

8/10/2019 Basic Geomatry 70 Min Test

13/32

Q1%.

The diagram shows a patio in the shape of a rectangle.

8iagram )Taccurately drawn

The patio is #. m long and # m wide.

9atthew is going to cover the patio with paving sla*s.:ach paving sla* is a s/uare of side ! cm.

9atthew *uys #' of the paving sla*s.

;a< 8oes 9atthew *uy enough paving sla*s to cover the patio=You must show all your working.

..............................................................................................................................................

($"

The paving sla*s cost .# each.

;*< Work out the total cost of the #' paving sla*s.

. . . . . . . . . . . . . . . . . . . . . .

($"

(Total or Question is & marks"

8/10/2019 Basic Geomatry 70 Min Test

14/32

Q1&.

The diagram shows a solid hemisphere of radius 5 cm.

4ind the total surface area of the solid hemisphere.&ive your answer in terms of .

. . . . . . . . . . . . . . . . . . . . . . . . cm

'

(Total or Question is $ marks"

Q17.

ABC is a triangle.

8/10/2019 Basic Geomatry 70 Min Test

15/32

;a< Work out the area of triangleABC. &ive your answer correct to # significant figures.

. . . . . . . . . . . . . . . . . . . . . . cm'

(#"

;*< Work out the length of the sideAB. &ive your answer correct to # significant figures.

.............................................................................................................................................. ($"

(Total or Question is % marks"

8/10/2019 Basic Geomatry 70 Min Test

16/32

Q1'.

The diagram shows a pyramid.

BCDE is a s/uare with sides of length 1! cm.The other faces of the pyramid are e/uilateral triangles with sides of length 1! cm.

;a< %alculate the volume of the pyramid. &ive your answer correct to # significant figures.

. . . . . . . . . . . . . . . . . . . . . . . . cm#

(!"

;*< 4ind the size of angle DAB.

..............................................................................................................................................

(#"

(Total or Question is & marks"

Mark +cheme

>1.

,orkin- ns/er Mark )otes

6 )ngleAED # alternateangles aree/ual

)ngleADE ;1! ? #< @ ' A1x 1! ? A1*ase angles ofan isosceles

x 1!2 + ,1 for angleAED # orAEF 1+'91 for a

completemethod to findone of the*ase angles ofthe isoscelestriangle

8/10/2019 Basic Geomatry 70 Min Test

17/32

triangle aree/ualangles ina triangle addup to1!angles on astraight linesum to 1!angleAEF

1+' alliedanglesBco3interioranglesadd up to 1!ADE 1+' @ ' A1*ase angles ofan isoscelestriangle aree/ualeteriorangle of atriangle is

e/ual to thesum of theinterioroppositeangles "x 1! ? A1angles in astraight lineadd to 1!)ngleAED # alternateangles aree/ual forangles BAE

andAED anBAD andADC;x.

8/10/2019 Basic Geomatry 70 Min Test

24/32

,orkin- ns/er Mark )otes

5x' + 91 for +x E +x91 for ;'xE+x

8/10/2019 Basic Geomatry 70 Min Test

25/32

Q1#.

Q1$.

Q1!.

8/10/2019 Basic Geomatry 70 Min Test

26/32

8/10/2019 Basic Geomatry 70 Min Test

27/32

Q1%.

Question ,orkin- ns/er Mark )otes

;a