past papers cxc maths

8/13/2019 Past Papers Cxc maths

1/77

TABLE OF CONTENTS TOPIC: PAGE

FractionsDecimals

Significant Figures Standard Form

Substitution

Subject To the FormulaSim lif!ing the E" ressionIndices

Sim lif!ing E#uations

$atio Pro ortional Parts Direct Pro ortion In%erse Pro ortion &ariation

Factorisation Sim le Grou ing 'uadratic

Sim le E#uation Grou ing (rac)ets Fractions *ord Problems

Simultaneous E#uations

'uadratic E#uations+inear and ,on-linear .Simultaneous/Consumer Arithmetic

Percentage Profit and +oss Sim le and Com ound Interest (ills and $ates *ages and Salaries 0ire Purchase and Instalment Pa!ments Currencies

1ensuration Perimeter Area Surface Area of Solids &olume 1easurement

Functions .2/Sim le Geometr!

Construction

Coordinate Geometr!SetsStatistics&ectorsCircle Theorem

Trigonometr! .2/Trigonometr! .3/1atricesS eed4 Distance4 TimeGra hs4 Cur%es

Dis lacement5Time Tem erature5Time Distance5Time 'uadratic Cubic Others

Earth Geometr!Ine#ualities+inear ProgrammingCom leting the s#uareTransformation1atri" TransformationSe#uence and PatternsTrigonometrical Gra hsAns6ersFormula Sheet

2


2/77

Pol!gons Similar Triangles

FRACTIONS Find the e"act %alue of each of the follo6ing 6ithout using a calculator7 All 6or)ing must be sho6n7 E" ress !our ans6ers inthe lo6est terms7

27 8une 9

a7

3; 3 2; 3 2< = =

>< mar)s?

b7 *rite !our ans6er to art a as a decimal tot6o significant figures >3 mar)s?

37 8an 9

32

3

=2

3;2

< >; mar)s?

=7 8an @

< mar)s?

3378un @22 3

==

B3

>= mar)s?

3=78an @33 2 =

2 3= 9 ;+ >; mar)s?

3;7 8un @32 2

= 3; =

= mar)s?

3; mar)s?

3B78an @;2 3

3 2< =

;

>= mar)s?

3 7

2 == 3

= 3 mar)s?

2978un Gi%en that 3 3; ; 3 p q r = and that p q r + = 4

sho6 that23

p q =

SUB"ECT OF T#E FORMULA

27 8un 1a)e the subject of the formula

3; = pr

$+= >; mar)s?

37 8un 9=1a)e $ the subject of the formula

3

3 R r

A = >; mar)s?

=7 8un 9;

Gi%en32

4n

mn

= e" ress n in terms of m

>< mar)s?

;7 8un 9B

If2 2 3

4 R %

= + e" ress in terms of R and T 7


8/77

2;7 8an @=Gi%en that = $ r =

a7 E" ress in terms of r and $ b7 Calculate the %alue of t 6hen r 3 and

$ 2&olume of a s here of radius =;=

r r = 7Assume that the orange is a s here?

b7 T6o thirds of the juice is oured into ac!lindrical container 2; cm high anddiameter cm7 0o6 man! ice-cubes4 eachof sides = cm can be added before the

juice begins to o%erflo6H

3;7 8un 9;A rectangular 6ooden beam of length < metreshas a cross section of 3@ cm b! 2< cm7 the 6oodhas a densit! of B@@ )g er m =7

a7 Calculate the %olume of the beam incubic metres

b7 E" ress the ans6er for MaN in standardform7

c7 Calculate the mass of the beam in )g7

3


34/77

3 7 8un 9B

The diagram abo%e4 not drawn to scale, sho6s aright triangular rism 6ith A( 2< cm4 AD AE 2@ cm and ED 23 c7 Calculate the%olume of the rism7

=@78un 2

The figure A(CDEF abo%e4 not drawn to scale,re resents a 6edge 6ith measurements assho6n7 (C is er endicular to the lane FEDC7Calculate

i7 the length in cm of (Dii7 the surface area4 in cm 34 of the 6edge

iii7 the %olume in cm =4 of the 6edgei%7 the si e of angle (DC7

=278an 2

To ans6er this #uestion use K 33

and

3V r = 4 6here V 5 %olume4 r radius and & 5height of the c!linder *

a7 The internal dimensions of a sauce ansha ed li)e a c!linder height 3@ cm anddiameter =< cm7 Calculate to the nearest6hole number4

i7 the area4 in cm 34 of the bottom ofthe sauce an

ii7 the largest %olume of li#uid4 incm=4 6hich the sauce an canhold7

b7 The sauce an is filled 6ith 6ater 6hichis then oured into a em t! c!lindrical

ot of radius 32 cm7 Calculate4 to thenearest cm4 the height of the 6ater le%elabo%e the bottom of the ot7

=37$esit ta)e33

= ?i7 Calculate4 in cm 4 the circumference of

the base of the cone7ii7 Sho6 that the height of the cone is

a ro"imatel! 7= cm7iii7 Calculate the %olume in cm = of thecone7

=;7 8an a7 A rectangular tan) is 9 m high and its

base is ; m long and = m 6ide7 The tan)is filled 6ith 6ater7CalculateRi7 the area4 in cm 34 of the base of the

tan) and 6rite !our ans6er instandard form7

ii7 the ca acit!4 in litres4 of the tan)7se 2@@cm= 2 litre7

b7 All the 6ater from the rectangular tan)is um ed into a c!lindrical tan) to aheight of 9 m7 Calculate to4 = significantfigures4 the radius of the base of thec!lindrical tan)7

=;


35/77

=Ta)e33

= ?i7 A c!lindrical metal drum of height 232@@ cm= 2 litre?

=B78un

A circular drain i e4 sho6n in the diagramabo%e4not drawn to scale 4 is 2 metre long4 6ithouter and inner radii of 3@ cm and 2< cmres ecti%el!7

i7 Dra6 a cross-sectional %ie6 of the

drain i e4 sho6ing the measurement ofthe inner and outer radii7

CalculateRii7 the area4 in cm 34 of the cross section of

the drain i e7iii7 the amount4 in cm =4 of the material

re#uired to construct the drain i e7i%7 The ca acit!4 in litres of the hallo6

s ace of the drain i e7%7 The %olume4 in litres 4 of 6ater assing

through the i e in 2 minute if the 6aterflo6s through the i e at a s eed of 2metre er second

>Ta)e =72; = ?

= 7 8un @2

>Ta)e =72;3 = ?>cur%ed surface area of a c!linder 3 r& ?The diagram abo%e4 not drawn to scale,re resents an o en metal container7 The cross-section of the container is a semi-circle ofdiameter 27


36/77

= 7 8an @=

The diagram abo%e4 not drawn to scale, sho6s a6ooden rism of length 3< cm7 the cross sectionA(CD is a tra e ium 6ith A( arallel to DC4

@ BAD = 4 A( 23 cm4 (C < cm49 cmCD = and AD = cm7

Calculatei7 The area4 in cm 34 of the cross-section4

A(CDii7 The %olume4 in cm=4 of the rism

iii7 The total surface area 4 in cm 34 of the

rism7

;@7 8an @=a7 The triangular rism4 sho6n the

diagram belo64 not drawn to scale 4 is29 cm long7 Triangle G0I has a heightof = cm4 0I 9 cm and G0 GI7

i7 The area of triangle G0Iii7 The %olume of the triangular

rismiii7 The length of GIi%7 The total surface area of the

rism7 b7 The triangular rism is melted do6n

and made into a cube7 Calculate thelength of an edge of the cube7

Mi ed Sha!es and Cross sections

;27 8un @

>Ta)e K 33

?

The diagram abo%e4 not drawn to scale,re resents a lot of land ADCBE in the sha e ofa s#uare of sides 32 m 6ith a semicircle at oneend7

i7 Calculate4 in metres the erimeter of the

lot7ii7 WXYZ is a rectangular flo6er bed of

length 2< m and 6idth 23 m7 Calculatein m 3 the area of the shaded section7

iii7 The soil in the flo6er bed is re laced toa de th of =@ cm7 calculate in cubiccentimetres4 the %olume of the soilre laced4 6riting !our ans6er instandard form7

;37 8un

A rectangular bloc) of 6ood is B cm high7 Thecross-section of the bloc) is a s#uare of side 2Bcm7 A C!lindrical container is car%ed out of the

bloc)7 The c!linder is < cm dee and thediameter of the cross section is 2; cm7 the figure

abo%e4not drawn to scale, sho6s the tosurface of the container7CalculateR

a7 the %olume of the rectangular bloc) of6ood

b7 the area of face of the c!linder c7 The %olume of the 6ood in the

container7

=B


37/77

>use33 = ?

;=7 8un @3

The diagram abo%e4 not drawn to scale, sho6s ABCDE, a %ertical cross-section of a container6ith ED being the to edge7 DC and EF are%ertical edges7 BC and AF are arcs of a circle ofradius cm4 and AB ZZ ED 7

ED =@cmR AB 2B cmR EF DC cm

i7 Ta)ing33 = 4 sho6 that the area of

ABCDEF is ;< cm 37ii7 *ater is oured into the container until

the 6ater le%el is ; cm from the to 7 Ifthe container is ;@ cm long and has auniformed cross-section4 calculate to thenearest the %olume of 6ater in thecontainer7

Nets "lans and #le$ations

;;7 8un 93

i7 ABCDEFG is a s)etch of the net of a

!ramid on a s#uare base BDFH of side= cm 6ith slant edges of length < cm7a7 Dra6 an accurate full si e

diagram of the net7 b7 1easure and 6rite do6n the

length of EA 7ii7 The net is assembled as a !ramid 6ith

a e" V and base BDFH 7a7 S)etch the cross section VDH of

the !ramid indicating clearl! on

!our s)etch the lengths of VDand DH 7

b7 (! calculation4 determine VX theheight of the !ramid7> X is the centre of the base?

;


38/77

iii7 The height of the !ramid is 3@ cm7Sho6 that the length of the slo ingedge4 VM + is 3@ = cm7

;97 8an =

The figure abo%e4 not drawn to scale 4 re resentsa solid in the sha e of a right c!linder joined tothe frustum of a cone7Dra6

i7 the lan of the solidii7 the ele%ation of the solid

; 7 8an =

The diagram abo%e not dra6n to scale4 sho6s thenet of a bo" in 6hich the sides are < cm high7The shaded area is the base of the bo"7Calculate to three significant figures

i7 the area of the material used to ma)ethe bo"

ii7 the %olume of the bo"

Ta)e ?

The cone is cut along a straight line dra6n fromX to &7 the a er is flattened out to form a lanefigure7

i7 Dra6 a diagram of the lane figure4sho6ing the osition of &7

ii7 *rite the length of each side on !ourdiagram7

iii7 Calculate the si e4 in degrees4 of theangle at &


39/77


40/77


41/77

B378an @;The diagram belo64 not drawn to scale, sho6s a

bloc) of 6ood in the sha e of a semi-circular rism7 The cross section of the rism has adiameter of =@ cm7 The length of the rism is 273metres7

> se K =72;?Calculate4 gi%ing !our ans6er to = significantfigures

i7 the area in cm 34 of the cross sectionii7 the %olume4 in cm=4 of the rism7

B=78un @;

> se 33 = in this #uestion?A iece of 6ire is bent in the form of a circle andit encloses an area of 2


42/77

ii7 Sho6 that if . / 3


43/77

2;7 8un

past papers cxc maths

Documents