CXCMaths - Jan 2006 Paper 02

8/13/2019 CXCMaths - Jan 2006 Paper 02

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LIST OF FORMULAE

Volume of prism V = Ah where A is the area of a cross-section and h is the

perpendicular length.

Volume of cylinder V = rh where r is the radius of the base and h is theperpendicular height.

Volume of a right pyramid V = Ah where A is the area of the base and h is theperpendicular height.

Circumference C = 2r where r is the radius of the circle.

Area of a circle A = r where r is the radius of the circle

Area of trapeium A = ! "a # b$ h where a and b are the lengths of theparallel sides and h is the perpendicular height.

%oots of &uadratic e&uations 'f a( # b( # c = )* then

+rigonometry ratios

Area of triangle

Area of , = ! bh where b is thelength of the base and h is the perpendicularheight.


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Area of AC = !ab sin C

Area of

/here

0ine rule

Cosine rule a = b # c - 2bc cos A

SECTION I

Answer ALL the questions in this section.

All working must e cle!rl" shown.

#. 1sing a calculator* or otherwise* calculate

"i$ the e(act alue of

$% m!rks&

"ii$ correct to 3 significant figures* the alue of 45.67 - "2.44$.


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$' m!rks&

"b$ A loan of 842 ))) was borrowed from a ban9 at 4:; per annum.

Calculate

"i$ the interest on the loan at the end of the first year $( m!rks&

"ii$ the total amount owing at the end of the first year. $# m!rk&

A repayment of 86 5)) was made at the start of the second year.

Calculate

"iii$ the amount still outstanding at the start of the second year $# m!rk&

"i$ the interest on the outstanding amount at the end of second year. $# m!rk&

Tot!l #( m!rks

(."a$ 'f a = 2* b = -3 and c = :* ealuate

"i$ ab - bc $# m!rk&

"ii$ b"a - c$ $( m!rk&

"b$ 0ole for ( where ( )n the answer sheet* , AC is mapped onto , ALLCL under a reflection.

"i$ /rite down the e&uation of the mirror line.

, ALLCL is mapped onto , APPCP by a rotation of 45)Q about the point "7* :$.

$# m!rk&

"ii$ Determine the coordinates of the ertices of , APPCP.

$' m!rks&

"iii$ 0tate the transformation that maps , AC onto , APPCP.

$( m!rks&

Tot!l ## m!rks


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. +he table below shows a fre&uency distribution of the scores of 4)) students in ane(amination.

Scores Frequenc"Cumul!ti/e

Frequenc"

24 - 27 7 7

2 - 3) 45

34 - 37 23

3 - :) 22

:4 - :7 24

: - 7) 44 4))

"i$ Copy and complete the table aboe to show the cumulatie fre&uency for thedistribution.

$( m!rks&

"ii$ 1sing a scale of 2 cm to represent a score of 7 on the horiontal a(is and a scale of 2cm to represent 4) students on the ertical a(is* draw a cumulatie fre&uency cure of thescores. 0tart your horiontal scale at 2).

$ m!rks&

"iii$ 1sing the cumulatie fre&uency cure* determine the median score for thedistribution.

$( m!rks&

"i$ /hat is the probability that s student chosen at random has a score greater than :)R

$( m!rks&

Tot!l #( m!rks

0."a$ +he diagram below* not +r!wn to sc!le* shows a prism of length 3) cm. +he cross-section /BST is a s&uare with area 4:: cm.


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Calculate

"i$ the olume* in cmU* of the prism

$( m!rks&

"ii$ the total surface area* in cm* of the prism.

$( m!rks&

"b$ +he diagram below* not +r!wn to sc!le* shows the sector of a circle with centre >.

Calculate* giing your answer correct to 2 decimal places

"i$ the length of the minor arc M?

$( m!rks&


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"ii$ the perimeter of the figure M>?

$( m!rks&

"iii$ the area of the figure M>?.

Tot!l #( m!rks

1.A large e&uilateral triangle is subdiided into a set of smaller e&uilateral triangles by thefollowing procedure is the centre of the circle. +he measureof angle >M is 44)Q.


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Calculate* giing reasons for your answers* the sie of each of the followingangles

"i$ ZM?

$( m!rks&

"ii$ ZM>

$' m!rks&

Tot!l #- m!rks

#(.A boat leaes a doc9 at point A and traels for a distance of 47 9m to poi on a bearing of437Q.

+he boat then changes course and traels for a distance of 5 9m to point c on a bearing of))Q.

"a$ 'llustrate the aboe information in a clearly labelled diagram.

$( m!rks&

+he diagram should show the

"i$ north direction $# m!rks&

"ii$ bearings 437Q and ))Q $( m!rks&


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"iii$ distances 5 9m and 47 9m. $( m!rks&

"b$ Calculate

"i$ the distance AC

$' m!rks&

"ii$ ZCA

$' m!rks&

"iii$ the bearing of A from C

$( m!rk&

Tot!l #- m!rks


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such that .

$# m!rk&

"ii$ Hroduce HB to I such that .

$# m!rk&

"b$ /rithe the following in terms of rand s.

"i$

$( m!rks&

"ii$

$' m!rks&

"iii$

$% m!rks&

"c$ 0how that

$% m!rks&

Tot!l #- m!rks


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#%."a$ Wien that is a singular matri(* determine the alue"s$ of p.

$% m!rks&

"b$ Wien the linear e&uations

2( # 7y =

3( # :y = 5

"i$ /rite the e&uations in the form AB = where A* B and are matrices.

$( m!rks&

"ii$ a$ Calculate the determinant of the matri( A.

$( m!rks&

b$ 0how that .

$' m!rks&

c$ 1se the matri( AN O to sole for ( and y.

$- m!rks&

Tot!l #- m!rks

CXCMaths - Jan 2006 Paper 02

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