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YEAR 8 YEARLY 2007

SECTION A ( 18 Marks ) Marks

1. Simplify )()( abba . 1

2. Write a formula for W, the number of weeks in M minutes. 1

3. If { }uoieaA ,,,,= and { }fedcbaB ,,,,,= , find2

(a) BA (b) BA

4. ind the mid!point and "radient of the inter#al between the 2

points )3,2(A and )$,%(B .

&. Write down the first fi#e ibona''i numbers. 1

%. pand and simplify )23)(32( + xx . 1

$. *wo sides of a ri"ht!an"led trian"le are 2 metres and 3 metres lon". 2ind the ea't len"th of its hypotenuse.

+. 'ar was sold for -34, whi'h was 1&/ less than its ori"inal 2sellin" pri'e. ind its ori"inal sellin" pri'e.

0. i#en that xy 2= , make x the sube't. 2

1. rom the set of s'ores { }11,14,4,$,12,1%,11,0,&,3,& ,4

(a) find the ran"e, median and interuartile ran"e.

(b) draw a bo and whisker plot showin" this data.

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SECTION B ( 18 Marks )

1. Sket'h the line .22 =+ yx . 1

2. raph the set { }xxx 3132 +>+ on a number line. 2

3. i#e less than twi'e a number is4

12 . Write an euation and sol#e it 2

to find the number.

4. In the dia"ram shown, ,3,& == ADAE 0=CD and ACBAED = 5

(a) 5ro#e that ABC issimilar to ADE .

(b) ind BE "i#in" reasons.

9

3

5

B

C

ED

&. *he mean of the set of s'ores { }x,0,%,4,3,&,2 is &. ind the #alue 2of s'orex.

%. rhombus has dia"onals of len"th +'m and 12'm. ind its 2ea't perimeter.

$. line of the form .=++ cbyax has a "radient of3

2 and 3

a y!inter'ept at )2,.( . ind the inte"er #alues of a, b and c.

+. *he numbers 1 to 2 are pla'ed in a ba" and one sele'ted at 1random. ind the probability that it is prime.

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SECTION C ( 18 Marks )

1. Sol#e 13

1

2

3=

xx2

2. *he two shapes shown are similar and ABEF 32 = . 2If the lar"er #olume is 1%2 3cm , find the smaller #olume.

D

G

F

B

C

3. 'ontainer is rd3

1full of fluid. If 40 6itres of fluid is added, 2

it would be ths+

&full. 7ow many 6itres in the full 'ontainer.

4. *hree points on a plane are )2,1(A , B(3,!1) and C(%,3).

3

(a) ind the len"th of AB.(b) Show that AB is perpendi'ular to BC.

(') ind the area of trian"leABC.

&. ully fa'tor

(a) 32 %4 xyyx 1

(b) 2+32 + xx 1

(') tytxyx 2+4 + 2

%. n amount of -+, is in#ested at a rate of /2

1% per annum 2

'ompounded annually. ind the #alue of the in#estment at the

end of fi#e years (to the nearest dollar).

$. uadrant of a 'ir'le of radius 12 cm is 'ut from a thin sheet of 3metal and uniformly 'ur#ed to form a 'one. ind the ea't #olumeof the 'one.

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SECTION D ( 18 Marks )

1. *ra'e the trian"le ABC onto your answer sheet and 'onstru't, 2usin" a ruleand 'ompass only, the 'ir'le passin" throu"h the

points A Band C. Show all 'onstru'tions.

C

B

2. 'ylinder has a base radius of cm& and a total surfa'e area of 2

+ 2cm . ind its len"th.

3. Se#en marbles, 3 bla'k, 2 red and 2 "reen, are pla'ed in a ba" and 2two drawn out togetherat random. 8sin" a dot dia"ram or otherwise,find the probability that

(a) at least one marble is red.(b) they are not the same 'olour.

4. rhombus has an area of 122

cm and one of its dia"onals is 24cm. 2ind the len"th of its other dia"onal.

&. "roup of 3 "irls 'an 'hoose to play 7o'key or 9etball. If % play 3only 7o'key, 3 play both and + play neither, draw a :enn dia"ram'ontainin" this information and use it to find the number of "irls that

play only 9etball.

%. person wishes to fen'e a re'tan"ular paddo'k ha#in" sides of len"th 4xmetres andymetres with 4metres of fen'in" material. ;ne side isalon" a bri'k wall and does not reuire fen'in".

(a) ind an epression for the area in terms ofx.(b) ind the maimum area of the paddo'k.

$. *rian"le ABC has a ri"ht!an"le at B, where xAB 2= and yBC 2= . 3If ! bise'ts AB and " bise'ts BC,

(a) draw a dia"ram showin" this information.

(b) show that ( ) ( ) 222 4)(& A"C!AC +=

END o !A!ER