8/13/2019 June Holiday Assignment

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Name : __________________________ Date : __________________

Class : 2___ Deadline: 28 Jun 2010

Topic : Semester 1 topics

1. Simplify the following expressions.(a) x(x 2) + 3x(x )(!) (x+ 2)(x2 "x+1) x2 (x 3)

(#)mn

r

$

32

3"

1%

nmrs

(&) x

x x

x2

2

3 21 3%

2

3

+

(e) "

2

3x x

(f)3

3 +

a

a

b

b

(g)2

2

3

+x x

(h) 2

1

3

1

12

x x

x

x+

+

2. 'a#torise the following expressions #ompletely.(a) 81 2 x(!) x2 2"y2

(#) 23 2 + xx

(&) %a2 23a+ 21

(e) 10x2 12ab 1"ax+ 8bx

(f) 10%"3 + yxxy

3. Sole the following euations.(a) xx $2 2 =(!) 0$2 2 =+ xx

(#) ( ) ( )$ 18x x+ =

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River Valley High School Integrated rogramme

!ear 2 "athematics

#$ne Holiday %ssignment

8/13/2019 June Holiday Assignment

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(&)

2

3

+

=

x

x

(e) 3 1 1

12 3

x x =

(f)

2

"

1

1

=

+

x

x

x

x

. -a/e a the su!e#t for ea#h of the following euations.(a) cbah =+

(!) dabgham += 2

(#)

3$

+=

a

ax

(&) "3 2 += ab

". Sole the following simultaneous euations.(a)

13

1$3

=

=+

wx

wx

(!)1$3%2

13103

=

=+

yx

yx

(#)

08%

013

1

2

1

=++

=

yx

yx

%. line passes through the points (4 1) an& (24 %).

(a) 'in& the gra&ient of the line.(!

)

'in& the euation of the line.

(#) 'in& the #oor&inates of thexan&yinter#epts.(&

)5f this line is parallel to 2

"=

h

yx4 fin& the alue of h.

$. 6he euation of a straight line is "23 =+ yx .(a) 'in& the #oor&inates of the y inter#ept

(!) 'in& the #oor&inates of the x inter#ept(#) 7ien that the point ( k 4 ) lies on the line4 fin& the alue of k .

8. 5n the &iagram4 Ais the point (04 10) an&Dis the poin (04 %). CDis a horiontal

line. 6he lineAC#uts thex-axis atBan& its gra&ient is2

".

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8/13/2019 June Holiday Assignment

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(a) 'in& the euation of the line CD.(!

)

'in& the euation of the lineAC.

(#) 'in& the #oor&inates ofB.(&

)

'in& the #oor&inates of C.

(e) ,en#e4 fin& the area of ACD .

. line has euation x

y=

2 . 'in&

(a) its gra&ient4(!

)

the #oor&inates of the point at whi#h it #uts the x axis4

(#) the #oor&inates of the point at whi#h the line interse#ts the line".1=y

4(&

)the euation of another line parallel to x

y=

2 4 passing through the

point (243).

10. 5n the rightangle& triangle ABC4 D is apoint onBC.7ien thatDC9 1 #m4AB9 12 #m an&AD9 20 #m4 #al#ulate

(a) BD4(!) 6he area of triangleADC,(#) AC,(&) 6he perpen&i#ular &istan#e fromDtoAC,

%ns&er the &hole o' this ($estion on a piece o' graph paper)

11. (a) 7ien the line 2x+ 3y 9 04 fin&(i) the gra&ient of the line4(ii) theyinter#ept.

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A

B CD

12

1

20

8/13/2019 June Holiday Assignment

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(!

)

:omplete the ta!le of alues for 2x+ 3y 9 0.

x 2 0 2

y

(#) ;lot the points an& &raw a straight line through them.(&

)

'rom the graph4 fin&

(i) the alue ofywhenx9 2.84(ii) the alue ofxwheny9 2.

12.

*e#tangular tiles are to !e lai& along the e&ges so that they #oer the unsha&e&

region only. 6he tiles measure ymetres !y (y") metres. ywhen it pro&u#esxtoys4 whereyis gien !y the

formula ( ) ( )1 3 20 10010

y x x= for 0 x 80. 6he ta!le !elow shows the

profit whi#h the firm ma/es when pro&u#ing &ifferent num!er of toys.

?um!er of toys(x)

0 10 20 30 0 "0 %0 $0 80

;rofit (>y) 200 0 320 0 %00 %"0 %0 "$0 p

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8/13/2019 June Holiday Assignment

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(a) 'in& the alue ofp.(!) @sing a s#ale of 2 #m to represent 10 toys for the horiontal axis for

0 x80 an& a s#ale of 2 #m to represent >100 for the erti#al axis

for 200 y$004 &raw the graph of ( ) ( )1

3 20 10010

y x x= .

(#) @se your graph to estimate(i) the profit ma&e when 1" toys are pro&u#e&.(ii) (a) the num!er of toys pro&u#e& to gie the maximum profit.

(!) the profit per toy when this num!er is pro&u#e&.(iii) the alue of ywhenx9 "4 explaining the signifi#an#e of your

answer.

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