F.2數學..........20marks

1.(a)
x2-(y-z)2
= [x+(y-z)][x-(y-z)]
= (x+y-z)(x-y+z)

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1.(b)
[(-4x/3)+2][(-4x/3)-2]
= (-4x/3)2-(2)2
= (16x2/9) - 4
[or = (16x2-36)/9]

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1.(c)
(x+y+z)(x+y-z)
= [(x+y)+z][(x+y)-z]
= (x+y)2-z2
= (x2+2xy+y2)-z2
= x2+2xy+y2-z2

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1.(d)
[2x+(3y-2)][2x-(3y-2)]
= (2x)2-(3y-2)2
= 4x2-[(3y)2-2(3y)(2)+(2)2]
= 4x2-9y2+12y-4

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2.(a)
x4+2x3-2x2-2x
= x(x+1)(x-1)(x+2)

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2.(b)
x4+3x2+2
=(x2+1)(x2+2)

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2.(c)
x4-x2
=x2(x+1)(x-1)

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3.
(x/4)+(y/3)=1
3x+4y=12 ...... (*)

y=(3/4)x
3x = 4y
3x-4y = 0 ...... (**)

(*)+(**):
6x = 12
x = 2

(*)-(**):
8y = 12
y = 1.5

Hence, x = 2 and y = 1.5

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4.
a+b+c=4 ...... (1)
2a-b+c=0 ...... (2)
2a+b-3c=10 ...... (3)

(1)+(2):
3a+2c = 4 ...... (4)

(2)+(3):
4a-2c = 10 ...... (5)

(4)+(5):
7a = 14
a = 2

Subst. a=2 into (4)
3(2)+2c=4
c = -1

Subst. a=2 and c=-1 into (1)
(2)+b+(-1) = 4
b = 3

Ans: a = 2, b = 3, c = -1

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5.
She can finish (1/6) of the job in one day.
He can finish (1/3) of the job in one day.

When they work together, fraction of job finished in one day
= (1/6)+(1/3)
= 1/2

No. of days they will take to finish the job = 2 days

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6.
Amount A = $3180
Interest rate R% = 4% (per annual)
No. of years = 18/12 = 1.5 years
Principal = ?

A = P(1+nR%)
3180 = P(1+1.5x4%)
1.06P = 3180
P = 3000

Hence, principal = $3000

Simple interest = $(3180-3000)
Simple interest = $180
=