Download Unit 8 Algebra II 1

Unit 8
Algebra II
Practice Questions: Unit 8 (Algebra II)
1. Expand the following
i.
Ans:
= 2x² 6x +7x 21
= 2x² + x – 21
ii.
Ans:
=18x² +24xy – 6xy – 8y²
= 18x² + 18xy – 8y²
2.
Factorize the following;
i.
Ans:
=3x(x 7)
ii.
Ans:
=y(y 3)
iii.
Ans:
=(2x)² –(3)
=(2x – 3) (2x + 3)
iv.
Ans:
=(1)² (3x)²
=(1 x)(1+3x)
v.
Ans:
3.
=(2x)² –(y)²
= (2x + y)(2x
y)
Factorize the following:
i.
Ans:
=
=
=
ii.
Ans:
=
=
iii.
Ans:
=
=
1
Unit 8
Algebra II
iv.
={
={
={
}
}
}
=
v.
Ans:
4.
=
=
=
Solve the equations:
i.
Ans:
3x(2x+7)-2(2x+7)=0
(2x+7)(3x-2)=0
2x+7=0
3x-2=0
2x=-7
3x=2
x=
x=
ii.
Ans:
(2x+3 -25=0
(2x+3)-(5
(2x+3-5)(2x+3+5)=0
2x+3-5=0
2x+3+5=0
2x-2=0
2x+8=0
2x=2
2x=-8
x=
x=
iii.
Ans:
3x(X+5)-1(x+5)-4x-3=3
3 +15x-x-5-4x-3=0
3 +10x-8=0
3 +12x-2x-8=0
3x(x+4)-2(x=4)=0
(x+4)(3x-2)=0
x+4=0
3x-2=0
x=-4
3x=2
x=
iv.
Ans:
3x(x-2)-1(x-2)=0
(x-2)(3x-1)=0
x-2=0
3x-1=0
x=2
3x=1
2
Unit 8
5.
Algebra II
Solve the simultaneous equations:
i.
Ans:
____(ii)
From equation 1
3x-4 = y
y = 3x-4 ________ (iii)
Putting in eq ii
-3x(3x-4)+8=0
-9 +12x+8=0
8 +12x +8=0
-4(2 -3x-2)=0
2 -3x-2=0
2
2x(x-2) + 1(x+2)=0
(x-2)(2x+1)=0
x-2=0
x=2
y=2
ii.
Ans:
2x+1=0
2x=-1
y=-1/2
x+y=3 ____(i)
xy=2 ______(ii)
x=3-y ______(iii)
(3-y)y=2
3y- =2
- +3y-2=0
- -3y+2=0
y(y-2)-1(y-2)=0
(y-1)(y-2)=0
y-1=0
y-2=0
y=1
y=2
iii.
+xy=0____(i)
___(ii)
y=
__________(iii)
Put in eq (i)
+ x(
)=0
=0
3
Unit 8
Algebra II
+7x=0
x=0
x+7=0
x =-7
y=7
y=7/3
6.
Write the following expressions in the form
i.
Ans:
Here a = 4, b = -9, c = 1
(
By formulae
= 4(
)
= 4(
ii.
Ans:
)
(
(
)
)
)
Here a = -2, b = -4, c = 1
By Formulae
=
(
)
=
(
)
=
(
)
(
)
7.
The area of a rectangle is 270 cm 2. If the shorter side was reduced by 2 cm and the longer side was
increased by 4cm then the area would increased by 16cm 2. Find the length of the sides of the original
rectangle.
Ans: Original area = 270
Let shorter side = x
Let longer side = y
xy=270
y=270/x
Shorter side = x-2
Longer side = y+4
New area = 270+16=286
(x-2) (y+4)=286
x(y+4)-2(y+4)-286=0
xy+4x-2y-8-286=0
4x+xy-2y-294=0
(it is not possible)
8. Find two numbers such that their sum is 12 and their product is 21.
Ans: It is not possible
4
Unit 8
9.
Algebra II
Solve the inequality
3x+4>
-3x<4
3)<4
-3x-4<0
-4x+x-4<0
4)+1(x-4)<0
. Represent the solution on a number line.
4)<0
x+1<0
x<-1
x-4<0
x<4
-3 -2 -1 0 1 2 3 4 5 6 7
12related such that y varies inversely as the square of x.
10. Two variables x and y are
a.
Write an equation in x, y and K to describe the inverse variation, where K is the constant of
variation.
Ans:
x²
x²
k=x²y
x
y
b.
3
1.8
f
2
r
8
Using the information in the table to calculate the value of
i.
K, the constant of variation
Ans:
k = 3 2 = 18
ii.
r
Ans:
r = k/x²
= 18/1.8² = 5.55
iii.
f
ans:
f ² = k/y
f=√
= 1.5
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