Factorize 121-d

^{2}

__Solution__
We use difference of two squares a

^{2}– b^{2}= (a - b)(a + b)
121-d

^{2}= 11^{2}-d^{2 }
= (11 - d)(11 +
d)

**Hence 121-d**

^{2}

^{ }**= (11 - d)(11 + d)**

__TRY THIS…………….__
Factorize 144 - c

^{2}
Factorize 121-d^{2}

We use difference of two squares a^{2} –
b^{2} = (a - b)(a + b)

121-d^{2} = 11^{2}-d^{2 }

= (11 - d)(11 +
d)

Factorize 144 - c^{2}

A card is
picked at random from a pack of playing cards. Find the probability that it is
a red card.

Total
playing card is normally 52. Half of them(26) are red.

n(E) = 26, n(S) = 52, P(E) = ?

P(E) = __n(E)__

n(S)

P(E) = __26__

52

A card is
picked at random from a pack of playing cards. Find the probability that it is
a red card.

A man got a profit of 130/= after
selling an item for 5200/=. Find the percentage profit.

%’ge profit = __Profit__
X 100 [where B. P.
represents Buying Price.]

B.P.

%’ge profit = __13__~~0~~
X 100

520~~0~~

%’ge profit = 2.5%

Hence Percentage Profit is 2.5%

A man got a profit of 10,000/= after
selling an item for 250,000/=. Find the percentage profit.

If n(A)= 60 , n(AuB) = 200 and
n(AnB)=20, find n(B)

n(AuB) = n(A) + n(B) - n(AnB)

200 =
60 + n(B) – 20

200 =
60 -20 + n(B)

200 =
40 + n(B)

200 -
40 = n(B)

160 = n(B)

How many US
Dollars are worth Tsh. 8,500,000/=?

1 US Dollar
= 1700 Tsh.

? = 10,200,000/=

After cross
multiply we have:

= __10,200,0__~~00~~x 1

17~~00~~

= __102,000 __^{6000}

= 6,000

How many US
Dollars are worth Tsh. 51,000,000/=?[ Assume 1USD=1700 Tsh.]

Express each
of the following as trigonometric ratios of positive acute angles: (i) Sin(-50^{0}) (ii) Cos(-210^{0}) (iii) Tan( -170^{0})

= Sin 310^{0}

Sin Î¸ =
-Sin(360^{0}- Î¸) [since it is in
the 4^{th} quadrant]

Sin 310^{0}
= -Sin(360^{0}- 310^{0})

= -Sin 50^{0 }

= Cos 150^{0}

Cos Î¸ =
-Cos(180^{0}- Î¸) [since it is in
the 2nd quadrant]

Cos 150^{0}
= -Cos(180^{0}- 150^{0})

= -Cos 30^{0
}

= Tan 190^{0}

Tan Î¸ =
-Tan(Î¸ - 180^{0}) [since it is
in the 3rd quadrant]

Tan 190^{0}
= -Tan(190^{0}- 180^{0})

= -Tan 10^{0
}

Express each
of the following as trigonometric ratios of positive acute angles.

(i) Sin(-60^{0}) (ii) Cos(-280^{0}) (iii) Tan( -130^{0})

Evaluate
Log1000 + log_{ }0.00001 + log_{3}243

= Log1000 +
log_{ }0.00001 + log_{3}243

= Log10^{3} + log_{ }10^{-5} + log_{3}3^{-5}

= 3Log10 +
(-5log_{ }10) + (-5log_{3}3) [since log_{a}a^{n }= nlog_{a}a]

= (3x1) +
(-5x1) + (-5x1) [since log_{a}a
= 1]

= 3 + (-5) +
(-5)

= 3 - 10

= -7

Evaluate
Log100,000 + log_{ }0.01 + log_{3}729

If F(x) = 13x + 14; Find F^{-1}(x).

HINT: F^{-1}(x) means
inverse.

PROCEDURE:

Make x the subject and then
interchange x and y variables.

Let y=F(x)

So,
y= 14x + 10

y – 10 = 14x

14 14

14

x
= __y – 10__ after rearranging

14

y^{-1} = __x – 10 __ after interchanging x and y variables.

14

F^{-1}(x) = __x – 10 __ after interchanging x and y variables.

14

If F(x) = 7x + 8; Find F^{-1}(x).

In a box of 500 books, 160
are red in colour while the rest are bluish in color. Give out the percentage
of blue books.

1st we have to get the
number of blue books.

blue books = 500 - 160 = 340

then,= __340__ x 1~~00~~

5~~00~~

then,= __340__

5

= 68%

In a box of 800 books, 300
are yellow in colour while the rest are bluish in color. Give out the
percentage of blue books.

Evaluate Log_{2}(512 ÷ 16).

= Log_{2}(512 ÷ 16)

= Log_{2}512 - Log_{2}16
(applying the quotient rule)

= Log_{2}2^{9}
- Log_{2}2^{4 } (
512= 2^{9} and 16=2^{4} )

= 9Log_{2}2 - 4Log_{2}2
( remember Log_{a}a^{c }= cLog_{a}a )

= (9 x 1) - (4 x 1)
( remember Log_{a}a^{
}= 1 )

= 9 - 4

= 5

Evaluate Log_{2}(1024 ÷ 32).

Evaluate 352^{2}
– 342^{2}

352^{2}
– 342^{2 }= (352 + 342)( 352 – 342)

= (694)( 10)

= 6940

352^{2}
– 342^{2 }= 6940

Evaluate 905^{2}
– 805^{2}

Dikshi
deposited the amount of 9000/= in a bank which gives an interest rate of 4% for
4 years. Find the simple interest she got.

I = ?,
P = 9,000/=, T = 4 years, R = 4%

I =__
PRT__

100

I = __9000
x 4 x 4__

100

I = __90__~~00~~
x 4 x 4

1~~00~~

I = 90
x 4 x 4

I = 1440/=

Hence the
simple interest was Tsh 1080/=

Edmund
deposited the amount of 55,000/= in a bank which gives an interest rate of 6%
for 6 years. Find the simple interest she got?

If
Log_{a}y = Log_{a}6 + Log_{a}11 ; find y.

Log_{a}y
= Log_{a}6 + Log_{a}11

Log_{a}y
= Log_{a}(6 x 11) [since Log_{a}m + Log_{a}n = Log_{a}(m
x n)]

If
Log_{a}x = Log_{a}5 + Log_{a}3 ; find x.

Find the midpoint of a line from
(31, 12) to (17, 10)

x1=31,
x2=17, y1=12, y2=10.

Mid point = (__x1 + x2__, __y1 +
y2__)

2
2

Mid point = (__31 + 17__, __12
+ 10__)

2 2

Mid point = (__48__, __22__)

2
2

Hence
midpoint = (24, 11)

Find the midpoint of a line from (24,
14) to (22, 18)

Find x in the following inequality
2x+50 ≤ 72

2x+50 ≤ 72

2x ≤ 72 – 50

2x≤ 22

2
2

x ≤ 11

Find x in the following inequality 3x
+ 36 ≤ 87

Given the
ratios U:V = 11: 2 and V:W = 20:7 Find the ratio U:W.

W V W

W _{1} ~~2~~ 7

W 1 x 7

W 7

Given the
ratios D:E = 5:7 and E:F = 3:35; Find
the ratio D:F.

Priya
deposited the amount of 210,000/= in a bank which gives an interest rate of 3%
for 5 years. Find the simple interest she got.

I
= ?, P = 210,000/=, T = 5 years, R = 3%

I
=__ PRT__

100

I
= __210,000 x 3 x 5__

100

I
= __210,0__~~00~~ x 3 x 5

1~~00~~

I
= 2100 x 3 x 5

I
= 31,500/=

Hence
the simple interest was Tsh 31,500/=

Edmund
deposited the amount of 70,000/= in a bank which gives an interest rate of 2%
for 4 years. Find the simple interest he got?

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