## Wednesday, 22 February 2017

### TRIGONOMETRY 1A

Given that Sin Ө = 1/9, Find Cos Ө.

__Solution__
Sin

^{2}Ө + Cos^{2}Ө = 1
(1/9)

^{2}+ Cos^{2}Ө = 1
Cos

^{2}Ө = 1 - (1/9)^{2}
Cos

^{2}Ө = 1 -^{1}/81
Cos

^{2}Ө =^{81}/81 -^{1}/81
Cos

^{2}Ө =^{ 80}/81
√Cos

^{2}Ө =^{ }√(^{80}/81) keeping under radical sign both sides
CosӨ =

^{ }√(^{80}/81)
CosӨ =

^{ }__√____80__since √81=9
9

CosӨ =

^{ }__√____(2x2x2x5)__
9

CosӨ =

^{ }2__√____(10)__
9

**CosӨ =**

^{ }2

__√__

__10__**answer**

**9**

__TRY THIS………__
Given that Sin Ө = 1/5, Find Cos Ө.

### FACTORIZE 1C

Factorize 3x

^{2}+ 8x - 16.

__Solution__
= 3x

^{2}+ 8x - 16. We split the middle term (8x) to be (12x - 4x).
= 3x

^{2}+ 12x - 4x - 16
= (3x

^{2}+ 12x) - (4x + 16) we group by using brackets.
= 3x(x + 4) - 4(x + 4).

= (3x - 4) (x + 4)

**Hence 3x**

^{2}+ 8x - 16= (3x - 4) (x + 4)answer.

__TRY THIS…..__
Factorize 3x

^{2}- 13x - 16.## Friday, 17 February 2017

### BODMAS 1A

Evaluate
50 x (45 – 37) ÷ (345-343)

__Solution__
We
apply BODMAS.

=
50 x (45 – 37) ÷ (345-343)

=
50 x 8 ÷ (345-343) [After dealing with 1

^{st}brackets]
=
50 x 8 ÷ 2 [After dealing with 2

^{nd}brackets]
=
50 x 4 [After dividing]

=
200 [After multiplying]

Hence 50 x (45 – 37) ÷ (345-343) = 200

__TRY THIS……………….__
Evaluate
8 x (96 – 16) ÷ (83-43)

### UNITS OF DISTANCE 1B

Change
21260m into Km.

__Solution__
1Km
= 1000m

?
= 21260m

=

__1 x 21260__
1000

=

__21260__
1000

=

**21.26Km**

__TRY THIS...................................__
Change
68042m into Km.

### SETS 1C

If n(A)= 60 , n(B)= 90 and n(AuB)= 130,
find n(AnB).

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

130 = 60 + 90 - n(AnB)

130 = 150 - n(AnB)

130 - 150 = - n(AnB) [after
transferring 150 on the left hand side]

-20 = -n(AnB)

n(AnB) = 20 [after dividing by -1 both
sides]

__Hence n(AnB) = 20 answer__

__TRY THIS………….__
If n(A)= 74 , n(B)= 86 and n(AuB)= 125,
find n(AnB).

==============================================

## Thursday, 16 February 2017

### PERCENTAGE PROFIT 1A

A man got a profit of 7400/=
after selling an item. Find the buying price if the percentage profit was 10%.

__Solution__
%’ge profit =

__Profit__X 100 [where B. P. represents Buying Price.]
B.P

10% =

__7400__X 100
B.P.

B.P. x 10% = ~~B.P.~~ [multiplying by B.P. both sides]

__740,000__x
B.P. x 10 = 740,000

__B.P. x__~~10~~=

^{1}__740,00__~~0~~

_{1}

B.P. =74,000

__Hence Buying Price was 74,000/=__

__TRY THIS………………__
A man got a profit of 17,500/=
after selling an item. Find the buying price if the percentage profit was 20%.

### GEOMETRY 1C

An
interior angle of a regular polygon is 72

^{0}greater than an exterior angle. Find the interior angle.

__Solution__
Let
i = interior angle, e = exterior angle.

Now
i + e=180

^{0}…………………(1)
But
i = e+72

^{0 }…………………(2)
Substitute
(2) in (1) above.

e+72

^{0 }+ e=180^{0}
e+
e+72

^{0 }=180^{0 }
2e+
72

^{0 }=180^{0 }
2e=180

^{0 }- 72^{0 }
2e=108

^{0 }__2__e=

__108__

^{0 }dividing by 2 both sides.

2 2

e
= 54

^{0}

__TRY THIS………………………__
An
interior angle of a regular polygon is 86

^{0}greater than an exterior angle. Find the interior angle.## Wednesday, 15 February 2017

### GEOMETRY 1B

If
7x + 3y= 8; find the x intercept.

**Solution**
x-intercept
is when y=0.

7x
+ 3(0)= 8.

7x
= 8.

__7x__=

__8__dividing by 7 both sides.

7 7

x
= 8/7

**Hence x-intercept is (**

^{8}/7,0)

__TRY THIS………………………__
If
4x -3y= 36; find the x intercept.

### CONGRUENCE 1B

In the
figure below, prove that ΔEFG and ΔGEH are congruent. (diagram not to scale)

__Solution__
GIVEN: Quadrilateral EFGH,

EF=GH,

<FGE=<GEH

REQUIRED TO
PROVE: ΔEFG ≡ΔEGH.

PROOF: EG=GE (given)

<FGE=<GEH (given)

EG= GE (common)

Hence ΔEFG ≡ΔEGH
(By SAS)

__TRY THIS…………………__
In the
figure below, prove that ΔSTU and ΔUSV are congruent.

================================================

### STATISTICS 1A

In a survey of 60 people, 28
people said their favourite sport was football. What angle in a pie chart would this represent?

__Solution__

We make a fraction of 28 ot
of 60, then multiply by 360

^{0}.
=

__28__x 360^{0}.
60

= ~~360~~

__28__x^{0}_{6}_{1}

=
28 x 6

=
168

^{0}.

__Hence the angle is 168__

^{0 }

__TRY THIS………………………__
In a survey of 90 people, 53
people said their favourite sport was football. What angle in a pie chart would this represent?

### SETS 1B

If n(A)= 60 , n(B)= 90 and n(AuB)= 130,
find n(AnB).

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

130 = 60 + 90 - n(AnB)

130 = 150 - n(AnB)

130 - 150 = - n(AnB) [after
transferring 150 on the left hand side]

-20 = -n(AnB)

n(AnB) = 20 [after dividing by -1 both
sides]

__Hence n(AnB) = 20 answer__

__TRY THIS………….__
If n(A)= 74 , n(B)= 86 and n(AuB)= 125,
find n(AnB).

### STANDARD FORM 1D

Evaluate the following giving your answer in standard form.

__2582.7 x 10__

^{-9}

5 x 10

^{-20}^{}

__Solution__
=

__2582.7 x 10__^{-9}
5 x 10

^{-20}^{}

=

__2582.7__x__10__^{-9}
5 10

^{-20}
= 516.54 x 10

^{-9}^{–(-20) }[after dividing 2582.7 by 5]
= 516.54 x 10

^{-9 + 20 }
= 516.54 x 10

^{11 }then we change 516.54 into standard form as well
= 5.1654 x 10

^{2}x 10^{11 }[when we have exponents with same base, we add
the powers.]

^{ }

= 5.1654 x 10

^{13}
= 5.17 x 10

^{13 }[correct to 2 d.p.]**Hence**

__2582.7 x 10__^{-9 }= 5.17 x 10^{13}**5 x 10**

^{-20}

^{}

__TRY THIS………………..__
Evaluate the following giving your answer in standard form.

__0.006647 x 10__

^{-9}

4 x 10

^{-30}^{}

## Wednesday, 8 February 2017

### GEOMETRY 1A

If A and B are complementary angles such that

*A*= 22° and*B*=*x*+ 25° , find the value of*x*.

__Solution__
A + B = 90

^{0}. [Since complementary angles add up to 90^{0}]
22

^{0}+ x + 25^{0}= 90^{0}.
x +47

^{0 }= 90^{0}.
x = 90

^{0}- 47^{0}^{}

x = 43

^{0 }answer.

__TRY THIS..............................__
If A and B are complementary angles such that

*A*= 35° and*B*=*x*+ 26° , find the value of*x*.### STANDARD FORM 1C

The radius of Mars
planet is about 1, 720, 000 meters. Express the radius in scientific notation.

__Solution__
=1, 720, 000

=1. 72 x 10

^{6}^{}

**Hence 1, 720, 000 = 1. 72 x 10**

^{6 }m

__TRY THIS..............................__
The radius of a certain planet is about 8, 760, 000
meters. Express the radius in scientific notation.

### ALGEBRA 1M

Calculate the value of 6

*x*+*k*+ 40 +*y*, when*x*= 8,*k*= 12 and*y*=− 30 .

__Solution__
=6

*x*+*k*+ 20 +*y*

=6

*(8)*+*12*+ 40 +*(-30)*

=6

*(8)*+*12*+ 40 +*(-30)*

=48 + 12 + 40 – 30

= 100 – 30

= 70 answer

__TRY THIS..............................__
Calculate the value of 3

*x*+*k*+ 50 +*y*, when*x*= 7,*k*= 14 and*y*=− 7 .## Tuesday, 7 February 2017

### EXPONENTIALS 1G

If y

^{2}= 3, find y^{10}.

**Solution**
= y

^{10}
= (y

^{2})^{5}
= (3)

^{5 }remember y^{2}= 3
= 3 x 3 x 3 x 3 x 3

= 243

Hence y

^{10}= 243.

__TRY THIS……………….__
If
y

^{7}= 10, find y^{21}.### ARC LENGTH 1A

Find the
length of an arc if the radius of the circle is 45cm.

__Solution__
L =

__∏____r__
180

^{0}
L = ∏ x

__45__
180

^{0}
L =

__∏__cm
4

**Hence length of an arc is**

^{∏}**/4**

**cm**

__TRY THIS………………..__
Find the
length of an arc if the radius of the circle is 20cm.

### REGULAR POLYGONS 1B

A regular polygon has 52 sides. Find
the total angles of that polygon.

__Solution__
n = 52

Total angles = (n - 2)180

^{0}
= (52 – 2)180

^{0}
= 50 x 180

^{0}
= 9000

^{0}
Total angles = 9000

^{0}

__TRY THIS……………………….__
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