Wednesday 22 February 2017

ALGEBRA 1N







TRIGONOMETRY 1A


Given that Sin Ө  = 1/9, Find Cos Ө.

Solution

Sin2Ө + Cos2Ө = 1

(1/9)2 + Cos2Ө = 1

Cos2Ө = 1 - (1/9)2

Cos2Ө = 1 - 1/81

Cos2Ө =81/81 - 1/81

Cos2Ө = 80/81

Cos2Ө = (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 =  210      answer
                 9
  
TRY THIS………


Given that Sin Ө  = 1/5, Find Cos Ө. 

FACTORIZE 1C

Factorize 3x2 + 8x - 16.

Solution

= 3x2 + 8x - 16. We split the middle term (8x) to be (12x - 4x).

= 3x2 + 12x - 4x - 16

=  (3x2 + 12x) - (4x + 16) we group by using brackets.

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

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

Hence 3x2 + 8x - 16= (3x - 4) (x + 4)answer.


TRY THIS…..


Factorize 3x2 - 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 1st brackets]

= 50 x 8 ÷ 2     [After dealing with 2nd 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)

MATRIX 1P



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.

MATRIX 1N



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).
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Thursday 16 February 2017

MATRIX 1M


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% = 740,000   x B.P.  [multiplying by B.P. both sides]
                       B.P.

B.P. x 10 = 740,000   

B.P. x 101 =   740,000   
  110                   10

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%.

MATRIX 1L


GEOMETRY 1C


An interior angle of a regular polygon is 720 greater than an exterior angle. Find the interior angle.

Solution

Let i = interior angle, e = exterior angle.

Now i  + e=1800…………………(1)

But i = e+720 …………………(2)

Substitute (2) in (1) above.

e+720   + e=1800

e+ e+720   =1800

2e+ 720   =1800

2e=1800 - 720   

2e=1080

2e=1080          dividing by 2 both sides.
2      2

e = 540


TRY THIS………………………   


An interior angle of a regular polygon is 860 greater than an exterior angle. Find the interior angle.

Wednesday 15 February 2017

MATRIX 1K



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.

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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.


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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 3600.

= 28 x 3600.
   60

= 28 x 36006
   601

= 28 x 6

= 1680.

Hence the angle is 168

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?

MATRIX 1J



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).

MATRIX 1H



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 1011      then we change 516.54 into standard form as well

= 5.1654 x 102 x 1011   [when we have exponents with same base, we add 
   the powers.]
 
= 5.1654 x 1013

= 5.17 x 1013 [correct to 2 d.p.]

Hence   2582.7 x 10-9   = 5.17 x 1013
                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 = 900. [Since complementary angles add up to 900]

220 + x + 250 = 900.

x +470 = 900.

x = 900 - 470

x = 430  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 106

Hence 1, 720, 000 = 1. 72 x 106 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 6x + k + 40 + y , when x = 8, k = 12 and y =− 30 .

Solution

=6x + 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 3x + k + 50 + y , when x = 7, k = 14 and y =− 7 .

Tuesday 7 February 2017

EXPONENTIALS 1G


If y2 = 3, find y10.

Solution

= y10

= (y2)5

= (3)5      remember y2 = 3

= 3 x 3 x 3 x 3 x 3

= 243

Hence y10 = 243.

TRY THIS……………….

If  y7 = 10, find y21.


ARC LENGTH 1A


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

Solution

L = r
      1800

L = x  45
             1800

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.

RADICALS 1C



REGULAR POLYGONS 1B


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

Solution

n = 52

Total angles = (n - 2)1800

                   = (52 – 2)1800

                   = 50 x 1800

                   = 90000

Total angles = 90000


TRY THIS……………………….

A regular polygon has 38 sides. Find the total angles of that polygon.