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 =  2√10      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.

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)

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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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%.