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).

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

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.

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.

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

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 360⁰.

= 28 x 360⁰.

   60

= 28 x 360⁰₆

   60₁

= 28 x 6

= 168⁰.

Hence the angle is 168⁰ 

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

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 .

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.