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.