ALGEBRA 2

Find a if 50 + 24 =56

                        a

Solution

50 + 24 =52

        a

   24  = 52 - 50

   a

   24  =  2

    a

¹ a  x  24  =  2 x a

        ₁ a

24 = 2a

24  = 2a

2       2

12 = a

Hence a=12.

TRY THIS.........................

If 30 + 24 = 38; find c

           c

VARIATIONS 1

x is directly proportional to y. x=12 while y=4. Find y when x is 69.

Solution

x ⍺ y

x = ky

12 = k x 4

12 = 4k

4      4

k = 3

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

k = 3, y= ? x = 69.

x = ky

69 = 3 x y

69 = 3y

3      3

y = 23.

TRY THIS…………….

x is directly proportional to y. x=28 while y=4. Find y when x is 70.

MATRIX 1

UNITS OF WEIGHT 1

Eight boxes have 0.24 tonne each. Find the total mass of the boxes in Kilograms.

Solution

Total mass = 0.24 x 8 = 1.92

1Tonne  = 1000Kg

1.92Tonnes = ?

After cross-multiplying;

= 1.92  x 1000

         1

=   1920

       1

= 1920 Kilograms

Hence total mass of boxes is 1920 kilograms

TRY THIS........

Nine boxes have 0.46 tonne each. Find the total mass of the boxes in Kilograms.

X INTERCEPT 1

If 36x + 5y -9 = 0; find x-intercept.

Solution

x-intercept is when y=0.

36x + 5y -9 = 0

36x + 5(0) - 9 = 0

36x - 9 = 0

36x = 0+ 9

36x = 9         [dividing by 9 both sides.]

36     36

x = ¹/4

Hence x=¹/4

TRY THIS………..

If 51x - 2y - 17 = 0; find x-intercept.

PERCENTAGES 1

What percentage of 1 hour is 12 minutes?

solution

1 hour = 60minutes

To get %'ge we take the fraction of 3min in 1 hour(60min) and multiply by 100.

= 12      x 100

  60

= 12 ¹     x 100

  60₅

= 1      x 100²⁰  

  5₁

= 20%

Hence percentage of 12 minutes in 1 hour is 20 %

TRY THIS.........................

NECTA FORM II - 2013 QN. 7

What percentage of 1 hour is 15 minutes?

ALGEBRA 1

Divide 58ax + 22ay - 10az by 2a

solution

= 58ax + 22ay - 10az

               2a

= ²⁹58ax  +  ¹¹22ay  -  ⁵10az       [cancelling by 2a throughout]

      2a             2a           2a

= 29x + 11y - 5z answer

TRY THIS...................

Divide 72am - 32an + 92ap by 4a

SIMPLIFY 1

 Simplify 21x-3(x-y)+5

Solution

=21x-3(x-y)+5

=21x-3x+3y+5

=18x+3y+5 answer

TRY THIS……..

Simplify 21x-9(x-y)+13

MID POINT 1

Find a if the midpoint of a line from (a, 6) to (8, 10) is (30, 7)

Solution

x1=a, x2=8, y1=6, y2=30.

(30, 7)= (x1 + x2, y1 + y2)

                   2             2

(30, 7)= (a + 8,  6 + 10)

                  2          2

(30, 7)= (a + 8, 16)

                  2      2

Equating values of x;

30= a + 8

         2      

2 x 30= (a + 8)  x 2 ¹

                2 ₁     

60 = a + 8

60-8 = a

a = 52.

Hence a = 52

TRY THIS……………………..

Find m if the midpoint of a line from (m, 19) to (13, 10) is (9, 11)

PIE CHART 1

In a survey of 60 people, 47 people said their favourite sport was football. What angle in a pie chart would this represent?

Solution

We make a fraction of 47 ot of 60, then multiply by 360⁰.

= 47 x 360⁰.

   60

= 47 x 360⁰₆

   60₁

= 47 x 6

= 168⁰.

Hence the angle is 168⁰ 

TRY THIS………………………   

In a survey of 30 people, 23 people said their favourite sport was football. What angle in a pie chart would this represent?