MATRIX-4

ARITHMETIC PROGRESSION-1

Find the sum of the 1st 16 terms of the following arithmetic progression: 5+11+17+…………………

Solution

d=6, A₁ = 5,n=16

S_n = n[2A₁ + (n-1)d]

       2

S₁₆ = 16[2(5) + (16-1)d]

         2

S₁₆ = 8[10 + 15d]

 

S₁₆ = 8[10 + 15(6)]       since d=6

S₁₆ = 8[10 + 90]

           

S₁₆ = 8 x 100  

         

S₁₆ = 800

Therefore the sum of 1st 16 terms is 800.

TRY THIS......

Find the sum of the 1st 16 terms of the following arithmetic progression: 6+14+22+…………………

MATRIX - 3

STATISTICS 1

In Kiswahili test the following marks were recorded.

marks	10-19	20-29	30-39	40-49	50-59	60-69
No. of students	2	5	9	6	5	3

Calculate the mean.

Solution

Here you are required to produce the frequency distribution table.

Class interval	Class mark (x)	Frequency(f)	fx
10-19	14.5	2	29
20-29	24.5	5	122.5
30-39	34.5	9	310.5
40-49	44.5	6	267
50-59	54.5	5	272.5
60-69	64.5	3	193.5
		∑f = 30	∑fx = 1195

Mean = ∑fx

               ∑f

Mean = 1195

                 30

Mean =  39.83

         

Hence Mean =  39.83

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

In a Biology test the following marks were recorded.

marks	10-19	20-29	30-39	40-49	50-59	60-69
No. of students	4	7	12	8	5	4

Calculate the mean.

MATRIX 2

PERFECT SQUARES 1

If 16x² + 24x + t is a perfect square, find t.

Solution

a = 16, b = 24, c = t.

b² = 4ac

(-24)² = 4 x 16 x t

576 = 64t

576 = 64t

 64      64

           

t = 9

Hence t = 9

TRY THIS………………..

If 9x² + 24x + f is a perfect square, find f.

MATRIX 1

PROBABILITY 1

The probability that it will rain tomorrow is ⁸/17. Find the probability that it won’t rain.

Solution

Let P(E)= probability that it will rain.

     P(E’) = probability that it won’t rain.

Let P(E)=  ⁸/17         P(E’) = ?

P(E)   + P(E’) = 1

⁸/17   + P(E’) = 1

P(E’) = 1 -  ⁸/17  

P(E’) = ¹⁷/17 -  ⁸/17  

P(E’) = ¹⁷/17 -  ⁸/17  

P(E’) =  17-8

               17

P(E’) =  9

             17

Hence the probability that it won’t rain is ⁹/17.

TRY THIS......

The probability that it will rain tomorrow is ²/11. Find the probability that it won’t rain.

DIFFERENCE OF 2 SQUARES - 1

Evaluate 780² – 680²

Solution

790² – 690² = (790 + 690)( 790 – 690)

                   = (1480)( 100)

                   = 148000

Hence 790² – 690² = 148000

TRY THIS……………………..

Evaluate 783² – 683²

SLOPE OR GRADIENT 1

Find the slope of a line which passes through (4, 13) and (14, 8).

Solution

x₁ = 4,  y₁ =13,  x₂ = 14,  y₂ = 8

m = y2 –y1

       x2 – x1

m =   8 –13

         14 –4

m =   -5

         10

m =   -1                           (After simplification)

          2

  

Hence the slope is -1/2

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

Find the slope of a line which passes through (4, 1) and (-1, 8).

INEQUALITIES 1

Find x if 4x – 21 ≤ x + 45 ≤ 6x.

Solution

4x – 21 ≤ x + 45 and  x + 45 ≤ 6x

4x – x ≤ 21+ 45 and  45 ≤ 6x - x

3x ≤ 66(divide by 3 both sides) and  45 ≤ 5x (divide by5 both sides)

x ≤ 22 and  15 ≤ x

x ≤ 22 and  x ≥ 15

TRY THIS……..

Find x if 4x – 31 ≤ x + 15 ≤ 4x