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	3	7	14	8	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	3	43.5
20-29	24.5	7	171.5
30-39	34.5	14	483
40-49	44.5	8	356
50-59	54.5	5	272.5
60-69	64.5	3	193.5
		∑f = 40	∑fx = 1520

Mean = ∑fx

              ∑f

Mean = 1520

               40

Mean =  38

         

Hence Mean =  38

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

In a Biology test the following marks were recorded.

marks	10-14	15-19	20-24	25-29	30-34	35-39
No. of students	4	7	12	8	5	4

Calculate the mean.




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ALSO READ Form IV Quizzes   

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PROBABILITY 2

The probability that it will rain tomorrow is ⁸/47. 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)=  ⁸/47         P(E’) = ?

P(E)   + P(E’) = 1

⁸/47   + P(E’) = 1

P(E’) = 1 -  ⁸/47  

P(E’) = ⁴⁷/47 -  ⁸/47  

P(E’) =  47-8

               47

P(E’) =  39

             47

Hence the probability that it won’t rain is ³⁹/47.

TRY THIS......

The probability that it will rain tomorrow is ²³/70. Find the probability that it won’t rain.

A. PROGRESSION 1

Find the sum of the 1st 20 terms of the following arithmetic progression: 5+11+17+…………………

Solution

d=6, A₁ = 5,n=16

S_n = n[2A₁ + (n-1)d]

       2

S₂₀ = 20[2(5) + (20-1)d]

         2

S₂₀ = 10[10 + 19d]

 

S₂₀ = 8[10 + 19(6)]       since d=6

S₂₀ = 8[10 + 114]

           

S₂₀ = 8 x 124  

         

S₂₀ = 992

Therefore the sum of 1st 20 terms is 992.

TRY THIS......

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

WORD PROBLEMS 3

Wema, Kim and Fred shared 1200 sweets such that Wema got 20 sweets less than Kim while Fred got three as much as what Ana got. Find those given to Fred.

Solution

The starting point is Kim. Let the sweets given to Kim be x. See the table below:

WEMA	KIM	FRED	TOTAL
x-20	x	3(x-20) =3x-60	1200

  

Then;

ANA + JOY + FRED = 1200

x-20 + x + 3x-60 = 1200

x + x + 3x - 60 - 20 = 1200

5x - 80 = 1200    [since -60-20 = -80]

5x = 1200 + 80

5x = 1280

5x = 1280

5       5

x = 256

The sweets given to Fred

= 3x – 60

= 3(256) – 30

= 768 – 30

= 738

Hence Fred got 738 sweets.

TRY THIS………………………

Kemi, Roy and Isaya shared 550 sweets such that Kemi got 10 sweets less than Roy while Isaya got four as much as what Kemi got. Find those given to Isaya.   [360 answer] 

LOGARITHMS 10

If log 2= 0.3010; find the value of log 500,000 without using tables.

Solution

=log500,000

=log(1,000,000 ÷2)

=log1,000,000 –log2

= log10⁶ - log2

= 6log10 - log2

=(6 x 1) - (0.3010)

= 6  -  0.3010

=5.699

Hence log500,000=5.699

TRY THIS……………

If log 2= 0.3010; find the value of log 250,000 without using tables.

INEQUALITIES 4

When 7 is subtracted from twice a certain number, the result is greater than 39. Find the number.

Solution

Let the number be w.

2w – 7 > 39

2w > 39 + 7

2w > 46

2w > 46

2        2

w > 23 answer

TRY THIS…………………………… 

When 30 is subtracted from thrice a certain number, the result is greater than 51. Find the number.

LOGARITHMS 9

Simplify Log₂1024 – Log₅3125 – Log₆216.

Solution

= Log₂1024 – Log₅3125 – Log₆216

= Log₂2¹⁰ – Log₅5⁵ – Log₆6³

= 10Log₂2 – 5Log₅5 – 3Log₆6  because Log_aaⁿ =  nLog_aa

= (10 x 1) – (5 x 1) – (3 x 1)    

= 10 – 5 – 3

= 10 – 8     [since -5 - 3 = -8]

= 2

Hence Log₂1024 – Log₅3125 – Log₆216= 2 

TRY THIS…………..

Simplify Log₂4096 – Log₃81 – Log₅3125

WORD PROBLEMS 2

The difference between two numbers is 10 and their sum is 680. Find the two numbers.

Solution

Let the two numbers be x and y.

x – y = 10 ----------- (i)

x +y = 680. ------------(ii)

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From (i)

 x – y = 10

x = 10+ y -------------- (iii)

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Substitute (iii) in (ii) above.

x +y = 680. ------------(ii)

(10+ y) +y = 680

10 + 2y = 680

2y = 680 - 10

2y = 670

¹2y = 670³³⁵

₁2      2₁

y = 335

from (iii)

x = 7+ y

x = 7+ 335

x = 342

Hence the two numbers are 335 and 342.

TRY THIS…………………………

The difference between two numbers is 10 and their sum is 226. Find the two numbers.