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**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) Fre...

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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...

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**A. PROGRESSION 1**

Find

the sum of the 1st 20 terms of the following arithmetic progression:

5+11+17+………………… Solution d=6,

A 1 = 5,n=16 S n = n [2A 1 + (n-1)d]

2 S 20 = 20 [2(5) + (20-1)d]

2 S 20 = 10[10 + 19d] S 20 = 8[10 + 19(6)] since d=6 S 20 = 8[1...

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**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...

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**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 = log10 6 - log2 = 6log10 - log2 =(6 x 1) - (0.3010) = 6 - 0.3010 =5.699 Hence

log500,000=5.699 TRY THIS…………… If log 2= 0.301...

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**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 2 w

> 46 2 2 w > 23 answer TRY THIS…………………………… When 30 is subtracted from thrice a cert...

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**LOGARITHMS 9**

Simplify Log 2 1024 – Log 5 3125

– Log 6 216. Solution = Log 2 1024 – Log 5 3125

– Log 6 216 = Log 2 2 10 –

Log 5 5 5 – Log 6 6 3 = 10Log 2 2 – 5Log 5 5 – 3Log 6 6 because Log a a n = nLog a a = (10 x 1) – (5 x 1) – (3 x 1) = 10 – 5 – 3 = 10 – 8 ...

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**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.

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**LOGARITHMS 8**

If Log a x = 40, find Log a ( 1 /x 5 ) Solution = Log a ( 1 /x 5 ) = Log a x -5 [since 1/a n = a -n ] = -5 x Log a x

[since Log a x n =

nLog a x ] = -5 x 40 = -200

answer TRY THIS……….. If Log a b= 300, find Log a ( 1 /b 4 )

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