RATIOS 2

Decrease 7000sh by 3:10.

Solution

= 3 x 7000sh

 10

= 3 x 7000⁷⁰⁰

 10₁

= 3 x 700

= 2100Tshs answer

TRY THIS…………………………

Decrease 18,000sh by 7:20.

SIMPLIFY 4

Simplify 20 + 6(6n ÷ ⁿ/2) - 80

Solution

=20 + 6(6n ÷ ⁿ/2) - 80

=20 + 6(6n x ²/n) – 80

=20 + 6(6n¹ x ²/n₁) – 80  cancelling n

=20 + 6(6 x  2) – 80 

=20 + 6(12) – 80 

=20 + 72 – 80 

=92 – 80 

=12 

=12 answer

TRY THIS……..

Simplify 13 + 4(10n ÷ ⁿ/5) - 29

WORD PROBLEMS 1

When 7 is subtracted from twice a certain number, the result is greater than 33. Find the number.

Solution

Let the number be w.

2w – 7 > 33

2w > 33 + 7

2w > 40

2w > 40

2        2

w > 20 answer

TRY THIS…………………………… 

When 30 is subtracted from thrice a certain number, the result is greater than 33. Find the number.

RATIOS 1

Increase 7000sh by 19:7.

Solution

= 19 x 7000sh

    7

= 19 x 7000¹⁰⁰⁰

    7₁

= 19 x 1000

= 19000Tshs  answer

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Increase 8000sh by 15:4.

MAKING THE SUBJECT 1

SIMPLIFY 3

Simplify 11x-9(x-y)+68

Solution

=11x-9(x-y)+68

=11x-9x+9y+68

=2x+3y+68 answer

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Simplify 24x-7(x-y)+35

LOGARITHMS 12

Simplify Log₂2048 - Log₃27

solution

= Log₂2048 - Log₃27

= Log₂2¹¹ - Log₃3³

= 11Log₂2 - 3Log₃3

= (11 x 1) - (3 x 1)

= 11 - 3

= 8

Hence Log₂2048 - Log₃27 = 8

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

Simplify Log₂2048 – Log₅125

SLOPE OR GRADIENT 2

A line passes through (4a, 9) and (8, 5a). If its slope is 2, find a.

Solution

x1=4a, y1 = 9, x2 = 8, y2 = 5a

Slope(m) =    y2 – y1

                     x2 – x1

               2 =  5a – 9

                     8 – 4a

    2 =    5a – 9     [cross multiplying]

    1      8 – 4a

2(8 – 4a) = 5a – 9

16 – 8a = 5a – 9

16 – 8a + 9 = 5a

16 + 9 = 5a+ 8a

25 = 13a

25 = 13a

13    13

²⁵/13 = a

Hence a = ²⁵/13

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

A line passes through (4e, 9) and (8, 42e). If its slope is 2, find e.

ARITHMETICS 1

Evaluate 413² – 403²

Solution

413² – 403² = (413 + 403)( 413 – 403)

                    = (716)( 10)

                    = 7160

413² – 403² = 7160

TRY THIS…………….

  

Evaluate 604² – 594²

EXPONENTIALS 8

If 5^2w (4^w) = 0.00001 ; Find w.

Solution

5^2w (4^w) = 0.00001

(5²)^w (4^w) = 0.00001

(25)^w (4^w) = 0.00001

(25 x 4)^w = 0.00001

(100)^w = 0.00001

(10²)^w = 10^-5 (Since  0.00001=10^-5)

10^2w = 10^-5   (Bases are alike, so they cancel out)

2w = -5

2w = -5

2       2

Hence w = ^-5/2 answer.

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If 3^2t (4^t) = 256 ; Find t.