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**ARITHMETIC 1**

Evaluate 396 2 – 386 2 Solution We apply difference of two squares:

a 2 - b 2 = (a+b)(a-b) 396 2 – 386 2 = (396 + 386)( 396 – 386) =

(782)( 10) =

7820 [only add a zero at 782] 396 2 – 386 2 = 13820 TRY THIS……………. ...

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**LOGARITHMS 2**

If Log a x = 0.9,

find Log a ( 1 /x) Solution = Log a ( 1 /x) = Log a x -1 = -1 x Log a x = -1 x 0.9 = -0.9 TRY THIS……….. If Log a w= 3.6,

find Log a ( 1 /w)

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**SLOPE OR GRADIENT 1**

Find the slope of a line which

passes through (-1, -8) and (6,-9) Solution x 1 = -1, y 1 =-8,

x 2 = 6, y 2 = -9 m = y2 –y1 x2 – x1 m = -9 –(-8)

6 –(-1) m = -9 + 8 6

+ 1 m = - 1

7 Hence the slope is -1/7 TRY...

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**BINARIES-1**

If p*k = 4pk + p – 2k; find 3*2. Solution p*k = (4 x p x k) + p –

(2xk) [rewriting the given expression more clearly] 3*2 = (4 x 3 x 2) + 7 –

(2x2) [substituting 7 for p and 2 for k] 3*2 = 24 + 7 – 4 3*2 = 31 – 4 [we add

first before subtracting] 3*2 ...

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**QUADRATICS-1**

Find

the maximum value of the quadratic equation:5-6t-8t 2 . Solution a=-8,

b=-6, c=5 Maximum

= 4ac-b 2 4a Maximum

= (4 x -8 x 5) - (-6) 2 4(-8) Maximum

= (-160)- 36 32 Maximum= -196...

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**POLYGONS 2**

A regular polygon has 62 sides. Find the total degrees of

that polygon. Solution n = 62 Total degrees = (n - 2)180 0 =

(62 – 2)180 0 =

60 x 180 0 =

10800 0 Total degrees = 10800 0 TRY...

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**LOGARITHMS 1**

Evaluate Log10000 + log 0.001

- log 0.00000001 Solution = Log10000 + log 0.001

- log 0.00000001 = Log10 4 + log 10 -3 – log 10 -8 = 4Log10 + (-3 log 10) –

(

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**MID-POINT 1**

Find the midpoint of a line from (23,

12) to (5, 20) Solution x1=23,

x2=5, y1=12,y2=20. Mid point = ( x1 + x2 , y1 +

y2 ) 2 2 Mid point = (2 3 + 5 , 12

+ 20 )

2 2 Mid point = ( 28 , 32 ) ...

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**PIE CHARTS 1**

In a survey of 60 people, 28 people said

their favourite sport was football. What angle in a pie chart would this represent? Solution We make a fraction of 28 ot of 60, then

multiply by 360 0 . = 28 x 360 0 . 60 = 28 x 360 0 6 60 1 =

28 x 6 =

168 0 . ...

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**POLYGONS 1**

An

interior angle of a regular polygon is 74 0 greater than an exterior

angle. Find the interior angle. Solution Let

i = interior angle, e = exterior angle. Now

i + e=180 0 …………………(1) But

i = e+74 0 …………………(2) Substitute

(2) in (1) above. e+74 0 + e=180 ...

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