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ndamugoba ivan
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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) –
(8log 10) = (4x1) + (-3x1) - (-8x1) =4 + (-3) – (-8) = 4 – 3 + 8 =9 Hence Log10000 +  log 0.001...

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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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