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Brief insight

3.1 Understand mathematical equations
appropriate to the solving of general
engineering problems

3.2 Understand trigonometric functions and
equations

3.3 Understand differentiation and
integration

3.4 Understand complex numbers
a2 x a3
= a2 + 3
a6
a4 ÷ a2
= a4 - 2
a2
(a2)3 = a6
3a2b3 x 2a4b
Separate the terms
3x2=6
a2 x a4 = a6
b3 x b = b4
Answer
=
6a6b4
Show that
3/2
4
=8
43/2 means the square root of 4 cubed
The square root of
4 = 2,
23 = 8
N = ax
logaN = x
4 = 22
log24 = 2
8 = 23
Log28 = 3
(2x + 5)(3x + 2) = 6x2 + 4x
+ 15x +10 =
6x2 +19x+10
6x + 3y = 9
2x + 3y = 1
4x = 8
X=2
Y = -1



sec x =
1
cos x
cosec x = 1
sin x
cot x =
1
= cos x
tan x
sin x
sin x = tan x
cos x
y = x2 + 4x
Calculate dy/dx when x = 3
dy/dx = 2x + 4 = 10
y = 6x3 + 2x2 +3 Calculate dy/dx when x = 2

dy/dx = 18x + 4x = 44
The gradient represents the
change in distance with respect to
time dy/dx
Speed is the differential of
distance
Acceleration is the differential of
speed
Let's use for our first example, the equation 2X2 -5X -7 = 0
The derivative dy/dx = 4x -5 = 0
4x = 5
x = 5÷4 = 1.25
Y = 2*(1.25)2 -5*1.25 -7
Y = -10.125
At minimum value
Y = -4X2 + 4X + 13 = 0
dY/dX =
-8X + 4
X = 4 ÷ -8 = -0.5
Y = -4*(.5*.5)2 +4*.5 + 13
Y = 14
At Maximum value
A complex number is a number
that can be expressed in the
form a + bi, where a and b are
real numbers and i is the
imaginary unit, where i2 = −1
When a Real number is squared
the result is always nonnegative. Imaginary numbers of
the form bi are numbers that
when squared result in a
negative number.