1. Brief insight

2.  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

3. a 2 x a 3 = a 2 + 3 a 6 a 4 ÷ a 2 = a 4 - 2 a 2

4. (a 2 ) 3 = a 6

5. 3a 2 b 3 x 2a 4 b Separate the terms 3 x 2 = 6 a 2 x a 4 = a 6 b 3 x b = b 4 Answer = 6a 6 b 4

6. Show that 4 3/2 = 8 4 3/2 means the square root of 4 cubed The square root of 4 = 2, 2 3 = 8

7. N = a x log a N = x 4 = 2 2 log 2 4 = 2 8 = 2 3 Log 2 8 = 3

8. (2x + 5)(3x + 2) = 6x 2 + 4x + 15x +10 = 6x 2 +19x+10

9. 6x + 3y = 9 2x + 3y = 1 4x = 8 X = 2 Y = -1

11.  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

12. y = x 2 + 4x Calculate dy/dx when x = 3 dy/dx = 2x + 4 = 10 y = 6x 3 + 2x 2 +3 Calculate dy/dx when x = 2  dy/dx = 18x + 4x = 44

13. 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

14. Let's use for our first example, the equation 2X 2 -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

15. Y = -4X 2 + 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

16. 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 i 2 = −1

17. When a Real number is squared the result is always non- negative. Imaginary numbers of the form bi are numbers that when squared result in a negative number.