Powers

Time table I want to practise

Eve 5.00 - 7.00 vocab
       7.00 - 8.00 coding
       8.00 - 9.00 dinner etc
       9.00 -12.00cs subject
       12.00-2.00 phone
       2.00-5.00 sleep
       5.00- 7

Quadratic Equation

Quadratic equations looks like: ax² + bx + c = 0
where a,b,c are real numbers, and a ≠ 0. Every quadratic equation can have 0, 1 or 2 real decidions derived by the formula:

The number D = b² - 4ac is called discriminant.
If D < 0 then the quadratic equation have no decidions. If D = 0 then the quadratic equation have 1 decidion x = - ^b/_2a. If D > 0 then the quadratic equation have 2 decidions.
Example:
If we have equation: x² + 3x - 4 = 0
a = 1, b = 3, c = -4

Parabola

The graph of a quadratic equatin is called a parabola.
If a > 0 then graph horns pointing down:

if a < 0 then graph horns pointing up:

The midpoint of any parabola is the point x = -b/2a.

Sign of Quadratic Equation
Let f(x) = ax^2 + bx + c , where a,b,c &# 949; R and a ≠ 0

Vieta's formulas

If x₁ and x₂ are the roots of the quadratic equation ax² + bx + c = 0 then:

These formulas are called Vieta's formulas.
We can find the roots x₁ and x₂ of a quadratic equation by solving the system above.

Maxima and minima
Maxima a>0  x= - b/2a  Max = -(b^2 -4ac)/4a
Minima a<0  -----------------------------------------(same)

Multiplication Tables

1 × 1 = 1	2 × 1 = 2 2 × 2 = 4	3 × 1 = 3 3 × 2 = 6 3 × 3 = 9	4 × 1 = 4 4 × 2 = 8 4 × 3 = 12 4 × 4 = 16	5 × 1 = 5 5 × 2 = 10 5 × 3 = 15 5 × 4 = 20 5 × 5 = 25
6 × 1 = 6 6 × 2 = 12 6 × 3 = 18 6 × 4 = 24 6 × 5 = 30 6 × 6 = 36	7 × 1 = 7 7 × 2 = 14 7 × 3 = 21 7 × 4 = 28 7 × 5 = 35 7 × 6 = 42 7 × 7 = 49	8 × 1 = 8 8 × 2 = 16 8 × 3 = 24 8 × 4 = 32 8 × 5 = 40 8 × 6 = 48 8 × 7 = 56 8 × 8 = 64	9 × 1 = 9 9 × 2 = 18 9 × 3 = 27 9 × 4 = 36 9 × 5 = 45 9 × 6 = 54 9 × 7 = 63 9 × 8 = 72 9 × 9 = 81	10 × 1 = 10 10 × 2 = 20 10 × 3 = 30 10 × 4 = 40 10 × 5 = 50 10 × 6 = 60 10 × 7 = 70 10 × 8 = 80 10 × 9 = 90 10 × 10 = 100
11 × 1 = 11 11 × 2 = 22 11 × 3 = 33 11 × 4 = 44 11 × 5 = 55 11 × 6 = 66 11 × 7 = 77 11 × 8 = 88 11 × 9 = 99 11 × 10 = 110 11 × 11 = 121	12 × 1 = 12 12 × 2 = 24 12 × 3 = 36 12 × 4 = 48 12 × 5 = 60 12 × 6 = 72 12 × 7 = 84 12 × 8 = 96 12 × 9 = 108 12 × 10 = 120 12 × 11 = 132 12 × 12 = 144	13 × 1 = 13 13 × 2 = 26 13 × 3 = 39 13 × 4 = 52 13 × 5 = 65 13 × 6 = 78 13 × 7 = 91 13 × 8 = 104 13 × 9 = 117 13 × 10 = 130 13 × 11 = 143 13 × 12 = 156 13 × 13 = 169	14 × 1 = 14 14 × 2 = 28 14 × 3 = 42 14 × 4 = 56 14 × 5 = 70 14 × 6 = 84 14 × 7 = 98 14 × 8 = 112 14 × 9 = 126 14 × 10 = 140 14 × 11 = 154 14 × 12 = 168 14 × 13 = 182 14 × 14 = 196	15 × 1 = 15 15 × 2 = 30 15 × 3 = 45 15 × 4 = 60 15 × 5 = 75 15 × 6 = 90 15 × 7 = 105 15 × 8 = 120 15 × 9 = 135 15 × 10 = 150 15 × 11 = 165 15 × 12 = 180 15 × 13 = 195 15 × 14 = 210 15 × 15 = 225
16 × 1 = 16 16 × 2 = 32 16 × 3 = 48 16 × 4 = 64 16 × 5 = 80 16 × 6 = 96 16 × 7 = 112 16 × 8 = 128 16 × 9 = 144 16 × 10 = 160 16 × 11 = 176 16 × 12 = 192 16 × 13 = 208 16 × 14 = 224 16 × 15 = 240 16 × 16 = 256	17 × 1 = 17 17 × 2 = 34 17 × 3 = 51 17 × 4 = 68 17 × 5 = 85 17 × 6 = 102 17 × 7 = 119 17 × 8 = 136 17 × 9 = 153 17 × 10 = 170 17 × 11 = 187 17 × 12 = 204 17 × 13 = 221 17 × 14 = 238 17 × 15 = 255 17 × 16 = 272 17 × 17 = 289	18 × 1 = 18 18 × 2 = 36 18 × 3 = 54 18 × 4 = 72 18 × 5 = 90 18 × 6 = 108 18 × 7 = 126 18 × 8 = 144 18 × 9 = 162 18 × 10 = 180 18 × 11 = 198 18 × 12 = 216 18 × 13 = 234 18 × 14 = 252 18 × 15 = 270 18 × 16 = 288 18 × 17 = 306 18 × 18 = 324	19 × 1 = 19 19 × 2 = 38 19 × 3 = 57 19 × 4 = 76 19 × 5 = 95 19 × 6 = 114 19 × 7 = 133 19 × 8 = 152 19 × 9 = 171 19 × 10 = 190 19 × 11 = 209 19 × 12 = 228 19 × 13 = 247 19 × 14 = 266 19 × 15 = 285 19 × 16 = 304 19 × 17 = 323 19 × 18 = 342 19 × 19 = 361	20 × 1 = 20 20 × 2 = 40 20 × 3 = 60 20 × 4 = 80 20 × 5 = 100 20 × 6 = 120 20 × 7 = 140 20 × 8 = 160 20 × 9 = 180 20 × 10 = 200 20 × 11 = 220 20 × 12 = 240 20 × 13 = 260 20 × 14 = 280 20 × 15 = 300 20 × 16 = 320 20 × 17 = 340 20 × 18 = 360 20 × 19 = 380 20 × 20 = 400