Module+5+Number+II

MODULE 5 NUMBER II Scheme of Work || Scheme of Work || || Core Assignment Module 5 || __ Indices __ 3³ = 3×3×3 2¹ = 2 etc. The ² and ³ are known as indices. Indices are useful (for example they allow us to represent numbers in standard form) and have a number of properties. http://www.youtube.com/watch?v=EU6JVRCfVQk __ Standard Form __
 * EXTENDED || CORE ||  ||
 * Can Do Statements
 * Extended Assignment Module 5
 * A ||
 * || **Indices/ Powers**
 * To //__multiply__// numbers with different powers (for example, 4² x 4³) simply //__add the powers together__// - the answer in this case is 45.
 * //__Any number to the power of 0 = 1.__//
 * A negative power, for example, 2-3 is the same as ½³.
 * When //__dividing__// same numbers with powers, __s__//__ubtract the powers__//, e.g. 25 ÷ 2² = 2³. ||  ||   ||
 * B ||
 * B ||
 * Standard form is a way to show really large or really small numbers without writng them all out.

n×10^y Let's take 4, 850, 000 000 for an example. To find n, we would only write the signifigant figures; 4, 8 and 5. We would wright it as 4.85. Only the first signifigant figure is a whole number; the others are shown as decimals. Y is the numer of places the decimal had to move in the first number to make n. In this place, it has moved 9 places. So y=9.The whole thing looks like this: mathematicians and scientists all over the world. It goes to the form of: It is used 4.85×10^9

Writing small numbers is farly similar. Lets take. 0. 000, 000, 000 56 for an example. Here, n would be 5.6, since they're the only signifigant figures. The decimal place moves 10 places. But y does not equal 10. This is because the decimal moved in the opposite dierction- it is negative. Overall, this number in standard form is: 5.6×10^-10

For small numbers, y is always negative. || __ Speed, Distance, Time Calculations and Graphs __ Tip: Velocity and speed are the same- velocity only has a direction. __Speed/Time Graphs__ In these graphs, speed is always on the y axis, time on the x. To find acceleration using this graph, you need to work out the gradient of the line (rise over run). Remember, a flat line means that the speed reamins the same, or constant.. To work out the distance travelled, you need to work out the area underneath the graph. This can ussually be done by splitting it up into rectangles and triangles. __Distance/Time Graphs__ Distance/Time graphs are useful, but make sure you dont ger them confused with Speed/Time. Here, the gradient=speed. (remember, Don't Stop There). The larger the gradient, the faster the speed. Here, a horizontal line means that the object is not moving. A curved line means that the object is accelerating.
 * [] ||
 * Speed, time, velocity and distance graphs are very common. They are also very easy once you understand how to use them.

|| __ Surds __ A surd is a square root which cannot be reduced to a whole number. For example, is not a surd, as the answer is a whole number. But is not a whole number. You could use a calculator to find that but instead of this we often leave our answers in the square root form, as a surd. You need to be able to simplify expressions involving surds. Here are some general rules that you will need to learn. http://www.bbc.co.uk/schools/gcsebitesize/maths/number/surdsrev2.shtml Surds are good sources of irrational numbers; only the surds of square numbers are rational. ||
 * D ||
 * =Basic rules=