Yr 10 Number Flashcards
(9 cards)
What are surds? How do you simplify and multiply them?
Surds are numbers that cannot be expressed rationally, e.g.√2. To multiply surds, times the two numbers within, e.g. √a x √b = √ab. To simplify them, find two different surds, one of which is a square root, which times to make that surd. Then square root that number and write it like this, a√b.
How do you divide surds?
Just write the first number over the second, but all in a root. Then, simplify to just a single number in a root. When multiplying or diving numbers with a surd and a rational, just do the two parts separately, rational multiple/divide, then sure multiply/divide.
How would you simplify multiple surds?
Find a surd that goes into them all. The other number to make the surd should be a rational surd, e.g √4. Then simplify each big surd into these two surds. Turn all the rational surds into numbers, then work out the rest of the equation easily. E.g. √32 + √128-√8 = √16 √2+√64√2-√4√2 = 4√2+ 8√2- 2√2 = 10√2.
How do you rationalise surds?
What you do is times the whole fraction by the denominator. If there is a plus or minus, reverse this sign. You can then simplify the fraction. Try to divide the top and bottom, i.e. 8(3+√5) / 4 can go to 2(3+√5), as you divide top and bottom by 4.
How do you work out the length of a line in coordinate geometry?
Name the points x, y, x2 and y2. Then do √(x2-x)2 + (y2-y)2
How do you work out the mid point of a line using co ordinate geometry?
((X+x2 / 2), (y+y2 / 2))
How do you work out the gradient of a line using coordinate geometry?
The gradient is y2-y / x2-x
What is the equation of a straight line?
Y=mx+c. M is the gradient, and you can substitute one of the points for the x and y values, to find c.
What is the rule about perpendicular and gradient?
Two lines that are perpendicular have a gradient that multiply to -1
