Recaps Flashcards
(40 cards)
percentage change
change/original x 100
product rule for total number of options
the number of options for a combination of choices equals the number of options for each choice multiplied together
e.g.
4 digit numbers that can be made with 1, 4, 5 and 7 with no repetition of each digit?
1st digit: 4
2nd: 3
3rd: 2
4th: 1
4 x 3 x 2 x 1 = 24
product rule when the number has to be above/below a certain amount or even/odd
there are less choices for the last digit as it can only be an even/odd number
there are less choices for the first digit as it can’t be too high or too low
ten power rules
- add when multiplying
- subtract when dividing
- multiply when raising one to another (e.g. outside brackets)
- anything to the power of one doesn’t change
- anything to the power of 0 is just 1
- 1 to any power is just 1
- apply the power to the top and bottom of fractions (e.g. when outside brackets)
- turn negative powers upside down and make the power positive
- fractional powers mean the root of the number on the bottom
- split two stage fractions into two different ones and apply them one at a time (e.g. 5/6 into 1/6 x 5)
What changes the direction of an inequality’s sign?
multiplying or dividing by a negative number
why shouldn’t you divide by unknown variables in an equation?
they could be negative, or 0
three rules for algebraic proof
even number: 2n
odd number: 2n + 1
consecutive numbers: n + 1
(e.g. even consecutive numbers - 2n + 2, 2n + 4 etc.)
formula for finding the nth term of non-quadratic sequences
nth term = dn + (a - d)
a is the first term
d is the common difference
finding the nth term of a quadratic sequence
1) find the second difference between each pair of terms
2) halve it to become the coefficient of the n[2] term
3) subtract the n[2] term from each term in the sequence to give you a linear sequence
4) find the formula for the linear sequence and add it to the n[2] term
gradients of parallel and perpendicular lines
parallel - same gradient
perpendicular - negative reciprocal gradient
equation of a circle
centred on (0,0): x[2] + y[2] = r[2]
centred on (a,b): (x - a)[2] + (y - b)[2] = r[2]
6 angle rules
- angles in a triangle add up to 180
- angles on a straight line add up to 180
- angles in a quadrilateral add up to 360
- angles round a point add up to 360
- exterior angle of a triangle = sum of opposite interior angles (the interior angles not on the same line as the exterior angle)
- isoceles triangles have two sides the same length and two angles the same
sum of interior angles
180 x (n - 2)
where n is the number of sides
sum of exterior angles
360
steps for completing the square
1) rearrange the quadratic into the standard format
2) take any factors of x outside the bracket (ignore the integer for now)
3) write out the whole bracket as being squared (divide b, the number before the second x, by two; and also divide all the values by x)
4) multiply out the brackets and compare to the original
5) add or subtract the missing number to make it equal to the original
solving an equation by completing the square
1) complete the square first and set it equal to 0
2) rearrange the number to be on the other side
2) square root both sides - REMEMBER THE + AND -
3) rearrange to get x on its own
lines that get closer together but never touch
asymptotes
shape of cubic graphs
down, up, then down (or the other way around)
like an s shape
shape of reciprocal graphs
graphs get closer to a certain line but never touch
coefficient
an unknown number of something
e.g. in a line the coefficient of x is just the gradient
What value are cos x, sin x and tan x at 0 degrees on a graph?
cos x is 1
sin x is at 0
(graph goes from -1 to 1)
tan x is at 0
What are the periods of cos x, sin x and tan x?
cos x and sin x: 360
tan x: 180
4 angle properties for parallel lines
F angles: corresponding angles are equal
Z angles: alternate angles are equal
vertically opposite angles are equal
co-interior angles add up to 180
area of a sector
x/360 x πr[2]
x/360 x area of full circle
