Flashcards in Pure Maths Deck (38):
What are the steps for a proof?
1. Specialise to understand eh problem
2. Make a generalisation
3. Calculate and simplify
4. Write a conclusion using wording of phrase
What are the three types of sequence?
Convergent (to a limit)
Oscillating (Period is number of different numbers)
Divergent (to infinity)
What is the equation for the sum of the first n terms of an arithmetic progression?
Sn = n/2(2a + (n-1)d)
-N is term
-A is first term
-D is difference between the terms
What is an example of a position to term rule and a term to term rule?
1. Position to term rule: tn = 6n + 5
2. Term to term rule: tn + 1 = tn + 6
For completing the square, how do you interpret it graphically?
Look at notes
How do you find the gradient of a line?
Y-Y1 / X-X1 = gradient
How do you fined the midpoint of the line?
(x1 + x2 ) / 2 = xm
(y1 + y2) / 2 = ym
How do you find the length of a line?
(deltay)^2 + (deltax)^2 = c^2
What is the trapezium rule?
-Find area under a curve, split into equal length
-((a+b) / 2)h
What is the equation for arc length?
Theta x r
What is the equation for area of a sector?
0.5 x r^2 x theta
How do you convert from radians to degrees?
How do you convert from degrees to radians?
Divide by 180/ pi
What is the equation of a circle?
(x-a) ^ 2 + (y-b)^2 = r^2
-Where (a,b) is the centre
What is the equation for a geometric sequence?
tn = a x r^n-1
-a is the first term
-r is the common ratio
What is the sum of the first n terms of a geometric progression?
Sn = a x (1-r^n) / (1-r)
What is the term to term rule of a geometric progression?
Un + 1 and state U1 =
What are the log addition rule?
logcA + logcB = logcAB
logcA + logcA = logcA^2
What is the log subtraction rule?
logcA - logcB = logc (A/B)
What is 2logcA also seen as?
What is the power rule for logs?
nlogcA = logcA^n
What are the steps for finding the stationary point?
1. Find dy/dx
2. Solve dy/dx = 0
3. Then plug these x values into the original equation to get y values
4. Then find the second derivative and plug in your x values to find out if the point is a maximum or minimum - (<0 it is a maximum) (>0 it is a minimum)
What are the trigometric value we need to know?
sin^2theta + cos^2theta = 1
sin / cos = tan
What is secX ?
secX = 1/cosX
What is cosecX?
cosecX = 1/sinX
What is cotX?
cotX = 1/tanX
What are the two conditions for a function?
1. Completeness Criteria: Every object in the domain has an image in the codomain
2. Uniqueness Criteria: each object in the domain has a unique image
Do you do g or f first in gf(x)?
What do you do in differentiation?
1. Bring the old power down to the front
2. Decrease the power by one
What do you do in integration? What do you always need to remember?
1. Increase power by one
2. Divide by new power
3. + c
What is dy/dx of y=e^x?
What is dy/dx of y=lnx?
What is the rule for chain rule?
nstuff^n-1 x stuff’
- (x^2 + 3x )^4
- 4(x^2 + 3x)^3 x (2x + 3)
What is e^stuff differentiated?
e^stuff x stuff’
What is ln(stuff) differentiated?
stuff’ / stuff
What is the infinite sum?
Sn = a / 1-r
What is the cosine rule?
-a squared = b squared + c squared - 2bcCosA
-CosA = b squared + c squared - a squared / 2bc