Flashcards
Core 2
Cards in this deck (57)
- 1How to differentiate with negative powers?Bring negative number down as normal and then increase negative value for new power by one
- 2How to differentiate a fraction?Rearrange into negative powers (1/x would be x^-1)
- 3How to differentiate with fractional powers?Bring fraction down and subtract 1 as normal
- 4How to find equation of tangent to curve using differentiation? (2)•Differentiate to find gradient at that point
•Sub point given and gradient into y-y1=m(x-x1) formula - 5How to find equation of normal to curve using differentiation? (3)•Differentiate to find gradient at that point of tangent
•Do the negative reciprocal of it to get gradient of perpendicular tangent
•Sub point given and gradient into y-y1=m(x-x1) formula - 6How to find coordinates of stationary points? (2)•Put dy/dx equal to 0 and solve to find x
•Sub into original equation to find y - 7How to determine whether the stationary point is a max/min? (2)•Sub x value into d2y/dx2 and solve
•If value > 0 it is a minimum point - 8What must you always remember when doing indefinite integration?Always add +c on the end
- 9How to find area under a curve using integration?Take larger integral away from smaller integral
- 10Formula for area of a trapezium?1/2(a+b)h
- 11What is the trapezium rule?The more trapeziums you use, the more accurate an estimate for an area under the curve will be to the integration value
- 12How to find an approximation using the trapezium rule? (3)•Find n and h (b-a all divided by n)
•Draw table of values for x0 and y0 onwards
•Substitute into trapezium rule formula - 13How to make a better approximation using the trapezium rule?Use more trapezia
- 14What is the basic trig rule?SOHCAHTOA
- 15In basic trig, when is regular sin, cos or tan used?To find lengths
- 16In basic trig, when is inverse sin, cos or tan used?To find angles
- 17How to solve the trig equation sinx = sink (where k is known) for 2+ solutions? (3)•First solution = k
•2nd solution = 180 - k
•More solutions = add/subtract 360 to first 2 solutions - 18How to solve the trig equation cosx = cosk (where k is known) for 2+ solutions? (3)•First solution = k
•2nd solution = 360 - k
•More solutions = add/subtract 360 to first 2 solutions - 19How to solve the trig equation tanx = tank (where k is known) for 2+ solutions? (2)•First solution = k
•More solutions = add/subtract 180 to first solution - 20What is the sine rule?
- 21What is the cosine rule?
- 22What is the formula for the area of a triangle?1/2 x a x b x sinC
- 23What happens when y = f(x) is translated by the vector [a,b]?Becomes y = f(x-a) +b
- 24What happens when y = f(x) is reflected in the x axis?Becomes y = -f(x)
All of the function changes sign - 25What happens when y = f(x) is reflected in the y axis?Becomes y = f(-x)
Only x part of function is affected - 26What happens when y = f(x) is stretched in the y direction by scale factor k?Becomes y = kf(x)
Y coordinate of any point on curve is multiplied by scale factor - 27What happens when y = f(x) is stretched in the x direction by scale factor k?Becomes y = f(x/k)
X coordinate of any point on curve is multiplied by scale factor - 28What has y = f(kx) been stretched by?Scale factor 1/k in x direction
- 29How to solve a quadratic trig equation? (e.g: 2cos^2x - cosx - 1 = 0)Let c = cosx, then make it into an easier quadratic. Find solution and do inverse function on them to obtain solutions, then calculate answers within inequality range
- 30What to do if you can't factorise a quadratic trig equation?Use the quadratic formula (minus b plus or minus the square root of b squared minus 4ac all over 2a)
- 312 trigonometric identities?
- 32What is (cosx)^2 the same as and what does this apply to?Cos^2x
Applied for (tanx)^2 and (sinx)^2 too. - 33Formula for binomial expansions?
- 34Formula to find the coefficient in a binomial expansion?Use the formula for the value k instead of 1 where you are finding the coefficient of x^k
- 35What are recursive/inductive formulae?Must know previous term to find out the next one
- 36In sequences, what does the n in Un stand for?Number (term)
1 2 3....
U1 U2 U3..... - 37Something to bear in mind when finding terms in recursive/inductive formulae?N must be the same number throughout the equation
- 38How to find the limit of a sequence?Replace any section of the formula containing Un with L and solve it. Can check on calc by continuously pressing = with equation typed in and it will reach a constant (limiting value)
- 39What is the nth term of an arithmetic sequence with first term a and common difference d?
- 40How to find the first term (a) and common difference (d)?Set up simultaneous equations
- 41What is the formula for the first n terms of an arithmetic sequence?
- 42What is the formula for the first n terms in an arithmetic sequence if we know the last term?
- 43How to interpret sigma notation in series?
- 44What happens in a geometric series?Each term is multiplied by common ratio r
- 45How to find the nth term in a geometric series?
- 46How to find the sum of the first n terms in a geometric series?
- 47What is the sum to infinity of a geometric series?Provided -1 < r < 1
- 48What is 180 degrees in radians?π
- 49What is 360 degrees in radians?2π
- 50What to remember when solving trigonometric equations in terms of π?Convert calculator to radians mode
- 51Formula to find arc length of a sector in radians?
- 52Formula to find sector area in radians?
- 53How to find area of a minor segment when it is inside a circle?Area of sector - area of triangle
- 54How to solve trigonometric equations using radians?Put calc in radian mode and continue as normal
- 55What is this written as using logarithms?
- 563 laws of logarithms?
- 574 important logarithm facts?
Information
- Description
- AS level AS Maths (Pure Core) Flashcards on Core 2, created by Tania Parvaiz on 04/04/2017.
- Created by
- Tania Parvaiz
- Views
- 1
- Rating