maths anki

• What is the Bayes’ Theorem for conditional probability? In other words, P (both occurred) / P (given one occurred) OR the probability of one event occurring given another has already occured.
• How can you check if event A depends on event B? If dependent: As given B has occurred, then the probability of A changes. Otherwise, if independent then: As B occurring doesn’t affect the probability of A occurring,
• What product-based formula holds true if event A and event B are independent? Why? This is because… As they’re independent. Finally, you can rearrange.
• What is the probability of event A OR event B? For mutually exclusive, P(A n B) = 0.
• How can you prove a number is prime by exhaustion? Prove 97 is a prime. 97 / 2 = 48.5, 97 / 3 = 32.333, 97 / 5 = 19.4, 97 / 7 = 13.86. We don’t need to go beyond 7 since 7 < sqrt(97) < 10. If there is a factor above 10, there must be one below 10.
• What is a conjecture? The claim you’re testing.
• What is consequence and equivalence? - Consequence: A ⇒ B means if A is true then B is also true. - Equivalence: A ⇔ B means A implies B and B implies A. - Eg, x = -1 ⇒ x3 = x yet not ⇔ since x3 = x can also have x = 0, 1.
• Prove that sqrt(2) is irrational n and m have a common factor and statement asumes there isn't
• Prove that there are infinitely many primes Assumption: there are a finite number of prime numbers, p1 , p2 , p3 up to pn . Let X = (p1 ×p2 ×p3 ×...×pn)+1 None of the prime no. ( p1 ×p2 ×p3 ×...×pn) can be a factor of X as they all leave a remainder of 1 when X is divided by them. But X must have at least one prime factor. This is a contradiction. So there are infinitely many prime numbers.
• What are the all arithmetic sequences formulae? Where a = first term, l = last term, d = difference.
• Derive the geometric sequence formula
• What is the arc length and area of segment formulae?
• What are the derivatives of sin(kx) and cos(kx)?
• zWhat does it mean when f''(x) < 0, = 0, > 0? And how do you find points of inflection? f’’(x) < 0 ⇒ concave ⇒ maximum point. f’’(x) = 0 ⇒ MAYBE a point of inflection YET point of inflection ⇒ f’’(x) = 0. To make sure you have a point, check for a change in concavity either side of the point (if so, is a point of inflection) and consider points where the f''(x) is undefined. f’’(x) > 0 ⇒ convex ⇒ minimum point.
• What is the z-score? How is it calculated? A measure of how many standard deviations a value is to the right of the mean which is calculated by: This is sometimes referred to as a test statistic in context.
• Where are the points of inflection of a Normal Distribution?
• How can the usage of the Normal Distribution as an approximate for the Binomial Distribution be refined? 1. n is large >50 2. p is close to 0.5 more than 75 you do X>75.5
• How is a sample normally distributed? How do you do the hypothesis ? u used is always for the predicted and then you compare to the acual u.
• How can we prove that a perpendicular line from the centre to a chord bisects the chord? equate phythagoras equations
• What is the proof of the arithmetic series ?
• WHat is the process of working this out ?
• What shape does have ? Exponential shape
• The values are the same but swapped around
• What happens when you differentiate e^x you get e^x
• What is the phrase for log base a to the power of what is equal to b
• How is the natural logarithm found ?
• What is the formula at the end memorise it !! you apply the natural logarithm and it can be written so x is no longer the exponent implict differentiation
• What is the chain rule?
• diff this function
• How do you diff this ?
• WHen do you use the product rule ? What is it ? WHen you have two or more functions of x multiplied by each other
• What is the quotient rule ?
• What does completing the square formula find ?
• What are the 3 situations for the discriminant ?what is it for 2 linear factors ?
• How do you work out the inequality's of a graph
• What is the mnemonic for negative transformations? News in Romania yucks = negative inside reverse y axis = f(-x) = x negative Newton owns red X-rays = negative outside reverse x axis =-f(x) = y negative
• Equ gradient
• What is The main equation to work out he gradient easily ?
• What is perpendicular to m
• What are the product of 2 lines that are perpendicular to each other ? -1