All AS Maths Equations/Calculations and Questions

Flashcards by , created about 4 years ago

All of the equations needed for formulae in the AS maths exams and questions on some of the theorems.

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Created by natashaaaa about 4 years ago
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Question Answer
√a x √b =√ab
√a/b =√a/√b
√ab/√b =√a
ax^2+bx+c=f(x) what happens when you: increase b? decrease b? increase a? decrease a? increase b = translates up the y axis decrease b = translates down the y axis increase a = translates left decrease a = translates right
ax^2+bx+c=f(x) what shape is the graph is the quadratic is: positive? negative? positive: the graph will make a 'u' shape negative: the graph will make an 'n' shape
If you use (x1+x2)/2 to find the x value of the root, how do you find the y value? Substitute the x value into the 'y=' equation of the quadratic
To complete the square, what does ax^2+bx+c turn into? (x-d)^2-e
Where does (x+2)^2+2 translate to on a graph? (x+2) = translates left (along x axis) by 2 +2 = translates up the y axis by 2
What is the quadratic formula? 86aa4bfc-477e-4e90-b30e-e09123bf9077.jpg (image/jpg)
What part of the quadratic equation is the discriminant and what does the discriminant mean in terms of roots? b^2-4ac b^2-4ac<0 = no relevant roots b^2-4ac=0 = two repeated roots b^2-4ac>0 = two distinct roots
What are the three ways of solving a quadratic? 1. factorising (always try first) 2. quadratic equation (if doesn't factorise or 'b' isn't even) 3. complete the square (only use if 'b' is even)
What is the factor theorem? f(7)=0 ∴ (x-7) is a factor of f(x) f(a)=0 ∴ (x-a) is a factor of f(x)
What is the equation of a circle? (x-a)^2+(x-b)^2=r^2
How do you work out the distance between two points? Pythagoras' theorem
What equation do you use to find the midpoint of a line? e57a2191-ae16-48f0-adc9-81ad21e625ae.png (image/png)
What do you use to find the equation of a line? y - y1 = m (x - x1)
What is the difference between a perpendicular and parallel line? Perpendicular: have gradients that are opposite signed (+/-) and reciprocals Parallel: have the same gradients but different y intercepts
What circle theorem is this? bf0940b1-5604-4714-88fe-390ef2d98d35.gif (image/gif) Angles in a semi circle: angle on the arch is always a right angle (perpendicular lines)
What circle theorem is this? d2105c2d-91a2-4d7d-b1f0-afce631872c8.gif (image/gif) Any chord, perpendicular line is drawn through center of circle, will bisect the chord
What circle theorem is this? 930a6909-5bb0-4744-bba4-36e7cb5b31b1.png (image/png) From any point outside the circle, there is exactly two tangents. The radius to the tangent is perpendicular.
What is this line? c78693eb-e2b1-4989-afb9-aa62bbb6d63c.gif (image/gif) Tangent (Has one repeated root)
What is this line? 4cccf716-d6f4-4607-b4a0-14872fdefabb.png (image/png) Secant (two distinct roots)
What is a scew line? A line that has no real roots/intersections with a circle
What does dy/dx equal? The gradient
What is: f(x) f'(x) f''(x) f(x) = before differentiation f'(x) = first derivative f''(x) = second derivative
What is d^2y/dx^2 > 0 Minimum
What is d^2y/dx^2 < 0 maximum
If f(x) represents displacement, what does f'(x) and f''(x) represent? f'(x) represents velocity f''(x) represents acceleration
What is an 'increasing function'? An increasing function is a function f(x) such that f'(x) > 0 for all values of x> (a function that is always increasing)
What is a 'decreasing function'? A decreasing function is a function f(x) such that f'(x) < 0 for all values of x (A function that is always decreasing)
Describe the graph transformations taking place from: f(x) = x^2 =2x^2 =2(x)^2 x^2 = original formulae 2x^2 = stretched in y direction by scale factor of 2 2(x)^2 = stretched in x axis by scale factor of 0.5
What is the difference in transformations if the number is inside or outside the bracket? inside the bracket : x direction outside the bracket : y direction
What does xn = a + d(n-1) calculate? Any number in a sequence (arithmetic)
What is a Sigma? The big E symbol. It means 'sum up'
What does this mean? S = (n/2) × (2a + (n-1)d) It calculates the sum of the first 'n' terms of an arithmetic series
What does xn = ar(n-1) calculate? Any term in a geometric progression
What is the sine rule? 8fd535eb-d64b-4b9c-9ca8-2af4b992845d.png (image/png)
What is the cosine rule? 4984d5d7-11b0-4a50-b802-c1a309d48b52.jpg (image/jpg)
How do you find the area of a triangle? 0.5(base x height) OR 0.5absinC
How do you work out the area of a sector? DEGREES: (θ/360) x πr^2 RADIANS: θr^2/2
How do you work arc length? DEGREES: (θ/360) x 2πr RADIANS: rθ
What does a tan graph look like? f55228a7-edb2-4468-a277-594881549de8.gif (image/gif)
What does a cos graph look like? 8b18fe38-df2f-45c0-9d85-19c83b6bbf9b.png (image/png)
What does a sin graph look like? 626b0d26-ad20-453d-9ed5-216582c177dc.png (image/png)
What does a CAST diagram look like? (DEGREES) a1b4002c-4311-4440-8ba8-a468fcd8da86.jpg (image/jpg)
What are the trig identities? 63ebc996-6a65-4d4e-8b55-04ef513caaf4.jpg (image/jpg)
What are the log rules? 0084e4c6-7a0f-40db-9a8b-6eface639e02.png (image/png)
How do you find the area of a trapezium? A = 0.5(a+b)h
What is the trapezium rule? 5c32e51a-9b0d-4855-8dc3-e44cc56fef1a.jpg (image/jpg)