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Karteikarten von natashaaaa, aktualisiert more than 1 year ago
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| Frage | Antworten |
| √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? | |
| 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? | |
| 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? | Angles in a semi circle: angle on the arch is always a right angle (perpendicular lines) |
| What circle theorem is this? | Any chord, perpendicular line is drawn through center of circle, will bisect the chord |
| What circle theorem is this? | From any point outside the circle, there is exactly two tangents. The radius to the tangent is perpendicular. |
| What is this line? | Tangent (Has one repeated root) |
| What is this line? | 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? | |
| What is the cosine rule? | |
| 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? | |
| What does a cos graph look like? | |
| What does a sin graph look like? | |
| What does a CAST diagram look like? (DEGREES) | |
| What are the trig identities? | |
| What are the log rules? | |
| How do you find the area of a trapezium? | A = 0.5(a+b)h |
| What is the trapezium rule? |
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