Flashcards
All AS Maths Equations/Calculations and Questions
Cards in this deck (49)
- 1√a x √b=√ab
- 2√a/b=√a/√b
- 3√ab/√b=√a
- 4ax^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 - 5ax^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 - 6If 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
- 7To complete the square, what does ax^2+bx+c turn into?(x-d)^2-e
- 8Where 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 - 9What is the quadratic formula?
- 10What 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 - 11What 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) - 12What 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) - 13What is the equation of a circle?(x-a)^2+(x-b)^2=r^2
- 14How do you work out the distance between two points?Pythagoras' theorem
- 15What equation do you use to find the midpoint of a line?
- 16What do you use to find the equation of a line?y - y1 = m (x - x1)
- 17What 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 - 18What circle theorem is this?Angles in a semi circle: angle on the arch is always a right angle (perpendicular lines)
- 19What circle theorem is this?Any chord, perpendicular line is drawn through center of circle, will bisect the chord
- 20What circle theorem is this?From any point outside the circle, there is exactly two tangents. The radius to the tangent is perpendicular.
- 21What is this line?Tangent (Has one repeated root)
- 22What is this line?Secant (two distinct roots)
- 23What is a scew line?A line that has no real roots/intersections with a circle
- 24What does dy/dx equal?The gradient
- 25What is: f(x) f'(x) f''(x)f(x) = before differentiation
f'(x) = first derivative
f''(x) = second derivative - 26What is d^2y/dx^2 > 0Minimum
- 27What is d^2y/dx^2 < 0maximum
- 28If f(x) represents displacement, what does f'(x) and f''(x) represent?f'(x) represents velocity
f''(x) represents acceleration - 29What 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) - 30What 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) - 31Describe the graph transformations taking place from: f(x) = x^2 =2x^2 =2(x)^2x^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 - 32What is the difference in transformations if the number is inside or outside the bracket?inside the bracket : x direction
outside the bracket : y direction - 33What does xn = a + d(n-1) calculate?Any number in a sequence (arithmetic)
- 34What is a Sigma?The big E symbol. It means 'sum up'
- 35What does this mean? S = (n/2) × (2a + (n-1)d)It calculates the sum of the first 'n' terms of an arithmetic series
- 36What does xn = ar(n-1) calculate?Any term in a geometric progression
- 37What is the sine rule?
- 38What is the cosine rule?
- 39How do you find the area of a triangle?0.5(base x height)
OR
0.5absinC - 40How do you work out the area of a sector?DEGREES: (θ/360) x πr^2
RADIANS: θr^2/2 - 41How do you work arc length?DEGREES: (θ/360) x 2πr
RADIANS: rθ - 42What does a tan graph look like?
- 43What does a cos graph look like?
- 44What does a sin graph look like?
- 45What does a CAST diagram look like? (DEGREES)
- 46What are the trig identities?
- 47What are the log rules?
- 48How do you find the area of a trapezium?A = 0.5(a+b)h
- 49What is the trapezium rule?
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- All of the equations needed for formulae in the AS maths exams and questions on some of the theorems.
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- natashaaaa
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