8619052
Description
Flashcards by Saavik Hipkins, updated more than 1 year ago
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Created by Saavik Hipkins
over 7 years ago
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| Question | Answer |
| Algebra and functions | Algebraic division by (x ± a) Remainder theorem: When f(x) is divided by (x – a), f(x) = (x – a) Q(x) + R where Q(x) is the quotient and R is the remainder Factor theorem: If f(a) = 0 then (x – a) is a factor of f(x) |
| Coordinate geometry | Circle, centre (0, 0) radius: x^2+ y^2= r^2 Circle centre (a, b) radius r: (x – a)^2 + (y – b)^2 = r^2 Useful circle facts: The angle between the tangent and the radius is 90° Tangents drawn from a common point to a circle are equal in length The centre of a circle is on the perpendicular bisector of any chord The angle subtended by a diameter at the circumference is 90° |
| Sequences and Series |
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| trigonometry |
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| trigonometry 2 |
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| trigonometry 3 |
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| Exponentials and Logarithms | If y = a^x then loga(y) = x Laws of logarithms: loga(pq) = loga(p) + loga(q) Other useful results: logax =logbx/logba log , loga1 = 0, loga(a) = 1 |
| Differentiation | If dy/dx = 0 d2x/dy2 > 0 it is a minimum If dy/dx = 0 d2x/dy2 < 0 it is a maximum For an increasing function, dy/dx > 0 d > 0, for a decreasing function, dy/dx < 0 Maxima and minima problems: (a) Find the point at which f´(x) = 0. (b) Find the nature of the turning point to confirm that the value is a maximum or minimum as required. (c) Make sure that all parts of the question have been answered (e.g. finding the maximum/minimum as well as the value of x at which it occurs). |
| Integration |
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