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43 Cards in this Set
- Front
- Back
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alpha + beta
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-b/a
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alpha x beta
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c/a
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a^2 + b^2
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(a+b)^2 - 2ab
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a^3 + b^3
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(a+b)^3 - 3ab(a+b)
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Quadratic equation?
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x^2 - (sum)x + product = o
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i^2
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-1
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i^3
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-i
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i^4
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1
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Complex number has what form?
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a+bi
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Conjugate of (a+bi)?
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a-bi
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Conjugate of z is denoted by?
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z*
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If a quadratic with real coefficients has a complex root, what must the other be?
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The complex conjugate
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What must you do if multiplying an inequality?
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Only multiply by something that is definately positive, if it's negative you must reverse the sign
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What can't you do with matrices of a different order?
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Multiply
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What is [1 0] called?
[0 1] |
The identity matrix
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What is Z
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The zero matrix
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sin30 and cos60 =
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1/2
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cos30 and sin60 =
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root3/2
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sin45 and cos45 =
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1/root2
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tan30 =
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1/root3
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tan45 =
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1
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tan60
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root3
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To find a general solution you?
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Find solutions between -180 and 180, and add the period
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Stretch in x?
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[k 0]
[0 1] |
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Stretch in y?
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[1 0]
[0 k] |
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Enlargement?
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[k 0]
[0 k] |
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Rotation though angle x, about the origin?
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[cosx -sinx]
[sinx cosx] |
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Reflection in the line y=(tanO)x
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[cos2x sin2x]
[sin2x -cos2x] |
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What is represented by BA
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Transformation A followed by B
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When finding a composite transformation you?
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Divide all by h, and find h using pythag.
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How do you find the gradient of a curve?
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Find f(x+h)-f(x)
h Divide by h, and find what happens as h tends to zero. |
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Sigma 1 =
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n
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A change of sign indicates what?
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root lying between, provided it is continuous
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Linear interpolation?
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af(b) - bf(a)
f(b) - f(a) |
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Horizontal asymptote
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Find what happens to y as x tends to infinity
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Vertical asymptote
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Solve the bottom of the equation for 0
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Find a set of values for which a y-coordinate exists
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Set the function equal to k, obtain a quadratic equal to zero and find the values for which the discriminant = 0
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How do you find a stationary point?
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Find the values of y for which the curve exists, these are the stationary points, put into original equation for find x
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How do you find the equation of a function reflected in the line y=x
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Swap y and x
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Hyperbolas have which form?
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x^2 - y^2 = k
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How do you translate a curve [k]
[0] |
x-k
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Translate [0]
[k] |
y-k
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To find if a function intersects a line
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Form quadratic, set = 0, b^2-4ac
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