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26 Cards in this Set
- Front
- Back
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General form of equation of a line |
Ax + By +C = 0 |
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Standard equation of line |
Y = MX + b |
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Point slope form |
(Y - y1) = m ( x - x1) |
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Equation for slope |
M = (y2 - y1) / (x2 - x1) |
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Equation for slope of 2 perpendicular lines |
M1 = - 1 / m2 |
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Angle between two lines with slope. Where do I find eq? |
Alpha = arctan[(m2-m1)/(1+m1*m2)] In NCEES, first page of mathematics section |
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Quadratic equation |
Ax^2 + bx + C = 0 or x =(-b +- √(b^2-4ac))/2A also in NCEES handbook first page Mathematica |
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b^2 - 4ac conditions |
> 0 real and unequal, = 0 real and equal, < 0 real and complex |
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Conic section equations cover what types of functions? |
Parabolas, hyperboles, ellipses, circles |
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What is general form of conics section eqs? How is general form eq simplified when when one of the principal axes of conic section is parallel to coordinate axis? What page are equations and ways to identify conic equations in NCEES handbook? |
Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 x^2 + y^2 + 2ax + 2by + c = 0 h = -a, k=-b, r =√(a^2+b^2-c) Mathematics section page 25 & 26. |
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Conditions of B^2 - 4ac for conic equations |
> 0 conics section is a hyperbola, < 0 conic section is an ellipse, = 0 conic section is a parabola |
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What is directix for parabola? What is vertex? Where is focus? |
X = h - p/2, is the line below parabola and indicates direction. Vertex is p/2 away from director. Where vertex is (h,k) |
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What is focus in parabola? Where can I find equations? |
It is p away from directix. It is the point on the inside of the curve. All parabola equations on page 25 with conic sections. |
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Equation for parabola vertical and horizontal |
(X-h)^2=2p(y-k). & reverse (x-h) with (y-k) for horizontal. (h,k) is vertex. |
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What is major axis for an ellipse? |
Runs through ellipse and middle of both shorter arcs indicating it's orientation. |
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What are b, a, and C for ellipse? What is equation and where can I find it? |
B is distance where ellipse intersects minor axis is from center. A is distance where ellipse intersects major axis is from center. C is distance Foci are from center of ellipse.
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
Page 25 mathematics section. |
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What is eq for hyperbola and where do you find it? What are h, k, a, b, c? |
(x-h)^2/a^2 - (y-k)^2/b^2 = 1 center at (h,k). Mathematics section. Page 26.
H and k are the points if the vertex (h,k). Solve for a and b with points in function. C is distance of F from vertex. B is distance from either vertex to assymptote. |
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What is equation of a circle? |
(X-h)^2 + (y-k)^2 = r^2 |
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What is equation for length of tangent line to a circle and where can I find it? What is t,h,k,r,x',y'? |
t^2 = (x'-h)^2 + (y'-k)^2 - r^2 Mathematics section page 26. T is length of tangent line. (h,k) for circle center. r is radius. (x',y') is PT in 2d space. |
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What is and where can I find quadric surface of sphere eq? |
(x-h)^2 + (y-k)^2 + (z-m)^2 = r^2 Center at (h,k,m). Mathematics section page 21 |
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Eq for distance between two lines in space? |
D = √((x2-x1)^2+(y2-y1)^2+(z2-z1)^2) |
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What are the general trig identities? |
Csc = 1/sin Sec = 1/cos Cot = 1/tan Tan = sin/cos Cos^2 + sin^2 = 1 Tan^2 + 1 = sec^2 Cot^2 + 1 = csc^2 |
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What is law of sines? When is it useful? |
a / sinA = b / sinB = c / sinC When given more angles than side lengths. Can use to find some of those side lengths. |
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What is law of cosines? When is it useful? |
a^2 = b^2 + c^2 - 2bccosA b^2 = a^2 + c^2 - 2accosB C^2 = a^2 + b^2 - 2abcosC When given all three sides and no angles.
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What is eq for area of an ellipse? Circular segments? Circular sector? |
A = π*a*b
A = [r^2(angle-sin(angle)]\2 Angle = s/r = 2[arccos((r-d)/r)] s is segment curve length r is radius d is height of arc
A = angle*r^2/2 = s*r/2 Angle = s/r |
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What is volume and surface area of a sphere? Circular cone? Cylinder? Parabloids? |
(4/3)π*r^3 4π*r^2 (π*r^2*h)/3 π*r(r+√(r^2+h^2)) π*r^2*h 2*π*r(h+r) (π*d^2*h)/8 |
