Useful notes about functions for people who want to take the SAT II Math Level 2 Subject Test
Useful notes about combinatorics for students who wish to take the SAT II Math Level 2 Subject TestFull description
Useful notes about polar coordinates for people who want to take the SAT II Math Level 2 Subject TestFull description
Useful notes about matrices for people who want to take the SAT II Math Level 2 Subject TestFull description
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Full description
Maths
MA 92
Useful notes about arithmetic and algebra for students who wish to take the SAT II Math Level 2 Subject TestFull description
Useful notes about arithmetic and algebra for students who wish to take the SAT II Math Level 2 Subject Test
Preparation Booklet 2006 - 2007
Preparation Booklet 2006 - 2007
Chemistry Subject Test for SATFull description
Scanned Version
Scanned Version
Syllabus of SAT PHYSICS, CHEMISTRY AND BIOLOGY compiledFull description
_Master_SAT_II_Math
Conic Sections Circles 2 2 2 General Equation for Circles: ( x x – h) + ( y y – k ) = r (h,k ) = center of o f circle r = r = radius of circle
Ellipses Definition: An ellipse is the set of points in a plane such that t he sum of the distances from each point to two fixed points, po ints, called foci called foci,, is a constant equal to 2a General Equations for Ellipses: 2 2 ( x x – h) + ( y y – k ) = 1 o 2 2 a b Major axis is parallel to the x the x-axis -axis 2 2 ( x x – h) + ( y y – k ) = 1 o 2 2 b a Major axis is parallel to the y the y-axis -axis (h,k ) = center of o f ellipse Length of major axis = 2a 2a Length of minor axis = 2b 2b 2 2 The distance between the center and a focus: c = √a – b
Parabolas Definition: A parabola is the set of points in a plane such that the distance from each point to a fixed point, called the focus the focus,, is equal to the distance to a fixed line, called the directrix General Equations for Parabolas: x – h)2 x o y – k = a ( The parabola opens up or down 2 y – k ) y o x – h = a ( The parabola opens out to the left or right (h,k ) = vertex of parabola a = (1 / 4 p p)) p = distance between the vertex and focus = distance between the vertex vert ex and directrix 2 General Form: y = ax + bx + c Axis of Symmetry S ymmetry:: x = (-b (-b) / (2a (2a) o o y-intercept: (0,c (0,c) If a If a is positive, the parabola opens upward o If a If a is negative, the parabola opens downward o
Hyperbolas Definition: A hyperbola is the set of points in a p lane such that the absolute value of the difference of the distances from each point po int to two fixed points, called foci called foci,, is a constant equal to 2a 2a General Equations for Hyperbolas: ( x x – h)2 – ( y y – k )2 = 1 o 2 2 a b The hyperbola opens out to the left and right The slopes of the two asymptotes are ± (b (b / a) 2 2 ( y y – k ) – ( x x – h) = 1 o 2 2 a b The hyperbola opens up and down The slopes of the two asymptotes are ± (a (a / b) (h,k ) = center of hyperbola Length of transverse axis = 2a 2a Length of conjugate axis = 2b 2b 2 2 The distance between the center and a focus: c = √a + b
Rectangular Hyperbolas Equation: xy Equation: xy = k , where k is k is a constant The asymptotes are the x the x-- and y and y-axes -axes If k If k > > 0, the branches of the hyperbola lie in quadrants I and III If k If k < < 0, the branches of the hyperbola lie in quadrants II and IV
