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Reference Sheet for the QualityCoreTM Algebra II End-of-Course Assessment Equations of a Line Standard Form Ax + By = C Slope-Intercept Form y = mx + b Point-Slope Form y − y1 = m(x − x1) A, B, and C are constants with A and B not both equal to zero. (x1,y1) is a point. m = slope b = y-intercept Quadratics Standard Form of a Quadratic Equation ax 2 + bx + c = 0 a, b, and c are constants, where a ≠ 0. −b ± 公b僓僓僓僓僓僓 − 4ac僓 x = _______________ 2 Quadratic Formula 2a Conic Sections Circle (x − h)2 + (y − k)2 = r 2 Parabola y = a(x − h)2 + k Parabola x = a(y − k)2 + h center (h,k) r = radius axis of symmetry x = h vertex (h,k) 1 directrix y = k − ___ 4a 1 focus h, k + ___ axis of symmetry y = k vertex (h,k) 1 directrix x = h − ___ 1 focus (h + ___ , k) 4a 4a 4a Ellipse 2 2 −__h) −__k) _(x ___ __ + _(y ___ __ = 1 2 2 a b foci (h ± c, k) where c 2 = a 2 − b 2, center (h,k) Ellipse 2 2 −__k) −__ h) _(y ___ __ + _(x ___ __ = 1 2 2 a b foci (h, k ± c) where c 2 = a 2 − b 2, center (h,k) Hyperbola 2 2 −__ h) −__k) _(x ___ __ − _(y ___ __ = 1 2 2 a b foci (h ± c, k) where c 2 = a 2 + b 2, center (h,k) Hyperbola 2 2 −__k) −__ h) _(y ___ __ − _(x ___ __ = 1 2 2 a b foci (h, k ± c) where c 2 = a 2 + b 2, center (h,k) Lines and Points y −y Slope 2 1 __ m = _____ x 2 − x1 Midpoint y +y x1 + x__ 2 _____ M = _____ , 1 __2 Distance d= 2 2 (x1,y1) and (x2,y2) are 2 points. m = slope M = midpoint d = distance 2 公僓僓僓僓僓僓僓 (x2 − x1)僓僓僓僓僓僓僓僓僓 + (y2 − y1僓僓 )2 continued Miscellaneous Distance, Rate, Time D = rt Simple Interest I = pr t Compound Interest r A = p 1 + __ Pythagorean Theorem a2 + b2 = c2 冢 n 冣 nt D = distance r = rate t = time I = interest p = principal A = amount of money after t years n = number of times interest is compounded annually a and b = legs of right triangle c = hypotenuse Laws of Sines and Cosines Law of Sines A B C _sin ____ ____ ____ = _sin = _sin a b c Law of Cosines a 2 = b 2 + c 2 − 2bc cos A A c b C a B Sequences, Series, and Counting Arithmetic Sequence an = a1 + (n − 1)d Arithmetic Series sn = _n_ (a1 + an) Geometric Sequence an = a1(r n − 1) Geometric Series a1 − a1r_ sn = _______ where r ≠ 1 Combinations kC m 2 n Permutations 1−r k! = C(k,m) = _________ (k − m)! m! k! ___ ____ k Pm = P(k,m) = (k − m)! an = n th term n = number of the term d = common difference sn = sum of the first n terms r = common ratio k = number of objects in the set m = number of objects selected Circumference, Area, and Volume Triangle A = _1_ bh Parallelogram A = bh Trapezoid A = _1_ (b1 + b2)h Circle A = πr2 C = πd General Prism V = Bh Right Circular Cylinder V = π r 2h Pyramid V = _1_ Bh Right Circular Cone Sphere ©2007 by ACT, Inc. All rights reserved. 2 2 A = area b = base h = height r = radius C = circumference d = diameter V = volume B = area of base π ≈ 3.14 3 V = _1_ π r 2h 3 _ V = 4_ π r 3 3 IC 019247080