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The document also includes continued series formulas, trigonometric identities (Pythagorean, sine/cosine laws, and double-angle identities), equation forms for lines and parabolas, quadratic solutions, and factorial, permutation, and combination 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set theory definitions are included in the document?","Question",{"text":63,"@type":64},"It lists implication (a implies b), equivalence (a if and only if b), intersection and empty set (a and b { } empty set), union, and complement (a → b, complement of A).","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Which geometry formulas are provided?",{"text":68,"@type":64},"The document includes area and volume formulas for shapes such as trapezoids, right cones and pyramids, cylinders and prisms, and spheres, along with surface and lateral surface area formulas for a cylinder and a right cone.",{"name":70,"@type":61,"acceptedAnswer":71},"What topics in algebra and trigonometry are covered?",{"text":72,"@type":64},"It provides formulas for arithmetic and geometric series, trigonometric identities including Pythagorean and double-angle identities, equation forms for lines and parabolas, the quadratic formula, and n-factorial with permutations and 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universal set  \na ∧ b a and b { } empty set  \na ∨ b a or b [a, b] a ≤ x ≤ b  \n~ a not a (a, b) a \u003C x \u003C b  \nA ∪ B A union B ABC ~ DEF ABC is similar to DEF  \nA ∩ B A intersect B AB  CD AB is congruent to CD  \nFORMULAS  \n\n| A =  (b1 + b2 )h 2\u003Cbr>V = 1~~3~~ Bh\u003Cbr>V = Bh\u003Cbr>V = ~~ ~~4~~3 ~~ πr3 A = 2πrh + 2πr2\u003Cbr>A = 4πr2\u003Cbr>A = πrr 2 + h2 = πr ℓ | Area of a trapezoid\u003Cbr>Volume of a right cone and a pyramid Volume of a cylinder and prism Volume of a sphere\u003Cbr>Surface area of a cylinder Surface area of a sphere\u003Cbr>Lateral surface area of a right cone |\n| --- | --- |\n\nFORMULAS (continued)  \n\n| Sn = ~~ ~~n2~~ ~~ [2a + (n – 1)d] = ~~ ~~n2~~ ~~ (a + an)\u003Cbr>Sn =  a(1– rn )\u003Cbr>1– r\u003Cbr>∞\u003Cbr>∑ arn = ~~ ~~a~~ ~~ , | r | \u003C 1\u003Cbr>1– rn = 0 |  | Sum of an arithmetic series\u003Cbr>Sum of a finite geometric series\u003Cbr>Sum of an infinite geometric series |\n| --- | --- | --- |\n| sinA sinB sinC\u003Cbr>~~ ~~ = ~~ ~~ = ~~ ~~\u003Cbr>a b cc2 = a2 + b2 – 2ab cos C |  | Law of sines\u003Cbr>Law of cosines |\n| sin2(θ) + cos2(θ) = 1 |  | Pythagorean identity |\n| sin(2θ) = 2 sin(θ) cos(θ)\u003Cbr>cos(2θ) = cos2θ – sin2θ\u003Cbr>cos(2θ) = 2 cos2θ – 1\u003Cbr>cos(2θ) = 1 – 2 sin2θ tan(2θ) = ~~ ~~12–tantanθ |  | Double angle identities |\n| y = mx + b Ax + By = Cy – y1 = m(x – x1)\u003Cbr>y = ax2 + bx + c |  | Equations of a line\u003Cbr>Equation of a parabola (standard form)\u003Cbr>Quadratic formula |\n| x = | –b ± b2 – 4ac\u003Cbr>2a |  |\n| n × (n – 1) × (n – 2) × … × 1\u003Cbr>n!\u003Cbr>(n – r )!\u003Cbr>n!\u003Cbr>(n – r )! × r ! |  | n factorial (n!)\u003Cbr>Number of permutations (nPr )\u003Cbr>Number of combinations (nCr ) |\n\nCONIC SECTIONS  \nCircle  \n\n| (x – h)2 + (y – k)2 = r 2 Equation of a circle\u003Cbr>Parabola |  |\n| --- | --- |\n| (y – k) = 4p(x – h)2\u003Cbr>\u003Cbr>y2 = 4px\u003Cbr>Ellipse | Equation of a parabola (vertex form)\u003Cbr>\u003Cbr>x2 = 4py |\n\n( x – h )2  + (y – k )2  = 1  \na2 b2  \nxa22~~ ~~ + ~~ ~~yb22~~ ~~ = 1, a \u003C b  \nEquation of an ellipse  \nxa22~~ ~~ + ~~ ~~yb22~~ ~~ = 1, a > b  \nCONIC SECTIONS (continued)  \nHyperbola   \n( x – h )2  –(y – k )2  = 1  \na2 b2  \n2 2 x y  \n~~ ~~ – ~~ ~~ = 1 a2 b2  \nEquation of a hyperbola  \n2 2 y x  \n~~ ~~ – ~~ ~~ = 1 a2 b2","cbCailqKzzR9iNX4","https://ap.wps.com/l/cbCailqKzzR9iNX4","pdf",274054,"English","# Definitions\n## Set theory relationships and operations\n# Formulas\n## Geometry: area, volume, surface area\n## Sequences and series\n## Trigonometry identities\n## Algebra: line and quadratic equations\n## Factorials, permutations, combinations\n# Conic Sections\n## Circle, parabola, ellipse, hyperbola","[{\"question\":\"What set theory definitions are included in the document?\",\"answer\":\"It lists implication (a implies b), equivalence (a if and only if b), intersection and empty set (a and b { } empty set), union, and complement (a → b, complement of A).\"},{\"question\":\"Which geometry formulas are provided?\",\"answer\":\"The document includes area and volume formulas for shapes such as trapezoids, right cones and pyramids, cylinders and prisms, and spheres, along with surface and lateral surface area formulas for a cylinder and a right cone.\"},{\"question\":\"What topics in algebra and trigonometry are covered?\",\"answer\":\"It provides formulas for arithmetic and geometric series, trigonometric identities including Pythagorean and double-angle identities, equation forms for lines and parabolas, the quadratic formula, and n-factorial with permutations and combinations.\"}]","MATHEMATICS DEFINITIONS AND FORMULAS - Definitions & Formulas | PDF",1790679399]