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% Document Info
\author{Jianmin Feng (taotao)}
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  /Title (psat-math-addition-topics-ch12.pdf)
  /Creator (Cheatography)
  /Author (Jianmin Feng (taotao))
  /Subject (PSAT MAth Addition topics ch12 Cheat Sheet)
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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{PSAT MAth Addition topics ch12 Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Jianmin Feng (taotao)} via \textcolor{DarkBackground}{\uline{cheatography.com/79308/cs/20441/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Jianmin Feng (taotao) \\
  \uline{cheatography.com/taotao} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 2nd September, 2019.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
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\begin{multicols*}{3}

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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Geometry references}}  \tn
% Row 0
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\mymulticolumn{2}{x{5.377cm}}{References} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
circle & A=pi{\emph{r\textasciicircum{}2\textasciicircum{}; C=2}}pi{\emph{r: 2}}pi=360 \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
rectangular & A=lw \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
trangle & A=1/2bh \tn 
% Row Count 5 (+ 1)
% Row 4
\SetRowColor{LightBackground}
 & c\textasciicircum{}2\textasciicircum{}=a\textasciicircum{}2\textasciicircum{}+b\textasciicircum{}2\textasciicircum{}; 3-4-5,5-12-13 \tn 
% Row Count 7 (+ 2)
% Row 5
\SetRowColor{white}
 & s-s-s{\emph{sqrt(2); x-x}}sqrt(3)-2x; 180=sum \tn 
% Row Count 9 (+ 2)
% Row 6
\SetRowColor{LightBackground}
rectangular prism & V=lwh; sa=2(lw +lh+hw) \tn 
% Row Count 11 (+ 2)
% Row 7
\SetRowColor{white}
cyclinder & V=pi*r\textasciicircum{}2\textasciicircum{}h; sa=2pi rh +pirr \tn 
% Row Count 12 (+ 1)
% Row 8
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cone & V=pi*r\textasciicircum{}2\textasciicircum{}h/3 \tn 
% Row Count 13 (+ 1)
% Row 9
\SetRowColor{white}
triangular prism & V=lwh/3 \tn 
% Row Count 15 (+ 2)
% Row 10
\SetRowColor{LightBackground}
sphere & V=4pi*r\textasciicircum{}3\textasciicircum{}/3; sa=4pirr \tn 
% Row Count 16 (+ 1)
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Line and angles}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{LINEs and ANGLES} \tn 
% Row Count 1 (+ 1)
% Row 1
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line,ray,line segment & 0,1,2 ends \tn 
% Row Count 3 (+ 2)
% Row 2
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supplementary angle & \seqsplit{180=angle+supplementary} angle \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
vertical angle & cross line \tn 
% Row Count 6 (+ 1)
% Row 4
\SetRowColor{LightBackground}
big/small angle & parallel line \tn 
% Row Count 7 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Being Aggressive on Geometry Problems: whenever you have \newline a diagram, ask yourself What else do I know? write it down anyway.  \newline  \newline ETS is also fond of disguising familiar figures within more complex \newline shapes by extending lines, overlapping figures, or combining several \newline basic shapes. So be on the lookout for the basic figures hidden in \newline complicated shapes.}  \tn 
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\begin{tabularx}{5.377cm}{x{1.74195 cm} x{3.23505 cm} }
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Triangles}}  \tn
% Row 0
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\mymulticolumn{2}{x{5.377cm}}{QUANDRILATERAL} \tn 
% Row Count 1 (+ 1)
% Row 1
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parallelogram & quadrilateral in which opposite sides are parallel \tn 
% Row Count 3 (+ 2)
% Row 2
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rectangule & a parallelogram in which all angles equal 90º \tn 
% Row Count 5 (+ 2)
% Row 3
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square & rectangle in which all angles and all sides are equal \tn 
% Row Count 8 (+ 3)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{TRIANGLES} \tn 
% Row Count 9 (+ 1)
% Row 5
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180 rules & A=bh/2 \tn 
% Row Count 10 (+ 1)
% Row 6
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isosceles triangles & s1=s2 \tn 
% Row Count 12 (+ 2)
% Row 7
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equilateral & 60 \tn 
% Row Count 13 (+ 1)
% Row 8
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pythagorean therorem & a2+b2=c2 \tn 
% Row Count 15 (+ 2)
% Row 9
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 & 3;4;5, 5:12:13 rues \tn 
% Row Count 16 (+ 1)
% Row 10
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special right trangles & 30-60-90: x-sqrt(3)x-2x (hypotenuse) \tn 
% Row Count 18 (+ 2)
% Row 11
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 & 45-45-90:x-x-sqrt(2)x \tn 
% Row Count 19 (+ 1)
% Row 12
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SOHCAHTOA & opposite, adjacent,hypotenuse \tn 
% Row Count 21 (+ 2)
% Row 13
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 & \seqsplit{SOH:sine=opposite/hypotenuse} \tn 
% Row Count 23 (+ 2)
% Row 14
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 & \seqsplit{CAH:cos=Adjacent/hypotenuse} \tn 
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% Row 15
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 & \seqsplit{TOA:tangent=opposite/Adjacent} \tn 
% Row Count 27 (+ 2)
% Row 16
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similar triangles & same shape(angles) \tn 
% Row Count 29 (+ 2)
% Row 17
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 & diff size, same corresponding side ratio \tn 
% Row Count 31 (+ 2)
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Circle & radius \tn 
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% Row 1
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 & diameter \tn 
% Row Count 2 (+ 1)
% Row 2
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 & chord: any line segment in side circle \tn 
% Row Count 4 (+ 2)
% Row 3
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 & arc:part of circumference(edge) \tn 
% Row Count 6 (+ 2)
% Row 4
\SetRowColor{LightBackground}
 & circumference=2pi *radius \tn 
% Row Count 7 (+ 1)
% Row 5
\SetRowColor{white}
 & area=pi{\emph{r}}r \tn 
% Row Count 8 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\seqsplit{Proportionality} & Arc measure is proportional to interior angle measure, which is proportional to sector area. \tn 
% Row Count 12 (+ 4)
% Row 7
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 & An interior angle is an angle formed by two radii. \tn 
% Row Count 14 (+ 2)
% Row 8
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 & A sector is the portion of the circle between the two radii. \tn 
% Row Count 17 (+ 3)
% Row 9
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tangents & OPN=90;oQN=90; PNQ=45, \tn 
% Row Count 18 (+ 1)
% Row 10
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Equation & (x,y) is point of circle,(h,k) is the center, r is radius \tn 
% Row Count 20 (+ 2)
% Row 11
\SetRowColor{white}
 & xy plane: (x-h)\textasciicircum{}2\textasciicircum{} + (y-k)\textasciicircum{}2\textasciicircum{}=r\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 22 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{What is the center of a circle with equation x2 + y2 – 2x + 8y + 8 = 0 ?}  \tn 
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Volume}}  \tn
% Row 0
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\mymulticolumn{2}{x{5.377cm}}{ref to equation of volumes} \tn 
% Row Count 1 (+ 1)
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Plug in on Genometry}}  \tn
% Row 0
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\mymulticolumn{2}{x{5.377cm}}{(Hidden )variable in choice answer} \tn 
% Row Count 1 (+ 1)
% Row 1
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\mymulticolumn{2}{x{5.377cm}}{180 rule for triangle} \tn 
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% Row 2
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\mymulticolumn{2}{x{5.377cm}}{A rectangular box is half as long as it is wide and one-third as wide as it is \newline tall. If the volume of the box is 96, then what is its surface area?}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\begin{tabularx}{5.377cm}{x{1.29402 cm} x{3.68298 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{imaginary and complex}}  \tn
% Row 0
\SetRowColor{LightBackground}
sqrt(-1) & italicized i \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
i\textasciicircum{}n\textasciicircum{} & i\textasciicircum{}1\textasciicircum{}=i; i\textasciicircum{}2\textasciicircum{}+-1; i\textasciicircum{}3\textasciicircum{}=-i; i\textasciicircum{}4\textasciicircum{}=1 \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
 & i\textasciicircum{}5\textasciicircum{}=i; i\textasciicircum{}6\textasciicircum{}+-1; i\textasciicircum{}7\textasciicircum{}=-i; i\textasciicircum{}8\textasciicircum{}=1 \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
complex number & a+bi \tn 
% Row Count 7 (+ 2)
% Row 4
\SetRowColor{LightBackground}
 & treat i as variable when do arithmetic \tn 
% Row Count 9 (+ 2)
% Row 5
\SetRowColor{white}
 & add/subtraction ( distribute the minus sign) \tn 
% Row Count 11 (+ 2)
% Row 6
\SetRowColor{LightBackground}
 & multiplication: FOIL \tn 
% Row Count 12 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Summary}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Be sure to review your basic geometry rules before the test; often, problems hinge on knowing that vertical angles are equal or that the sum of the angles in a quadrilateral is 360°.} \tn 
% Row Count 4 (+ 4)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{On all geometry problems, draw figures out and aggressively fill in everything you know.} \tn 
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% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{When two parallel lines are cut by a third line, the small angles are equal, the big angles are equal, and the sum of a big angle and a small angle is 180°.} \tn 
% Row Count 10 (+ 4)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{The perimeter of a rectangle is the sum of the lengths of its sides. The area of a rectangle is length × width.} \tn 
% Row Count 13 (+ 3)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{The perimeter of a triangle is the sum of the lengths of its sides. The area of a triangle is 1/2 base × height.} \tn 
% Row Count 16 (+ 3)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Knowing the Pythagorean Theorem, common right triangles (such as 3-4-5 and 5- 12-13), and special right triangles (45°-45°-90° and 30°-60°-90°) will help you figure out angles and lengths in a right triangle.} \tn 
% Row Count 21 (+ 5)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{For trigonometry questions, remember SOHCAHTOA: \seqsplit{sine=opposite/hypotenuse;} \seqsplit{cosin=adjacent/hypotenus;} \seqsplit{tangent=opposite/adjacent}} \tn 
% Row Count 24 (+ 3)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Similar triangles have the same angles and their lengths are proportional.} \tn 
% Row Count 26 (+ 2)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{The circumference of a circle is 2πr. The area of a circle is πr2.} \tn 
% Row Count 28 (+ 2)
% Row 9
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Circles that show an interior angle (an angle that extends from the center of the circle) have proportionality. The interior angle over the whole degree measure (360°) equals the same fraction as the arc enclosed by that angle over the circumference. Likewise, both of these fractions are equal to the area of the segment over the entire area of the circle.} \tn 
% Row Count 36 (+ 8)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Summary (cont)}}  \tn
% Row 10
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{When you see a line that is "tangent to" a circle, remember two things: The line touches the circle at exactly one point. The radius of the circle that intersects the tangent line is perpendicular (90°) to that tangent line.} \tn 
% Row Count 5 (+ 5)
% Row 11
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{The formulas to compute the volumes of many three-dimensional figures are supplied in the instructions at the front of both Math sections.} \tn 
% Row Count 8 (+ 3)
% Row 12
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{When plugging in on geometry problems, remember to use your knowledge of basic geometry rules; e.g., there are still 180° in a triangle when you're using Plugging In.} \tn 
% Row Count 12 (+ 4)
% Row 13
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{The imaginary number i = , and there is a repeating pattern when you raise i to a power: i, –1, –i, 1. When doing algebra with i, treat it as a variable, unless you are able to substitute –1 for i2 when appropriate.} \tn 
% Row Count 17 (+ 5)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
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% That's all folks
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