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PSAT MAth Addition topics ch12 Cheat Sheet (DRAFT) by

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Geometry references

References
circle
A=pir2; C=2pir: 2pi=360
rectan­gular
A=lw
trangle
A=1/2bh
 
c2=a2+b2; 3-4-5,­5-12-13
 
s-s-ssqrt(2); x-xsqrt(3­)-2x; 180=sum
rectan­gular prism
V=lwh; sa=2(lw +lh+hw)
cyclinder
V=pi*r2h; sa=2pi rh +pirr
cone
V=pi*r2h/3
triangular prism
V=lwh/3
sphere
V=4pi*r3/3; sa=4pirr

Line and angles

LINEs and ANGLES
line,r­ay,line segment
0,1,2 ends
supple­mentary angle
180=an­gle­+su­ppl­eme­ntary angle
vertical angle
cross line
big/small angle
parallel line
Being Aggressive on Geometry Problems: whenever you have
a diagram, ask yourself What else do I know? write it down anyway.

ETS is also fond of disguising familiar figures within more complex
shapes by extending lines, overla­pping figures, or combining several
basic shapes. So be on the lookout for the basic figures hidden in
compli­cated shapes.

Triangles

QUANDR­ILA­TERAL
parall­elogram
quadri­lateral in which opposite sides are parallel
rectangule
a parall­elogram in which all angles equal 90º
square
rectangle in which all angles and all sides are equal
TRIANGLES
180 rules
A=bh/2
isosceles triangles
s1=s2
equila­teral
60
pythag­orean therorem
a2+b2=c2
 
3;4;5, 5:12:13 rues
special right trangles
30-60-90: x-sqrt­(3)x-2x (hypot­enuse)
 
45-45-­90:­x-x­-sq­rt(2)x
SOHCAHTOA
opposite, adjace­nt,­hyp­otenuse
 
SOH:si­ne=­opp­osi­te/­hyp­otenuse
 
CAH:co­s=A­dja­cen­t/h­ypo­tenuse
 
TOA:ta­nge­nt=­opp­osi­te/­Adj­acent
similar triangles
same shape(­angles)
 
diff size, same corres­ponding side ratio

Circles

Circle
radius
 
diameter
 
chord: any line segment in side circle
 
arc:part of circum­fer­enc­e(edge)
 
circum­fer­enc­e=2pi *radius
 
area=pirr
Propor­tio­nality
Arc measure is propor­tional to interior angle measure, which is propor­tional to sector area.
 
An interior angle is an angle formed by two radii.
 
A sector is the portion of the circle between the two radii.
tangents
OPN=90­;oQ­N=90; PNQ=45,
Equation
(x,y) is point of circle­,(h,k) is the center, r is radius
 
xy plane: (x-h)2 + (y-k)2=r2
What is the center of a circle with equation x2 + y2 – 2x + 8y + 8 = 0 ?

Volume

ref to equation of volumes

Plug in on Genometry

(Hidden )variable in choice answer
180 rule for triangle
outside angle=­inner angle1­+ingger angle2
A rectan­gular box is half as long as it is wide and one-third as wide as it is
tall. If the volume of the box is 96, then what is its surface area?

imaginary and complex

sqrt(-1)
italicized i
in
i1=i; i2+-1; i3=-i; i4=1
 
i5=i; i6+-1; i7=-i; i8=1
complex number
a+bi
 
treat i as variable when do arithmetic
 
add/su­btr­action ( distribute the minus sign)
 
multip­lic­ation: FOIL

Summary

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°.
On all geometry problems, draw figures out and aggres­sively fill in everything you know.
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°.
The perimeter of a rectangle is the sum of the lengths of its sides. The area of a rectangle is length × width.
The perimeter of a triangle is the sum of the lengths of its sides. The area of a triangle is 1/2 base × height.
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.
For trigon­ometry questions, remember SOHCAHTOA: sine=o­ppo­sit­e/h­ypo­tenuse; cosin=­adj­ace­nt/­hyp­otenus; tangen­t=o­ppo­sit­e/a­djacent
Similar triangles have the same angles and their lengths are propor­tional.
The circum­ference of a circle is 2πr. The area of a circle is πr2.
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.
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.
The formulas to compute the volumes of many three-­dim­ens­ional figures are supplied in the instru­ctions at the front of both Math sections.
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.
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.