Quantitative Reasoning Flashcards
What is the difference of squares?
a2-b2=(a+b)(a-b)
What is this square binomials?
a2+2ab+b2=(a+b)2
a2-2ab+b2=(a-b)2
What is the quadatic equation?
x=(-b(+/-)(b2-4ac)1/2)/(2a)
What is the quadratic equation?
ax2+bc+c=0
What to do when you have a simultaneous equation?
add them together
ex:
2x-9y=11
x+12y=-8
3x+3y=3
What to do when you absolute value?
Do both + and - numbers
ex
Ix-12l=3
x-12=3;x-12=-3
What to do with inequality?
It is just like an = sign
X or / by number when the sign is flipped
*General Rule of absolute value
IwhateverI < p when p>0
IwhateverI < p means -p<whatever></whatever>
<p>IwhateverI>p p>P</p>
</whatever>
What are the su of interior angles?
180
How to find exterior angle?
subtract interior angle by 180
Area formula of a triangle
1/2bh
Triangle inequality therom
Length on 1 side of triangle must be greater than the difference of the other 2 side
Length of 1 side of triangle less than sum of other 2 sides
What do similar tirangel have?
have same shape
corresponding angles equal
corresponding sides proportion
What are the 3 special triangles?
Isoceles, equalateral, right
Isosoceles triangle
2 sides equal
angles opposide side are =
Equilateral triangle
3 sides equal
all angles equal to 60
area= s2 *(3)1/2/4
Right Triangles
2 sides
legs are base and height
Pythagorean Therom
a2+b2=c2
Pythagorean Tripelet
3,4,5 and interger
5, 12, 13
45-45-90( ratio 1:1:(2)1/2)
30-60-90 triangles
ratio: 1:(3)1/2:2
Area of trapezoids
((b1+b2)/2)(height)
Paralelogram
Opposite sides equal
area=base*height
Height perpendicular to base
Area of rectangle
L*W
Area of Rhombus
base*height
Area of square
(s)2
Area of Hexagon
(3s2(3)1/2)/2
Length of Arc
(n/360)(2πR)
Circumference of a circle
2πR
Area of circle
πr2
Area of a sector of a circle
(n/360)(πr2)
Lateral area of cone
1/2*circumference*l(slant height)
Volume of Cone
1/3πr2h
Surface area of sphere
4πr2
Volume of a sphere
4/3πr3
Volume of pyramid
1/3bh
Distance formula
(L2+W2+h2)1/2
Volume of rectangular solid
lwh
Volume of cube
c3
Volume of Cylinder
πr2h
Distance between two points fomrula
((x1-x2)2+(y1-y2)2)1/2
Slope of parallel lines
same
Line perpendicular lines to each other
negative recipicals of each other
Graph of absolute value
Bend in graph
bends at 0 usually
Trig identites
sin2x+cos2x=1
1+cot2x=cscx
tan2x+1=sec2x
Double angle formulas
sin(2x) = 2sinxcosx
cos(2x)= cos^2x-sin^2x = 2cos^2x-1 = 1-2sin^2x tan(2x)= (2tanx)/(1-tan^2x)
Convert radians to degrees
x/(desired radian)=360/2π
Convert degrees to radians
x/degree=2π/360
Sinx=y graph
Repeats every 360
Cosx=y graph
Repeats every 360
Tanx=y graph
Repeats every 90
Inverse of sin
arcsingx
-90<= x<= 90
can not be defined at x<-1 and x>1
Inverse tan
arc tan
undefined at -90 and 90
Sine recipical
Cosine reciprocal
Tangent reciprcal
Cosecant
Secant
Cotangent
Surface area of retangular solid
2lw+2wh+2lh
Permuation
Specific order
N!/(N-R)!
Combination
N!/(R!(N-R)!
order does not matter
ABC=BCA
