How many of these formulas do you recognize, remember, and know how to use?
c2 = a2 + b2
d = (x2 ! x1 )2 + (y2 ! y1 )2
! x + x2 y1 + y2 $
midpt = # 1
,
2 &%
" 2
m=
y2 ! y1
x2 ! x1
y – y1 = m (x – x1)
y = mx + b
Ax + By = C
m=
!A
B
Parallel lines – same slope
xint =
Perpendicular lines – negative reciprocal slopes
x=
ax 2 + bx + c = 0
r1 + r2 = ! b a
!b ± b2 ! 4ac
2a
r1r2 = c a
1
(x ! h)2
4m
y–k=
( x ! h) + ( y ! k )
2
2
= r2
x2 y2
+
=1
a 2 b2
x 2 y2
!
=1
a2 b2
xy=k
C
A
yint =
C
B
log b x = n iff bn = x
log x1 = log x2 iff x1 = x2
log a
log ab = log a + log b
b
= log a – log b
x
blogb = x
log b bx = x
log a n = n log a
y = kx
xy = k
xm xn = x m+n
xm/xn = x m–n
(xm)n = x mn
x–m = 1/xm
x0 = 1, x≠0
an = a1 + (n ! 1)d
n
Sn = "# 2a1 + (n ! 1)d $%
2
=
n
a + an
2 1
(
an = a1r n!1
)
Sn =
i 2 = !1
i = –1
!=
a1 ! a1r n
1! r
i 3 = !i
s
r
i4 = 1
deg rees 180
=
radians
!
x = r cos!
y = r sin !
SOHCAHTOA
tan ! =
sin !
cos!
cos2x + sin2x = 1
sin A sin B sin C
=
=
a
b
c
c 2 = a 2 + b 2 ! 2ab cosC
sin(A ± B) = sin A cos B ± sin B cos A
sin2A= 2sinAcosA
cos(A + B) = cos A cos B ! sin Asin B
cos2A = 1 – 2sin2A
tan(A + B) =
sin
tan A ± tan B
1 ! tan A tan B
tan2A =
2 tan A
1 – tan 2 A
!
1 " cos!
=
2
2
cos
!
1 + cos!
=
2
2
tan
P(n, r) =
n!
n ! r)!
n
n!
xn! k yk
k = 0 (n ! k)!k!
(x + y)n = "
!
sin !
1 " cos!
=
=
2 1 + cos!
sin !
C(n, r) =
n!
n ! r)!r!