Reference Sheet for the QualityCoreTM
Algebra II End-of-Course Assessment
Equations of a Line
Standard Form
Ax + By = C
Slope-Intercept Form
y = mx + b
Point-Slope Form
y − y1 = m(x − x1)
A, B, and C are constants with A and B not
both equal to zero.
(x1,y1) is a point.
m = slope
b = y-intercept
Quadratics
Standard Form of a
Quadratic Equation
ax 2 + bx + c = 0
a, b, and c are constants, where a ≠ 0.
−b ± 公b僓僓僓僓僓僓
− 4ac僓
x = _______________
2
Quadratic Formula
2a
Conic Sections
Circle
(x − h)2 + (y − k)2 = r 2
Parabola
y = a(x − h)2 + k
Parabola
x = a(y − k)2 + h
center (h,k)
r = radius
axis of symmetry x = h
vertex (h,k)
1
directrix y = k − ___
4a
1
focus h, k + ___
axis of symmetry y = k
vertex (h,k)
1
directrix x = h − ___
1
focus (h + ___
, k)
4a
4a
4a
Ellipse
2
2
−__h)
−__k)
_(x
___
__ + _(y
___
__ = 1
2
2
a
b
foci (h ± c, k) where c 2 = a 2 − b 2, center (h,k)
Ellipse
2
2
−__k)
−__
h)
_(y
___
__ + _(x
___
__ = 1
2
2
a
b
foci (h, k ± c) where c 2 = a 2 − b 2, center (h,k)
Hyperbola
2
2
−__
h)
−__k)
_(x
___
__ − _(y
___
__ = 1
2
2
a
b
foci (h ± c, k) where c 2 = a 2 + b 2, center (h,k)
Hyperbola
2
2
−__k)
−__
h)
_(y
___
__ − _(x
___
__ = 1
2
2
a
b
foci (h, k ± c) where c 2 = a 2 + b 2, center (h,k)
Lines and Points
y −y
Slope
2
1
__
m = _____
x 2 − x1
Midpoint
y +y
x1 + x__
2 _____
M = _____
, 1 __2
Distance
d=
2
2
(x1,y1) and (x2,y2) are 2 points.
m = slope
M = midpoint
d = distance
2
公僓僓僓僓僓僓僓
(x2 − x1)僓僓僓僓僓僓僓僓僓
+ (y2 − y1僓僓
)2
continued
Miscellaneous
Distance, Rate, Time
D = rt
Simple Interest
I = pr t
Compound Interest
r
A = p 1 + __
Pythagorean Theorem
a2 + b2 = c2
冢
n
冣
nt
D = distance
r = rate
t = time
I = interest
p = principal
A = amount of money after t years
n = number of times interest is
compounded annually
a and b = legs of right triangle
c = hypotenuse
Laws of Sines and Cosines
Law of Sines
A
B
C
_sin
____
____
____
= _sin
= _sin
a
b
c
Law of Cosines
a 2 = b 2 + c 2 − 2bc cos A
A
c
b
C
a
B
Sequences, Series, and Counting
Arithmetic Sequence
an = a1 + (n − 1)d
Arithmetic Series
sn = _n_ (a1 + an)
Geometric Sequence
an = a1(r n − 1)
Geometric Series
a1 − a1r_
sn = _______
where r ≠ 1
Combinations
kC m
2
n
Permutations
1−r
k!
= C(k,m) = _________
(k − m)! m!
k!
___
____
k Pm = P(k,m) =
(k − m)!
an = n th term
n = number of the term
d = common difference
sn = sum of the first n terms
r = common ratio
k = number of objects in the set
m = number of objects selected
Circumference, Area, and Volume
Triangle
A = _1_ bh
Parallelogram
A = bh
Trapezoid
A = _1_ (b1 + b2)h
Circle
A = πr2
C = πd
General Prism
V = Bh
Right Circular Cylinder
V = π r 2h
Pyramid
V = _1_ Bh
Right Circular Cone
Sphere
©2007 by ACT, Inc. All rights reserved.
2
2
A = area
b = base
h = height
r = radius
C = circumference
d = diameter
V = volume
B = area of base
π ≈ 3.14
3
V = _1_ π r 2h
3
_
V = 4_ π r 3
3
IC 019247080