KEYSTONE
Re f E FERENCE
ALGEBRA I FORMULA SHEET
Formulas that you may need to solve questions on this exam are found below.
You may use calculator π or the number 3.14.
Arithmetic Properties
A = lw
w
Additive Inverse:
a + (ˉa) = 0
l
Multiplicative Inverse:
Commutative Property:
h
V = lwh
Associative Property:
w
l
Identity Property:
Linear Equations
Slope:
m=
y2 – y1
x2 – x1
Point-Slope Formula:
Slope-Intercept Formula:
y = mx + b
Standard Equation of a Line:
Ax + By = C
a+b=b+a
a·b=b·a
(a + b) + c = a + (b + c)
(a · b) · c = a · (b · c)
a+0=a
a·1=a
Distributive Property:
(y – y 1) = m(x – x 1)
1
a· =1
a
a · (b + c) = a · b + a · c
Multiplicative Property of Zero:
a·0=0
Additive Property of Equality:
If a = b, then a + c = b + c
Multiplicative Property of Equality:
If a = b, then a · c = b · c
Copyright © 2011 by the Pennsylvania Department of Education. The materials contained in this publication
may be duplicated by Pennsylvania educators for local classroom use. This permission does not extend to the
duplication of materials for commercial use.
KEYSTONE
Re f E FERENCE
ALGEBRA II FORMULA SHEET
Formulas that you may need to solve questions on this exam are found below.
You may use calculator π or the number 3.14.
Shapes
Logarithmic Properties
loga x = y ↔ x = a y
A = lw
w
log x = y ↔ x = 10 y
In x = y ↔ x = ey
loga (x · y ) = loga x + loga y
l
loga x p = p · loga x
x
loga y = loga x − loga y
h
V = lwh
w
l
Quadratic Functions
f(x) = ax 2 + bx + c
General Formula:
Data Analysis
f (x) = a(x − h )2 + k
Standard (Vertex) Form:
Permutation:
nPr
Combination:
=
n!
(n − r)!
n!
nCr =
r !(n − r )!
f(x ) = a(x − x 1)(x − x 2)
Factored Form:
Quadratic Formula:
x=
ˉb ± b 2 − 4ac
2a
when ax 2 + bx + c = 0 and a Þ 0
Exponential Properties
am · an = am + n
(a m )n = a m · n
am
= am − n
an
a ¯1 =
1
a
Compound Interest Equations
Annual:
A = P (1 + r ) t
Periodic:
A =P 1+
i3 = ¯ i
i 2 = ¯1
nt
n
P = principal amount
r = annual rate of interest
t = time (years)
Continuous:
¯1
r
( )
Powers of the Imaginary Unit
i=
A = account total after t years
A
= Pert
n = number of periods interest
is compounded per year
i4 = 1
Copyright © 2011 by the Pennsylvania Department of Education. The materials contained in this publication
may be duplicated by Pennsylvania educators for local classroom use. This permission does not extend to the
duplication of materials for commercial use.
KEYSTONE
Re f E FERENCE
GEOMETRY FORMULA SHEET ─ PAGE 1
Formulas that you may need to solve questions on this exam are found below.
You may use calculator π or the number 3.14.
Properties of Circles
Right Triangle Formulas
Angle measure is represented by x. Arc measure is represented
by m and n. Lengths are given by a, b, c, and d.
Pythagorean Theorem:
Inscribed Angle
n°
x°
If a right triangle has legs with
measures a and b and hypotenuse
with measure c, then...
c
a
a2 + b2 = c2
b
1
x= n
2
Trigonometric Ratios:
x°
sin θ =
Tangent-Chord
n°
x=
1
n
2
hypotenuse
opposite
cos θ =
θ
adjacent
m°
a
c
x°
hypotenuse
adjacent
hypotenuse
tan θ =
2 Chords
d
opposite
opposite
adjacent
a·b=c·d
n°
x=
b
1
(m + n)
2
Coordinate Geometry Properties
a
x°
n°
Tangent-Secant
b
a 2 = b (b + c)
m°
x=
c
1
(m − n)
2
Distance Formula:
Midpoint:
Slope:
m°
x1 + x2
2
n° x°
b
b (a + b) = d (c + d )
d
c
x=
1
(m − n)
2
,
(x2 – x 1)2 + (y2 – y 1)2
y1 + y2
2
y2 − y1
m=
x2 − x1
2 Secants
a
d=
Point-Slope Formula:
(y − y 1) = m (x − x 1)
Slope Intercept Formula:
y = mx + b
Standard Equation of a Line:
2 Tangents
a
m°
n°
a=b
x°
b
Ax + By = C
x=
1
(m − n)
2
Copyright © 2011 by the Pennsylvania Department of Education. The materials contained in this publication
may be duplicated by Pennsylvania educators for local classroom use. This permission does not extend to the
duplication of materials for commercial use.
KEYSTONE
Re f E FERENCE
GEOMETRY FORMULA SHEET ─ PAGE 2
Formulas that you may need to solve questions on this exam are found below.
You may use calculator π or the number 3.14.
Plane Figure Formulas
Solid Figure Formulas
P = 4s
A=s · s
s
w
s
l
P = 2l + 2w
A = lw
w
SA = 4r 2
4
V = r 3
3
r
l
a
P = 2a + 2b
A = bh
h
h
b
SA = 2r 2 + 2rh
V = r 2h
r
a
c
d
h
P=a+b+c+d
1
A = 2 h (a + b)
SA = r 2 + r r 2 + h 2
1
V = r 2h
3
h
b
r
c
SA = 2lw + 2lh + 2wh
V = lwh
h
d
h
P=b+c+d
1
A = 2bh
b
SA = (Area of the base) +
1 (number of sides)(b)( )
2
h
b
base
r
C = 2r
A = r 2
V=
1
(Area of the base)(h)
3
b
Euler’s Formula for Polyhedra:
Sum of angle measures = 180(n – 2),
where n = number of sides
V−E+F=2
vertices minus edges plus faces = 2
Copyright © 2011 by the Pennsylvania Department of Education. The materials contained in this publication
may be duplicated by Pennsylvania educators for local classroom use. This permission does not extend to the
duplication of materials for commercial use.