Your concern: College Transcripts
Colleges require four years of high school math: Two years of algebra, one year of geometry, and one year of advanced math.
Life of Fred: Beginning Algebra Expanded Edition covers more material than is usual taught in the first year of high school algebra.
Life of Fred: Advanced Algebra Expanded Edition covers more material than is usual taught in the second year of high school algebra.
Life of Fred: Geometry Expanded Edition (omitting chapters 5½, 7½, 8½, 11½, 12½, and 13½) covers more material than is usually taught in a year of high school geometry.
Including all the chapters, the book is a solid honors course in geometry.
Life of Fred: Trigonometry Expanded Edition is a complete pre-calculus senior-year mathematics course.
If your college demands a detailed list of what was covered in each course, that's easy to supply. (I'll do the work!)
Just cut and paste each of these descriptions into your transcript.
Beginning Algebra
Numbers and Sets
finite and infinite sets
natural numbers, whole numbers, integers
set notation
negative numbers
ratios
the empty set
The Integers
less than (<) and the number line
multiplication
proportion
π
coefficients
Equations
solving equations with ratios
formulas from geometry
order of operations
consecutive numbers
rational numbers
set builder notation
distance = (rate)(time) problems
distributive property
proof that (negative) × (negative) = positive
Motion and Mixture
proof of the distributive property
price and quantity problems
mixture problems
age problems
Two Unknowns
solving two equations, two unknowns by elimination
union of sets
graphing of points
mean, mode, and median averages
graphing linear equations
graphing any equation
Exponents
solving two equations, two unknowns by graphing
solving two equations, two unknowns by substitution
(x^m)(x^n), (x^m)^n and x^m ÷ x^n
inconsistent and dependent equations
factorials
commutative laws
negative exponents
Factoring
multiplying binomials
solving quadratic equations by factoring
common factors
factoring x² + bx + c
factoring a difference of squares
factoring by grouping
factoring ax² + bx + c
Fractions
solving equations containing fractions
simplifying fractions
adding and subtracting fractions
multiplying and dividing fractions
complex fractions
Square Roots
solving pure quadratic equations
principal square roots
Pythagorean theorem
the real numbers
the irrational numbers
cube roots and indexes
solving radical equations
rationalizing the denominator
extraneous roots
Quadratic Equations
solving quadratic equations by completing the square
the quadratic formula
long division of a polynomial by a binomial
Functions and Slope
definition of a function
domain, codomain, image
six definitions of slope
slope-intercept (y = mx + b) form of the line
range of a function
Inequalities and Absolute Value
graphing inequalities in two dimensions
division by zero
algebraically solving linear inequalities with one unknown
Advanced Algebra
Ratio, Proportion, and Variation
median average
cross multiplying
constant of proportionality
Looking Back
exponents
square roots
rationalizing the denominator
Radicals
radical equations
extraneous answers
The History of Mathematics
irrational numbers
imaginary numbers
Looking Back
Venn diagrams (disjoint sets, union, intersection)
significant digits
scientific notation
Logarithms
exponential equations
the laws of logs
three definitions of logarithm
Looking Back
graphing by point-plotting
ordered pairs, abscissa, ordinate, origin, quadrants
Graphing
slope
distance between points
slope-intercept form of the line
double-intercept form of the line
point-slope form of the line
two-point form of the line
slopes of perpendicular lines
Looking Back
factoring
common factors
easy trinomials (of the form x² + bx + c)
difference of squares
grouping
harder trinomials (of the form ax² + bx + c)
fractions
simplifying
adding, subtracting
multiplying, dividing
complex fractions
equations
linear
fractional
quadratic
by factoring
pure quadratics
the quadratic formula
radical equations
Systems of Equations
solving by elimination
solving by substitution
solving by graphing
inconsistent and dependent systems
solving by Cramer’s rule
expanding determinants by minors
Conics
ellipse
major and minor axes
vertices and foci
reflective property
circle
parabola
hyperbola
graphing inequalities in two variables
conic sections not centered at the origin
Functions
definition
domain, codomain, range, image
1-1, onto, 1-1 correspondence
inverse functions
relations
identity function
Looking Back
long division of polynomials
Linear Programming, Partial Fractions, and Math Induction
the four cases for partial fractions
numerals vs. numbers
very large numbers
Sequences, Series, and Matrices
arithmetic
last term formula
sum
matrix addition and multiplication
geometric
last term
sum of finite series
sum of infinite series
sigma notation
Permutations and Combinations
the fundamental principle
factorial
P(n, r)
C(n, r)
permutations where some of the items are identical
binomial formula
Pascal’s triangle
Geometry
Points and Lines
line segments
collinear points
concurrent lines
midpoint
circular definitions
undefined terms
postulates and theorems
coordinates of a point
Angles
rays
Euclid’s The Elements
acute, right, and obtuse angles
congruent angles
degrees, minutes, and seconds
vertical angles
supplementary angles
linear pair
Triangles
right triangles, hypotenuse, and legs
acute and obtuse triangles
isosceles triangles
scalene triangles
SSS, SAS, ASA postulates
drawing auxiliary lines
equilateral and equiangular triangles
Parallel Lines
coplanar and skew lines
indirect proofs
exterior angles
alternate interior angles and corresponding angles
Perpendicular Lines
theorems, propositions, lemmas, and corollaries
Hypotenuse-Leg Theorem
perpendicular bisectors
distance from a point to a line
Chain the Gate
P & Q (“and”)
P ∨ Q (“or”)
P implies Q
Quadrilaterals
parallelogram
trapezoid
rhombus
kite
rectangle
square
Honors Problem of the Century
midsegment of a triangle
intercepted segments
Area
triangles
parallelograms
rectangles, rhombuses, and squares
perimeter
trapezoids
polygons
Pythagorean Theorem
Heron’s formula
triangle inequality
Junior Geometry and Other Little Tiny Theories
three-point geometry
models for axiom systems
group theory
Similar Triangles
AA postulate
proportions
generalization of the Midsegment Theorem
altitudes
Angle Bisector Theorem
Symbolic Logic
If ∙∙∙ then ∙∙∙ statements
contrapositive
¬ P (“not” P)
truth tables
transitive property of implication
tautology
Right Triangles
mean proportional ( = geometric mean )
three famous right triangles:
3–4–5
45º–45º–90º
30º–60º–90º
adjacent, opposite, hypotenuse
tangent function (from trigonometry)
Circles
center, radius, chord, diameter, secant, tangent
concentric circles
central angles
arcs
inscribed angles
proof by cases
circumference
π
inductive and deductive reasoning
hunch, hypothesis, theory, and law
sectors
Constructions
compass and straightedge
rules of the game
rusty compass constructions
golden rectangles and golden ratio
trisecting an angle and squaring a circle
incenter and circumcenter of a triangle
collapsible compass constructions
46 popular constructions
Non-Euclidean Geometry
attempts to prove the Parallel Postulate
Nicolai Ivanovich Lobachevsky’s geometry
consistent mathematical theories
Georg Friedrich Bernhard Riemann’s geometry
Solid Geometry
a line perpendicular to a plane
distance from a point to a plane
parallel and perpendicular planes
polyhedrons
hexahedron (cube)
tetrahedron
octahedron
icosahedron
dodecahedron
Euler’s Theorem
volume formulas
Cavalieri’s Principle
lateral surface area
volume formulas: cylinders, prisms, cones, pyramids, spheres
Geometry in Four Dimensions
how to tell what dimension you live in
how two-dimensional people know that there is no third dimension
getting out of jail
organic chemistry and why you don’t want to be flipped in the fourth dimension
tesseracts and hypertesseracts
the Chart of the Universe (up to 14 dimensions)
Chapter 13 Coordinate Geometry
analytic geometry
Cartesian/rectangular/orthogonal coordinate system
axes, origin, and quadrants
slope
distance formula
midpoint formula
proofs using analytic geometry
Flawless (Modern) Geometry
proof that every triangle is isosceles
proof that an obtuse angle is congruent to a right angle
19-year-old Robert L. Moore’s modern geometry
∃ (“there exists”)
e, π and √–1
∀ (“for all”)
Senior Year Mathematics
Sine
angle of elevation
opposite and hypotenuse
definition of sine
angle of depression
area of a triangle (A = ½ ab sin θ)
Looking Back
graphing (axes, quadrants, origin, coordinates)
significant digits
Cosine and Tangent
adjacent side
slope and tan θ
tan 89.999999999999999999999º
solving triangles
Looking Back
functions
identity function
functions as machines
domain
range
Trig Functions of Any Angle
initial and terminal sides of an angle
standard position of an angle
coterminal angles
expanding the domain of a function
periodic functions
cosine is an even function
sine is an odd function
Looking Back
factoring
difference of squares
trinomials
sum and difference of cubes
fractions
adding and subtracting
complex fractions
Trig Identities
definition of an identity
proving identities
four suggestions for increasing your success in proving identities
cotangent, secant and cosecant
cofunctions of complementary angles
eight major tricks to prove identities
Looking Back
graphing y = a sin x
graphing y = a sin bx
graphing y = a sin b(x + c)
Radians
degrees, minutes, seconds
sectors
conversions between degrees and radians
area of a sector (A = ½ r²θ)
Conditional Equations and Functions of Two Angles
definition of a conditional equation
addition formulas
double-angle formulas
half-angle formulas
sum and difference formulas
product formulas
powers formulas
Oblique Triangles
law of sines
law of cosines
Looking Back
inverse functions
1-1 functions
finding f inverse, given f
Inverse Trig Functions
using a calculator to find trig inverses
principal values of the arctan, arcsin and arccosine
the ambiguous case
Polar Coordinates
Cartesian coordinates
graph polar equations
converting between Cartesian and polar coordinates
the polar axis and the pole
symmetry with respect to a point and with respect to a line
Looking Back
functions
1-1, onto
domain, codomain
1-1 correspondence
the definition of the number 1
natural numbers
the definition of the number zero
whole numbers
rational numbers
irrational numbers
transcendental numbers
natural logarithms and common logarithms
e
real numbers
algebraic numbers
pure imaginary numbers
complex numbers
the complex number plane
i to the ith power is a real number (≈ 0.2078796)
Polar Form of Complex Numbers
r cis θ means r(cos θ + i sin θ)
de Moivre’s theorem
proof of de Moivre’s theorem
the five answers to the fifth root of 1
Looking Forward to Calculus
the three parts of calculus
what’s in each of the 24 chapters of calculus
what you’ll need to remember from your algebra, geometry, and trig to succeed in each chapter
Click here to return to the Frequently Asked Questions page.
Click here to return to the Home Page.