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 5 1/2, 7 1/2, 8 1/2, 11 1/2, 12 1/2, and 13 1/2) 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

 

 

 

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