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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