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Life of Fred: Linear Algebra Answer Key

Life of Fred: Linear Algebra Answer Key
Click to enlarge image(s)
Louisa used to hate math. Then we discovered The Life of Fred and now she LOVES math!

I was highly suspicious as I listened to Louisa laugh through her math lessons and totally enjoy doing them. I was stunned to watch her go straight for math when she started her homeschool work each morning. I picked up the book and read an outlandish story about a miniature boy named Fred and all his adventures. I couldn't imagine she was really learning math, so I asked her to tell me what she had learned so far in the 16 lessons she had completed. She quickly jotted down this list for me:

infinite sets
natural numbers
set notation
coefficients . . . (need I go on?)

I was impressed to say the least! How could a girl who hates math actually be enjoying Algebra and really learning the terminology as well as how to do the operations? I contacted Stan Schmidt, the author of The Life of Fred, and a retired college math professor of 28 years whose self-proclaimed mission is to help kids love math. I asked him, "How do I know a student who does Life of Fred will retain it?," to which he replied, "How much of your school algebra did you retain?" Ouch!

The idea behind Life of Fred is that if students have an enjoyable experience and have fun doing their math, they will remember it and use it and have a good taste in their math about the whole subject. The sub-title on each of his math books is "As Serious As it Needs to Be". And that is just the point: math doesn't need to be horrid and dry. This is math—just as serious as it needs to be—and I can tell you from Louisa's smiles and chuckles, that's not very serious at all!

As a bonus, these books are very low priced compared to any other math books on the market. (Compare to Saxon at $50-70)

If you have a creative child who is languishing on traditional math programs, try Life of Fred!

Math, As Serious As it Needs to Be!

Beware: This is not a traditional math book. This is a child-directed course. The student reads the adventure story, does the math problems that occur as a natural part of the story, and checks their answers (the solutions are right there for the looking.) And learns to love math in the process! You will not get the detailed formula explanations that you get in a traditional math book. I am still amazed that kids can read the story and learn the concepts, but they do!

Life of Fred: Trigonometry


angle of elevation
opposite and hypotenuse
definition of sine
angle of depression
area of a triangle (A = ½ ab sin θ)

Cosines and Tangents

adjacent side
slope and tan θ
tan 89.999999999999999999999º
solving triangles

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

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

Radian Measurement

degrees, minutes, seconds
conversions between degrees and radians
area of a sector (A = ½ r²θ)

Conditional Trig 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

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

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 fifth root of 1

Plus a review of:

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
real numbers
algebraic numbers
pure imaginary numbers
complex numbers
the complex number plane
i to the ith power is a real number (≈ 0.2078796)

Hardcover, 318 pages.

Click here for Life of Fred Questions and Answers.

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