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Tutors
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YOU are better than YOU think. Show
yourself how:
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Logic
Mastery
Amazing, Amusing, Amorous, Delicious, Delightful,
Edifying, Strengthening Elixir.
It eases work & learning difficulties Makes the hard easier. Opens
eyes. Leads to greater precision.
in reading and writing
Do not leave here without it - Logic
mastery will develops critical thinking, improve reading and
writing, and give a firmer base for work and studies at many levels.
Good luck.
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Caution: Site advice is
approximately correct, for some circumstances, not all. Site How-TOs
are logically developed, but not tried and tested. That leaves
room for thought and refinement.. |
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After logic,
(a) continue reading Three
Skills for Algebra, chapters 8 to 14 and do so alongside site
area on solving
linear2007 Equations ; or (b) see this calculus
starter lesson and Volume 3, Why
Slopes & More Math, chapters 2 to 6;
For online automated help in senior
high school maths & calculus, visit quickmath.com
For Automatic Calculus and Algebra Help with derivatives, integrals,
graphs, linear equations, matrix algebra, visit calc101.com
With overlap, each site quickmath
& calc101offers a different
range of services, some free, some not, all based on webmathematica.
Good luck.
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Explore collaborative whiteboards from groupboard,
twiddla or
scriblink.
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Finished
[ Area Intro ] [ Up ] [ 6A Introductory Exercises ] [ 6B Algebra Described and Derived Theory ] [ 6C Theory Summary ] [ 6D Example: Compound Growth & Decay ] [ 6E Example: More Growth & Decay ]
Compound Growth and Decay
Objective: (i) Develop algebraic reasoning skills and
sense by comparing and contrasting arithmetic and algebraic approaches to the
solution of an equation; (ii) give an immediate, practical, calculator
oriented application of powers and radicals, if not logarithms.
The online version of Chapter
14, Compound Interest Formula, in the site Volume 2, Three
Skills for Algebra, begins a numerical exercise to imply the compound
interest formula
where P is the initial deposit, i is the percentage growth (decay if
negative) per period expressed as a decimal, and A is the amount present after n
periods.
The formula here with different interpretations of the variables may be
used to model, population growth for bacteria and fish in ideal or
controlled situations, radio-active decay and dating, and investment
growth and decay (if i = rate of return on investment).
The chapter shows how to use this formula directly and indirectly.
Direct use involves calculation of A given the values of the other three
quantities P, i and n in the formula. Indirect use means given A, and two of the
quantities P, i and n, find the third. The arithmetic approach entails of
substitution of the numerical values of the given quantities into the formula
and then algebraically solving the resulting equation for the the missing
quantity. The algebraic approach entails algebraically solving the resulting
equation to obtain a general formula for the missing quantity in terms of
the given quantities, and then using the formula. Chapter
14 includes and contrasts arithmetic and algebraic approaches to the
indirect use of the compound interest formula. Arithmetic approach and the
evaluation of the formulas in this chapter depend on a calculator to compute n-th
powers and n-th roots, and, optionally, on calculators to compute the natural
logarithm. Here the logarithmic formula for the number of periods n can be given
to motivate the use of the calculator.
Using the properties of logarithms to the derive the formula would be a
continuation of the enriched topic in the above treatment of exponents and
radicals.
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www.whyslopes.com
Lesson & Lesson Plans for
Secondary IV
a reference for learning and teaching functions, polynomials, solving linear
systems,
powers + exponents + bases + radicals (roots) , quadratic formulas, equations
of straight lines
1A. Master Logic
1B. Problems Solving Method
2A Solve Linear Equations i
2B.Solve Linear Equation II
2C Use Equal Sign Properly
2D. Perfect Arithmetic Skills
3 Words & Symbols
3 Goals to Set for Students
4 Use Equations Backwardly
5. Master Functions & Relations
6. Exponents & Radicals I
7. Straight Lines
8. Polynomials (x,/,+/-)
9. Quadratics
10 Prove it
13 Similarity Scale Factors
12 Trig & Triangles
14 Statistics
MEQ Intermediate Objectives
Remarks for Teachers
Sit down and study - no one else can do that for you.
Advice and Directions
What to do in School & Why
How
to Study Maths & Why
Preparing
for Science
Good News: If you can learn to follow a multi-step
methods in any subject precisely, you should be able to do so in other
subjects, as well. Hint: Start with arithmetic
Words Before Symbols:
What is a Variable?
Level: Secondary II to VI, or Grades 7 to 12)
Introduction
Variation between Examples
Variation of Letters
A letter denotes a variable
Cases of Double Variation
Three Notions of a Variable
Constants, Parameters
& Variables
Talking about numbers
Dependent
or Independent
Variable, a Matter of Choice
Complex number starter lesson
Arithmetic Videos
Fractions
Primes
Greatest Common Divisors
Least Common Multiples
Square Root Simplification
Arithmetic Videos
Decimal Addition Methods
Decimal
Subtraction Methods
Decimal
Multiplication Methods
Decimal Division Methods
Fraction
Starter Lesson
(simplify, multiply, divide &
then add or subtract)
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