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YOU are better than YOU think. Show
yourself how:
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Logic
chapters 1 to 5 re- appear not in sequence, as is or longer,
in Volume 1A, Pattern Based
Reason, Bon Appetite.
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
Logic
mastery makes the hard, easier. Logic
mastery leads to better, stronger and richer comprehension. Logic
mastery improves reading and writing. Logic
mastery ease learning difficulties. Logic
mastery gives a headstart. In sum, logic
mastery will develops critical thinking, improve reading and writing,
and give a firmer base for work and studies at many levels. Good luck.
After logic,
(a) continue reading Three
Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving
liinear Equations ; or (b) see this calculus
starter lesson and Volume 3, Why
Slopes & More Math, chapters 2 to 6;
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Caution: Site advice is approximately
correct, for some circumstances, not all. That leaves room for thought |
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What may be learnt and when depends on how skills
and concepts are developed. Making the hard easier and clearer will allow
earlier & richer development of skills and concepts.
Try the Twiddla
Whiteboard. In principle, it allows
to people to draw and chat together online on a copy of this webpage or a clean
sheet. The chat may be via text or audio. Visit www.twiddla.com
to set up whiteboards to work with the webpage of your choice.
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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Calculation of Velocity
Note that speed is an everyday term. It is never negative. In the above
graph, the speed is given by the magnitude (absolute value) of the slope m.
In contrast, velocity is a technical term. In can be positive, zero or negative.
In a distance d versus time t graph, the velocity v is
given by the slope m, and can be positive, zero or negative.
A graph of Barbara's position versus time follows. Find her velocity for each
portion of her journey }
if the coordinates of the ends of each line segment in the above graph are as
follows.
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P1 = (0min,80 km)
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P2 = (30min,40 km) |
| P3 = (60min,120 km) |
P4 = (90min,120 km) |
| P5 = (150min,90 km) |
P6 = (210min,0 km) |
Solution. The rise over run ratio gives the following
slope mj on the j-th interval for 1 £
j £ 5, that is for j=1,2,3,4 or 5. The
calculations ad nauseum follow.
ad nauseum follow.
Solution.
The rise over run ratio gives the following
slope mj on the j-th interval for 1 £ j £ 5, that
is for j=1,2,3,4 or 5. The calculations ad nauseum follow.
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40 30 |
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km min |
= - |
4 3 |
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km min |
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120 km-40 km 60 min -30min |
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120 km-120 km
90 min -60min |
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90 km-120 km 150min- 90min |
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= - |
30 60 |
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km min |
= - |
1 |
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km min |
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90 60 |
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km min |
= - |
3 2 |
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km min |
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www.whyslopes.com
Fractions, Ratios, Units, Rates
& Proportionality
Fraction
Starter Lesson
(simplify, multiply, divide & then add or subtract)
Area Map & Intro Fraction Starter Lesson A Fraction Starter Lesson B 1 What is a Fraction 2 Multiplication I 3 Multiplication II 4 Multiplication III 5 Equivalent Fractions 6. Mixed Numbers 7 Comparison 8 Addition I 9 Addition II 10 Addition III 11 Multiplication IV 12 Division 13 Two Term Ratios 14 Implied Ratios 15 Multiple Ratios 16 Units in Arithmetic 16 Longer Explanation 16 Change Units 16 Products of Quantities 16. Fractions with Units 16. Division+Reciprocals 17 Proportionality 17 Examples 18 Rates & Slopes EGs 18 Constant Rate 18 Varying Rate 18 Velocity Calc., EGs 18 Changing Units 18 Slopes and Units 18 Slopes, No Units 19 RealPlayer Videos Links
Arithmetic Videos - Real Player Format
Decimal Addition
Methods
Decimal
Subtraction Methods
Decimal
Multiplication Methods
Decimal Division
Methods
Fractions
Primes
Greatest Common
Divisors
Least Common Multiples
Square Root
Simplification
Area Content Summary
- Fraction Starter Lesson
- Real Player Videos on Operations with Primes and
Fractions
- Continuous Ruler & Line Segment
model for fractions and operations on fractions - Number Theory Area
points to the general model.
- Distinction between Ratios and Fractions, a nuance:
While binary ratios a:b may be identified with a fraction, triple
ratios a:b:c and further multiple ratios cannot.
- Saying how to add and subtract like monomials in
units and their powers, and saying how multiply and divide like and
unlike monomials leads to fraction like expressions involving units
and a framework for discussion rates - ratios of quantities - a
framework for handling proportionality constants, and framework for
carrying units through calculation in quantitative disciplines
Hint: See site area on solving linear equations to strengthen
fraction sense and algebra skills together. Good luck. |
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