YOU are better than YOU think. Show yourself how:
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Read logic
chapters 1 to 5 in online volume Three
Skills for Algebra for greater skills & confidence
in work |
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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.
Slopes and Velocity
Distance Versus Time
Signed Distance along a Road
Suppose in traveling along a road, position at time t is given say by d = f(t). The coordinate d gives a signed distance to the origin or point of reference. Assume positions on one side of this origin have a positive d-coordinate and the positions on the other side of this origin have a negative d coordinate. The absolute value or magnitude of d, that is |d|, gives the unsigned distance to the origin or point of reference. The coordinate d will just be called the distance or signed distance hereafter.
Constant Speed and Velocity Example
Henry Snail walks along a path away from its origin for four hours at a rate of 6 kilometers per hour. He started at 1 p.m., eight kilometers from the origin.
Problem: Graph his distance d to the origin versus the time t since he began.
Solution. His speed s = 6 kilometers per hour = 6 ·[km/hour]· Thus he travels
| 6 km in 1 hour | and | 12 km in 2 hours, |
| 3 km in [1/2] hour | and | 18 km in 3 hours, |
| 0.1 km in [1/60] hour | and | 120 km in 20 hours. |
Harry travels a distance Dd = s Dt in time Dt. This information allows us to form the following table,
| elapsed time t |
distance Dd traveled |
distance d to origin |
point (t,d) on graph |
| 0hr | 0km | 8km | A = (0 hr, 8 km ) |
| 1hr | 6km | 14km | B = (1 hr, 14 km ) |
| 2hr | 12km | 20km | C = (2 hr, 20 km ) |
| 3hr | 18km | 26km | D = (3 hr, 26 km ) |
| 4hr | 24km | 34km | E = (4 hr, 34 km ) |
Here the slope m has the role of speed or velocity. That is,
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everywhere on the graph. Observe that
| d | = | 6 | · | km hour |
+ 8 km. |
Area Content Summary
Hint: See site area on solving linear equations to strengthen fraction sense and algebra skills together. Good luck. |