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.
Angle-Side-Angle Method for Triangle
Construction and Duplication.
Given the length of one side and the two adjacent angles, an isometric copy can be constructed. Click on diagram for steps.
Four ASA Variations: If the line segment DF is drawn "horizontally", then the given angles may be drawn above DF with the larger angle at D or the larger angle at F. That gives two isometric triangles. Alternatively, the given angles may be drawn on the down side of DF, again with the larger angle at D or at F. That leads to two more triangles.
ASA Isometry Assumption (and Criteria)
If there is a correspondence between the vertices such that two angles and the included side are isometric then the triangles are isometric. Moreover, both could be built or rebuilt by the same construction ASA method, and each may be moved by a sequence of translations, rotations and/or reflections, so that sides and vertices coincide with the other.An Angle-Side-Angle Method for Triangulization of Position in Navigation
answering the question where were we?
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With the aid of a compass that determines the direction of the north pole, the navigator on a boat or plane at P measures angle PAN and angle PNB in the direction of two points A and B (buoys or landmarks) on land or water, points whose location on the map is known and marked. The navigator then draws rays with those angles from the points A and B. His location at the time of measurement is their P point of intersection. The three points A B and P determine a triangle.
Remark: There is a time delay between measuring the angles and determining the location P on the map. During that time, the boat or plane may have moved away from P. The direction and distance from P may be estimated using the direction and speed of travel away from P.
Remark: Satellite-based GPS (Geo Positioning Systems) give an alternate method for determining the location of P on a paper map or an on-screen display of one.
www.whyslopes.com
4. Euclidean Geometry
Advice & Directions Correspondence Isometry Side-Side-Side Side Angle Side Angle-Side-Angle Isoceles Right Bisector Construction, Etc. Perpendicular - Point to Line SSS Failure SAS Failure ASA Failure Parallel Lines Angle Sum Similarity Right Triangle Similarity Trig or Similarity Parallelograms Kites From Triangles Duplication Parallelogram from Triangle Duplication Addition of points in the plane Multiplication of Points in the Plane Distributive Law, Step I Distributive Law, Step II Distributive Law, Step III
Above Average Students in Geometry may enjoy the site geometric introduction of complex numbers and the wordy volume 1A, Pattern Based Reason.
For algebra, logic starter lessons, see Volume 2, chapters 1 to 12, plus 14, 16 and 17.
Analytic Geometry, Functions & Trig
(FN) What are Functions?
(FN) Functions - More
SZM: Sign, Zero, Monoticity
(L) Lines Summary
(P) Polynomials (*,+,-)
(Q) Quadratics
(D) Simplify Square Roots
(T) Unit Circle Trig
Conic Sections
More For Analytic Geometry:
Real Numbers
Say More Positive
Linear Inequalities
Triangle Inequality
Absolute Value |x|
|x| Eq'ns & Inequalities
Rectangular Coords
Shortest Path
Distance Formulas
Add & Multiply Points
Polar Coordinates
Radians
(A) Vectors
(A) Coordinate Arithmetic
(A) Navigation on Maps
(A) Addition Geometrically
(A) Rotation
(PT) Translations
(PT) Dilatations
PT: Rotations Easy Consequences of this (newest) Complex Number. Starter Lesson follow below to provide an alternate development of HS or college maths.
Vec & Cmplx No Applet
B2 C. Conjugates
B3 Pythagoras
B4 Distance
B5 Rt Triangle Similarity
B6 Trig., Functions
B7 Dot & Cross Products
B8 Cosine Law
B9 Exponential & cis fns
B10 Easy Trig Identities
B11 Set Viewpoint Lesson Plans and lessons
Secondary I - fractions & allied concepts (decimals, percentages)Secondary IV - Functions to Trig & Statistics
Algebra Lesson Notes - All levels
Great_Expectations: If you can learn to follow a multi-step methods in any subject precisely, you can do so in other subjects, as well.
Good news: Site pages identify what you need to study.
Bad news: Site pages do not explain everything
Worse news: Learning takes time, yours