Math is FUN and EASY =)

Introduction of a straight line using The Geometer's Sketchpad

2011-04-25T22:31:00.000-07:00

okey ini adalah satu sofware yang agak mudah digunakan. Jadi tujuan entry ini adalah untuk menguguhkan lagi konsep adik-adik atau kawan-kawan atau cikgu-cikgu kat luar sana, samada untuk belajar mahupun mengajar. Ilmu untuk dikongsi kan.. =)

modul saya ini bertajuk Introduction of a straight line.

Jadi jom kita explore........................... =)

saya dah upload dekat scribd. harap membantu :)

http://www.scribd.com/doc/53921317/Introduction-of-a-Straight-LIne-using-GSP-software

logarithms

2010-08-22T02:34:00.000-07:00

Basic rule of logarithms

mathematics symbols

2010-08-22T02:22:00.000-07:00

Prefix

2010-08-22T02:19:00.000-07:00

Polygon 2

2010-08-22T01:26:00.000-07:00

Name	Sides	Interior Angle
Triangle (or Trigon)	3	60°
Quadrilatetal (or Tetragon)	4	90°
Pentagon	5	108°
Hexagon	6	120°
Heptagon (or Septagon)	7	128.571°
Octagon	8	135°
Nonagon (or Enneagon)	9	140°
Decagon	10	144°
Hendecagon (or Undecagon)	11	147.273°
Dodecagon	12	150°
Triskaidecagon	13	152.308°
Tetrakaidecagon	14	154.286°
Pentadecagon	15	156°
Hexakaidecagon	16	157.5°
Heptadecagon	17	158.824°
Octakaidecagon	18	160°
Enneadecagon	19	161.053°
Icosagon	20	162°
Triacontagon	30	168°
Tetracontagon	40	171°
Pentacontagon	50	172.8°
Hexacontagon	60	174°
Heptacontagon	70	174.857°
Octacontagon	80	175.5°
Enneacontagon	90	176°
Hectagon	100	176.4°
Chiliagon	1,000	179.64°
Myriagon	10,000	179.964°
Megagon	1,000,000	~180°
Googolgon	10¹⁰⁰	~180°
n-gon	n	(n-2) × 180° / n

Polygons

2010-08-22T01:13:00.000-07:00

Mathematical reasoning & logic

2010-08-21T22:47:00.000-07:00

MATHEMATICAL REASONING (CHAPTER 4 FORM 4)

LOGIC ( CHAPTER 1 TMC 2013 )

Statement

A sentences that is either true or false

ØDetermine whether the given sentence is a statement.

ØTo determine whether the statements are true or false.

ØConstruct true or false statements using given numbers and mathematics symbols.

Proposition

A declarative statements that either true or false

ØTo determine whether the propositions are true or false.

Quantifiers

·All

·Some

ØConstruct statements using quantifiers.

ØDetermine whether the statements contain quantifiers are true or false.

ØDetermine quantifiers can be generalized to cover all cases by using quantifier ‘all’.

ØConstruct a true statement using quantifiers.

Predicates and Quantifiers

·universal quantifiers ["x P(x)]

·existential quantifiers [$x P(x)]

ØIdentifying predicates.

ØDetermine true or false predicates.

ØQuantifier negation

ØMultiple quantifiers.

Operations on statement

Negation of a statement

ØChange the truth value of given statement by placing the word not or no

Using symbols : ~

Compound statement :

AND and OR

ØIdentify two statements from compound statements.

ØForm a compound statement by combining two given statements using word ‘and’ and ‘or’

ØDetermine the truth value of a compound statement which is the combination of two statements.

Logical operators

Negation

ØSymbol of negation : ¬

Logical operators.

Conjunction [AND (Ù)], disjunction [OR (Ú)], exclusive OR [ XOR (⊕)]

ØTo construct the truth tables based on logical operators.

Precedence of logical operators

Negation (¬), conjunction (Ù), disjunction (Ú), implication (→), biconditional (↔).

Propositional equivalence

ØLogical equivalences if pΞq is tautology

ØProving using logic laws

Implication

Antecedent and consequent of an implication.

ØIdentify the antecedent and consequent of an implication ‘if p, then q’.

ØConstruct the mathematical statements in the form of if p then q.

Combining two implications using ‘if and only if’

ØWrite two implications from a compound statement

ØConstruct a mathematical statements

Converse of an implication

ØDetermine the converse of a given implication

ØDetermine whether the implication is true or false

Logical connective : implication

Biconditional statement (↔)

ØConstruct the truth table.

ØTo prove about tautology

Converse, inverse, contrapositive

ØDetermine the converse, inverse, contrapositive of a given proposition.

Argument

Premise and conclusion of an argument.

ØIdentify the premises and conclusion of a given simple argument

ØDraw a conclusion based on two given premise and vise versa.

Argument form

ØMake a conclusion based on

·argument I

·argument II

·argument III

ØComplete an argument, given a premise and the conclusion.

Rules of inference

ØPattern of logically valid deductions from hypotheses to conclusion

ØProving using all rules of inferences.

ØTo produce a valid argument.

There are:

·Hypothetical syllogism

·Modus ponens

·Modus tollen

·Addition

·Simplification

·Conjunction

·Disjunctive syllogism

·Resolution

vThere are various forms of incorrect reasoning called fallacies that lead to invalid argument. (Affirming the conclusion and denying the hypotheses.

DEDUCTION AND INDUCTION

•Deductive and inductive reasoning.

•Conclusion by deductive reasoning.

•Conclusion by inductive reasoning.

Proof techniques

Lemma, corollary, conjecture

ØDirect proof

ØIndirect proof

ØTrivial proof

ØVacuous proof

ØProof by contradiction.

Circles formula

2010-08-21T10:45:00.000-07:00

Diameter = 2 x radius of circle.

Circumference of Circle = PI x diameter = 2 PI x radius
where PI = = 3.141592...

Area of Circle:
area = PI r²

Length of a Circular Arc: (with central angle )
if the angle is in degrees, then length = x (PI/180) x r
if the angle is in radians, then length = r x

Area of Circle Sector: (with central angle )
if the angle is in degrees, then area = (/360)x PI r²
if the angle is in radians, then area = ((/(2PI))x PI r²

Equation of Circle: (Cartesian coordinates)

for a circle with center (j, k) and ra

dius (r):

(x-j)^{^2} + (y-k)^{^2} = r^{^2}

Equation of Circle: (polar coordinates)

for a circle with center (0, 0

): r() = radius

for a circle with center with

polar coordinates: (c, ) and

radius a:
r² - 2cr cos( - ) + c² = a²

Equation of a Circle: (parametric coordinates)
for a circle with origin (j, k) and radius r:
x(t) = r cos(t) + j y(t) = r sin(t) + k

Circles

2010-08-21T10:31:00.000-07:00

Circles is eveywhere.. :)

In class we learn about geometry, and learn about circles.

Definition : A circle is the locus of all points equidistant from a central point.

radius : distance from center of circle to any point on it.

Arc : a curved line that is part of the circumference of a circle.

circumference: the distance around the circle.

diameter : the longest distance from one end of a circle to the other.

origin : the center of the circle.

pi () : A number, 3.141592..., equal to (the circumference) / (the diameter) of any circle.

sector : is like a slice of pie (a circle wedge).

tangent of circle: a line perpendicular to the radius that touches ONLY one point on the circle.

Quadratic equations

2010-08-18T09:22:00.000-07:00

Functions

2010-08-18T07:20:00.000-07:00

Study Maths (advice for teachers)

2010-08-17T11:43:00.000-07:00

Time and Place Available for studying Mathematics

Due to differences in home and social life, some students have more time and a better environment for studying mathematics than others. Many students' out-of-class time is dominated by jobs or nonacademic school-sponsored activities such as athletics or service organizations. Understanding restrictions on the time students have doing mathematics helps you diagnose difficulties and plan assignments. Many students need to be taught how to set priorities, schedule their time, and faithfully complete assignments.

Tables of Integrals

2010-08-02T21:20:00.000-07:00

Power of x.

xⁿ dx = xⁿ⁺¹ (n+1)^-1 + C
(n -1)

x^-1 dx = ln|x| + C

Exponential / Logarithmic

e^x dx = e^x + C	b^x dx = b^x / ln(b) + C
ln(x) dx = x ln(x) - x + C

Trigonometric

sin x dx = -cos x + C	csc x dx = - ln\|csc x + cot x\| + C
cos x dx = sin x + C	sec x dx = ln\|sec x + tan x\| + C
tan x dx = -ln\|cos x\| + C	cot x dx = ln\|sin x\| + C

Trigonometric Result

cos x dx = sin x + C	csc x cot x dx = - csc x + C
sin x dx = -cos x + C	sec x tan x dx = sec x + C
sec² x dx = tan x + C	csc² x dx = - cot x + C

Inverse Trigonometric

arc sin x dx = x arc sin x + (1-x²) + C

arc csc x dx = x arc cos x - (1-x²) + C

arc tan x dx = x arc tan x - (1/2) ln(1+x²) + C

Inverse Trigonometric Result

(1 - x²)

= arc sin x + C

x (x² - 1)

= arc sec|x| + C

1 + x²

= arc tan x + C

Useful Identities

arccos x = /2 - arcsin x
(-1 <= x <= 1)

arccsc x = /2 - arcsec x
(|x| >= 1)

arccot x = /2 - arctan x
(for all x)

Hyperbolic

sinh x dx = cosh x + C	csch x dx = ln \|tanh(x/2)\| + C
cosh x dx = sinh x + C	sech x dx = arctan (sinh x) + C
tanh x dx = ln (cosh x) + C	coth x dx = ln \|sinh x\| + C

Differentiation Rules =)

2010-08-02T21:03:00.001-07:00

Happy learning with all this rules! =)
Eventhough most of this formula is given in your examination.. I hope all of us can memorize this rules so that we can answer the question quickly without wasting our time to check the formula. yehaaa!
Math is FUN!

Conversion Table

2010-08-02T20:49:00.000-07:00

IMPERIAL

Length	Area	Capacity	Weight
1 mile = 1760 yards 1 mile = 8 furlong 1 furlong = 10 chains 1 chain = 4 rods 1 rod = 5 1/2 yards 1 yard = 3 feet 1 foot = 12 inches	1 sq. mile = 640 acres 1 acre = 4840 sq. yard 1 sq. yard = 9 sq. feet 1 sq. foot = 144 sq. inches	1 gal. = 4 quarts 1 quart = 2 pints 1 pint = 4 gills 1 pint = 34.6774 inchs³ 1 gill = 5 fl. oz. 1 fl. oz. = 8 fl. drachms 1 US gal = 0.8327 gal 1 US pint = 0.8327 pint 1 US pint = 16 fl. oz. 1 yard³ = 27 feet³ 1 foot³ = 1728 inches³	1 ton = 20 cwt 1 ton = 2240 lb. 1 ton = 1.12 US ton 1 cwt = 4 quarters 1 quarter = 2 stone. 1 stone = 14 lb. 1 lb. = 16 oz. 1 oz. = 16 drams 1 oz. = 437.5 grains 1 US ton = 2000 lb.

METRIC

Length	Area	Capacity	Weight
1 km = 10 hm 1 km = 1000 m 1 hm = 100 m 1 m = 10 dm 1 dm = 10 cm 1 cm = 10 mm	1 km² = 100 hectares 1 hectare = 100 ares 1 are = 100 m² 1 m² = 100 dm² 1 dm² = 100 cm² 1 cm² = 100 mm²	1 m³ = 1000 litres 1 litre = 1 dm³ 1 litre = 1000 cc 1 litre = 1000 ml	1 tonne = 1000 kg 1 kg = 1000 g 1 g = 1000 mg

IMPERIAL to METRIC

Length	Area	Capacity	Weight
1 mile = 1.609 km 1 yard = 0.9144 m 1 foot = 0.3048 m 1 inch = 25.4 mm	1 sq. mile = 2.59 km² 1 acre = 0.4047 hectares 1 acre = 4046.86 m² 1 sq. yard = 0.8361 m² 1 sq. foot = 0.0929 m² 1 sq. inch = 645.16 mm²	1 gallon = 4.5461 litres 1 US gallon = 3.785 litres 1 pint = 0.5683 litres 1 cu. inch = 16.3871 cm³	1 ton = 1.016 tonnes 1 lb. = 0.4536 kg 1 oz. = 28.3495 g 1 US ton = 0.9072 tonnes

METRIC to IMPERIAL

Length	Area	Capacity	Weight
1 km = 0.6214 miles 1 m = 1.0936 yards 1 m = 3.2808 feet 1 mm = 0.0394 inches	1 km² = 0.3861 mile² 1 km² = 247.105 acres 1 hectares = 2.4711 acres 1 m² = 10.7639 feet² 1 mm² = 0.0016 inches²	1 litre = 0.22 gal. 1litre = 0.2642 US gal. 1 litre = 1.7598 pint 1 m³ = 219.969 gal. 1 m³ = 35.3147 feet³	1 tonne = 0.9842 ton 1 tonne = 1.1023 US ton 1 kg = 2.2046 lb. 1 kg = 35.274 oz.

TEMPERATURE

deg. C to deg. F	deg. F to deg. C
deg. C x 9/5 + 32 = deg. F	(deg. F - 32) x 5/9 = deg. C

Maths Trick in Multiplying

2010-08-02T12:01:00.000-07:00

I hope this video will help student to answer multiply questions quickly without wasting time.

sin x dx = -cos x + C	csc x dx = - ln\|csc x + cot x\| + C
cos x dx = sin x + C	sec x dx = ln\|sec x + tan x\| + C
tan x dx = -ln\|cos x\| + C	cot x dx = ln\|sin x\| + C