[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (6) Counting and Probability āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã1ãPermutation and Combination āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã6.1.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã6.1.aãāĻŦāĻŋāĻ¨ā§āĻ¯āĻžāĻ¸ āĻ āĻ¸āĻŽāĻžāĻŦā§āĻļ Counting problems āĻāĻ° āĻāĻāĻāĻŋ āĻŽā§āĻ˛āĻŋāĻ āĻŦāĻŋāĻˇā§ āĻšāĻ˛ā§āĻ āĻāĻāĻāĻŋ āĻāĻāĻ¨āĻž [latex]n[latex] āĻāĻĒāĻžā§ā§ āĻāĻ°āĻžāĻ° āĻĒāĻ°ā§ āĻĻā§āĻŦāĻŋāĻ¤ā§ā§ āĻāĻ°ā§āĻāĻāĻŋ āĻāĻāĻ¨āĻž āĻ¯āĻĻāĻŋ [latex]m[latex] āĻāĻĒāĻžā§ā§ āĻāĻ°āĻž āĻ¯āĻžā§, āĻ¤āĻžāĻšāĻ˛ā§ āĻĻā§āĻāĻāĻŋ āĻāĻāĻ¨āĻž āĻāĻāĻ¸āĻžāĻĨā§ [latex]mn[latex] āĻāĻĒāĻžā§ā§ āĻāĻāĻžāĻ¨ā§ āĻ¯āĻžā§āĨ¤ āĻāĻŋāĻā§ āĻāĻĻāĻžāĻšāĻ°āĻŖ āĻĻā§āĻā§āĻ¨āĻ […]
Category: Math Center
MC1: Geometry
MC2: Algebra
MC3: Number Properties
MC4: Decimals, Fraction, Percentage
MC5: Statistics and D.I.
MC6: Counting and Probability
ã1.4.aã āĻŦāĻŋāĻāĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻŦāĻšā§āĻā§āĻ āĻāĻŦāĻ āĻ¤āĻžāĻĻā§āĻ° āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛ā§āĻ° āĻŦāĻŋāĻļāĻĻ āĻāĻ˛ā§āĻāĻ¨āĻž
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (1) Geometry āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã4ã Polygons āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã1.4.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã1.4.aã āĻŦāĻŋāĻāĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻŦāĻšā§āĻā§āĻ āĻāĻŦāĻ āĻ¤āĻžāĻĻā§āĻ° āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛ā§āĻ° āĻŦāĻŋāĻļāĻĻ āĻāĻ˛ā§āĻāĻ¨āĻž Introduction Polygons āĻŦāĻž āĻŦāĻšā§āĻā§āĻ A polygon is defined as a closed shape formed by line segments. Three-sided shapes (Triangles) Four-sided shapes (Quadrilaterals) Other polygons with [latex]n[latex] sides (where [latex]n[latex] is five […]
ã1.5.aã Mixed Geometric Shapes
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (1) Geometry āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã5ã Mixed Geometric Shapes āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã1.5.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã1.5.aã Mixed Geometric Shapes (āĻāĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻā§āĻ¯āĻžāĻŽāĻŋāĻ¤āĻŋāĻ āĻāĻžāĻ āĻžāĻŽā§āĻ° āĻāĻ˛ā§āĻāĻ¨āĻž) āĻŦā§āĻ¤ā§āĻ¤ā§āĻ° āĻā§āĻ¤āĻ°ā§ āĻŦāĻ¨ā§āĻĻā§ āĻāĻ¤ā§āĻ°ā§āĻā§āĻ āĻŦā§āĻ¤ā§āĻ¤ā§āĻ° āĻŽāĻ§ā§āĻ¯ā§ āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻ˛āĻŋāĻāĻŋāĻ¤ āĻāĻ¤ā§āĻ°ā§āĻā§āĻā§āĻ° āĻŦāĻŋāĻĒāĻ°ā§āĻ¤ āĻā§āĻŖāĻĻā§āĻŦā§ā§āĻ° āĻ¯ā§āĻāĻĢāĻ˛ [latex]180[latex]0 āĻšā§āĨ¤ āĻ¯ā§āĻŽāĻ¨, āĻāĻĒāĻ°ā§ āĻŦā§āĻ¤ā§āĻ¤ā§āĻ° āĻŽāĻ§ā§āĻ¯ā§ āĻāĻāĻāĻŋ āĻāĻ¤ā§āĻ°ā§āĻā§āĻ āĻāĻāĻāĻž āĻšā§ā§āĻā§, āĻ¯āĻžāĻ° āĻāĻžāĻ°āĻāĻŋ āĻā§āĻŖ āĻšāĻ˛ā§ [latex]p, q, r, s[latex] āĨ¤ āĻ¤āĻžāĻšāĻ˛ā§, […]
ã1.2ã(b) āĻŦāĻŋāĻāĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻ¤ā§āĻ°āĻŋāĻā§āĻ āĻāĻŦāĻ āĻ¤āĻžāĻĻā§āĻ° āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (1) Geometry āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§ (2) Triangle āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã1.2.bãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã1.2ã(b) āĻŦāĻŋāĻāĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻ¤ā§āĻ°āĻŋāĻā§āĻ āĻāĻŦāĻ āĻ¤āĻžāĻĻā§āĻ° āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛ Median āĻŦāĻž āĻŽāĻ§ā§āĻ¯āĻŽāĻž āĻ¤ā§āĻ°āĻŋāĻā§āĻā§āĻ° āĻ¯ā§ āĻā§āĻ¨ āĻļā§āĻ°ā§āĻˇ āĻĨā§āĻā§ āĻŦāĻŋāĻĒāĻ°ā§āĻ¤ āĻŦāĻžāĻšā§āĻ° āĻŽāĻ§ā§āĻ¯āĻŦāĻŋāĻ¨ā§āĻĻā§āĻ° āĻ¯ā§āĻāĻ āĻ°ā§āĻāĻžāĻā§āĻ āĻŦāĻ˛ā§ āĻŽā§āĻĄāĻŋā§āĻžāĻ¨ āĻŦāĻž āĻŽāĻ§ā§āĻ¯āĻŽāĻžāĨ¤ It is the line segment joining any vertex of a triangle with the midpoint […]
ã1.2 .aãāĻ¤ā§āĻ°āĻŋāĻā§āĻ āĻĒāĻ°ā§āĻŦ ā§§āĻ āĻā§āĻŖ, āĻŦāĻžāĻšā§, āĻĒāĻŋāĻĨāĻžāĻā§āĻ°āĻŋā§āĻžāĻ¨ āĻ¸ā§āĻ, āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛ āĻ āĻŦāĻŋāĻļā§āĻˇ āĻā§āĻāĻ¸
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (1) Geometry āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§ (2) Triangle āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã1.2 .aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã1.2 .aãāĻ¤ā§āĻ°āĻŋāĻā§āĻ āĻĒāĻ°ā§āĻŦ ā§§āĻ āĻā§āĻŖ, āĻŦāĻžāĻšā§, āĻĒāĻŋāĻĨāĻžāĻā§āĻ°āĻŋā§āĻžāĻ¨ āĻ¸ā§āĻ, āĻā§āĻˇā§āĻ¤ā§āĻ°āĻĢāĻ˛ āĻ āĻŦāĻŋāĻļā§āĻˇ āĻā§āĻāĻ¸ Introduction: āĻŦāĻŋāĻāĻŋāĻ¨ā§āĻ¨ āĻĒāĻ°ā§āĻā§āĻˇāĻžā§ āĻā§āĻ¯āĻžāĻŽāĻŋāĻ¤āĻŋ āĻ āĻāĻļ āĻĨā§āĻā§ āĻ¤ā§āĻ°āĻŋāĻā§āĻ āĻ¸āĻāĻā§āĻ°āĻžāĻ¨ā§āĻ¤ āĻĒā§āĻ°āĻļā§āĻ¨ āĻ¸āĻŦāĻā§ā§ā§ āĻŦā§āĻļāĻŋ āĻĨāĻžāĻā§āĨ¤ āĻ¸āĻŦāĻā§ā§ā§ āĻŦā§āĻļāĻŋ āĻā§āĻ°ā§āĻ¤ā§āĻŦāĻ°ā§āĻĒā§āĻŖ āĻšāĻ˛ā§ āĻ¸āĻŽāĻā§āĻŖā§ āĻ¤ā§āĻ°āĻŋāĻā§āĻ āĻŦāĻž Right triangles (those with a [latex]90[latex]° angle)āĨ¤ […]
ã2.1.aãVariables related basics
 [Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (2) Algebra āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã1ãAlgebra āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã2.1.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã2.1.aãVariables related basics Algebraic Translations āĻŦāĻŋāĻāĻŋāĻ¨ā§āĻ¨ āĻĒāĻ°ā§āĻā§āĻˇāĻžāĻ° āĻŽā§āĻ¯āĻžāĻĨ āĻ¸ā§āĻāĻļāĻ¨ā§ āĻĒāĻžāĻāĻŋāĻāĻŖāĻŋāĻ¤ āĻāĻžāĻ¤ā§ā§ āĻ āĻ¨ā§āĻ āĻ āĻā§āĻ āĻāĻ¸ā§ āĻ¯ā§āĻā§āĻ˛ā§ āĻ āĻ¨ā§āĻ āĻ¸āĻŽā§ algebraic equation āĻāĻ° āĻāĻžāĻˇāĻžā§ āĻ āĻ¨ā§āĻŦāĻžāĻĻ āĻāĻ°āĻžāĻ° āĻĻāĻ°āĻāĻžāĻ° āĻšā§āĨ¤ āĻ¯ā§āĻŽāĻ¨, âāĻĻā§āĻ āĻ āĻāĻā§āĻ° āĻāĻāĻāĻŋ āĻ¸āĻāĻā§āĻ¯āĻž āĻ¸ā§āĻĨāĻžāĻ¨ āĻŦāĻŋāĻ¨āĻŋāĻŽā§ āĻāĻ°āĻ˛ā§â āĻŦāĻžāĻā§āĻ¯ āĻĨā§āĻā§ āĻāĻŽāĻ°āĻž āĻ§āĻ°ā§ āĻ¨āĻŋāĻ¤ā§ āĻĒāĻžāĻ°āĻŋ […]
ã2.4.aãāĻĢāĻžāĻāĻļāĻ¨ āĻāĻŦāĻ āĻāĻ° āĻ¸āĻžāĻĨā§ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻŦāĻŋāĻāĻŋāĻ¨ā§āĻ¨ āĻŦāĻŋāĻˇā§āĻžāĻĻāĻŋ
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (2) Algebra āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã4ãFunctions āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã2.4.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã2.4.aãāĻĢāĻžāĻāĻļāĻ¨ āĻāĻŦāĻ āĻāĻ° āĻ¸āĻžāĻĨā§ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻŦāĻŋāĻāĻŋāĻ¨ā§āĻ¨ āĻŦāĻŋāĻˇā§āĻžāĻĻāĻŋ FUNCTIONS āĻŦāĻŋāĻˇā§āĻ āĻ¸āĻŽāĻ¸ā§āĻ¯āĻžāĻā§āĻ˛ā§ āĻ āĻ¨ā§āĻāĻāĻž āĻāĻ¤āĻŋāĻĒā§āĻ°ā§āĻŦā§ āĻāĻ˛ā§āĻāĻ¨āĻž āĻāĻ°āĻžÂ sequence problem -āĻ° āĻŽāĻ¤ā§āĻāĨ¤ āĻāĻĻā§āĻ°āĻā§ āĻ¸āĻžāĻ§āĻžāĻ°āĻŖāĻ¤āĻ āĻāĻāĻ°ā§āĻāĻŋ āĻ āĻā§āĻˇāĻ° [latex]f()[latex] āĻŦāĻž [latex]g()[latex] āĻ āĻĨāĻŦāĻž āĻ āĻ¨ā§āĻ¯ āĻā§āĻ¨ āĻ āĻā§āĻˇāĻ°ā§āĻ° āĻĒāĻžāĻļā§ āĻāĻāĻāĻŋ āĻŦā§āĻ°āĻžāĻā§āĻā§āĻ° āĻŽāĻ§ā§āĻ¯ā§ variable [latex]x[latex] āĻā§ āĻŦāĻ¸āĻŋā§ā§ āĻāĻŦāĻ āĻ¤āĻžāĻ° āĻĄāĻžāĻ¨ […]
ã1.6.aã āĻ¸ā§āĻĨāĻžāĻ¨āĻžāĻā§āĻ āĻŦāĻŋāĻˇā§āĻ āĻā§āĻ¯āĻžāĻŽāĻŋāĻ¤āĻ āĻāĻ˛ā§āĻāĻ¨āĻž
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (1) Geometry āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã6ãCoordinate Geometry āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã1.6.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã1.6.aã Coordinate Geometry (āĻ¸ā§āĻĨāĻžāĻ¨āĻžāĻā§āĻ āĻā§āĻ¯āĻžāĻŽāĻŋāĻ¤āĻŋāĻ° āĻāĻ˛ā§āĻāĻ¨āĻž) Introduction: āĻŦāĻŋāĻāĻŋāĻ¨ā§āĻ¨ āĻĒāĻ°ā§āĻā§āĻˇāĻžā§Â āĻā§āĻŦ āĻāĻāĻāĻž coordinate geometry āĻĒā§āĻ°āĻļā§āĻ¨ āĻāĻ¸āĻ¤ā§ āĻĻā§āĻāĻž āĻ¯āĻžā§ āĻ¨āĻžāĨ¤ āĻ¤āĻžāĻ°āĻĒāĻ°ā§, āĻāĻŽāĻ°āĻž āĻāĻ āĻ āĻ§ā§āĻ¯āĻžā§ā§ āĻāĻŋāĻā§ āĻŽā§āĻ˛āĻŋāĻ āĻŦāĻŋāĻˇā§ āĻ¨āĻŋā§ā§ āĻāĻ˛ā§āĻāĻ¨āĻž āĻāĻ°āĻŦā§ āĻ¯āĻžāĻ¤ā§ āĻ¸ā§āĻā§āĻĄā§āĻ¨ā§āĻāĻ°āĻž āĻĒāĻ°ā§āĻā§āĻˇāĻžā§ āĻ āĻ§āĻ°āĻŖā§āĻ° āĻĒā§āĻ°āĻļā§āĻ¨ āĻĻā§āĻā§ āĻŦāĻŋāĻĒāĻžāĻā§ āĻ¨āĻž āĻĒā§ā§āĻ¨āĨ¤ The Coordinate […]
ã2.5.aãāĻ āĻ¸āĻŽāĻ¤āĻž āĻŦāĻŋāĻˇā§āĻ āĻāĻ˛ā§āĻāĻ¨āĻž
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (2) Algebra āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã5ãInequality āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã2.5.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã2.5.aãāĻ āĻ¸āĻŽāĻ¤āĻž āĻŦāĻŋāĻˇā§āĻ āĻāĻ˛ā§āĻāĻ¨āĻž Equations āĻāĻ° āĻā§āĻˇā§āĻ¤ā§āĻ°ā§ āĻĻā§āĻāĻāĻŋ āĻāĻŋāĻ¨ā§āĻ¨ āĻ°āĻžāĻļāĻŋāĻ° āĻŽāĻ§ā§āĻ¯ā§ āĻ¸āĻŽāĻ¤āĻž āĻāĻŋāĻšā§āĻ¨ (=) āĻŦā§āĻ¯āĻŦāĻšā§āĻ¤ āĻšā§āĨ¤ āĻāĻ° āĻĒāĻ° āĻ¸ā§āĻāĻžāĻ¨ā§ āĻā§āĻ¨ variable āĻĨāĻžāĻāĻ˛ā§ āĻ¤āĻžāĻ° āĻŽāĻžāĻ¨ āĻāĻŽāĻ°āĻž āĻŦā§āĻ° āĻāĻ°āĻŋāĨ¤Â inequalities āĻāĻ°Â āĻā§āĻˇā§āĻ¤ā§āĻ°ā§ āĻ¸āĻŽāĻ¤āĻž āĻāĻŋāĻšā§āĻ¨ āĻŦā§āĻ¯āĻŦāĻšā§āĻ¤ āĻšā§ āĻ¨āĻž, āĻāĻŋāĻ¨ā§āĻ¤ā§ āĻŦā§āĻšāĻ¤ā§āĻ¤āĻ° (greater than) āĻŦāĻž āĻā§āĻˇā§āĻĻā§āĻ°āĻ¤āĻ° (smaller […]
ã2.6.aãāĻ¸āĻŽāĻžāĻ¨ā§āĻ¤āĻ° āĻāĻŦāĻ āĻā§āĻŖā§āĻ¤ā§āĻ¤āĻ° āĻ§āĻžāĻ°āĻž
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (2) Algebra āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã6ãSeries and Sequences āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã2.6.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã2.6.aãāĻ¸āĻŽāĻžāĻ¨ā§āĻ¤āĻ° āĻāĻŦāĻ āĻā§āĻŖā§āĻ¤ā§āĻ¤āĻ° āĻ§āĻžāĻ°āĻž FORMULAS Formulas are another means by which the your ability is tasted to work with unknowns. Formulas are specific equations that can involve multiple variables. There are [latex]3[latex] major types of Formula problems […]
ã2.3.aãāĻĻā§āĻŦāĻŋāĻāĻžāĻ¤ āĻ¸āĻŽā§āĻāĻ°āĻŖ āĻāĻŦāĻ āĻ¤āĻž āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨ā§āĻ° āĻŦāĻŋāĻāĻŋāĻ¨ā§āĻ¨ āĻāĻĒāĻžā§
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (2) Algebra āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã3ãQuadratic Equations āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã2.3.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã2.3.aãāĻĻā§āĻŦāĻŋāĻāĻžāĻ¤ āĻ¸āĻŽā§āĻāĻ°āĻŖ āĻāĻŦāĻ āĻ¤āĻž āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨ā§āĻ° āĻŦāĻŋāĻāĻŋāĻ¨ā§āĻ¨ āĻāĻĒāĻžā§ āĻāĻ āĻ¨āĻāĻ°ā§ āĻāĻ āĻ āĻ§ā§āĻ¯āĻžā§ā§āĻ° āĻ¸ā§āĻ¤ā§āĻ°āĻ¸āĻŽā§āĻš: [latex]a{ x }^{ 2 }+bx+c=0[latex] āĻāĻāĻžāĻ°ā§āĻ° āĻ¸āĻŽā§āĻāĻ°āĻ¨āĻā§ āĻĻā§āĻŦāĻŋāĻāĻžāĻ¤ āĻ¸āĻŽā§āĻāĻ°āĻŖ āĻŦāĻ˛ā§āĨ¤ solution of this equation is: [latex]\frac { -b\pm \sqrt { { b }^{ 2 }-4ac } […]
ã3.2.aãāĻ˛āĻ¸āĻžāĻā§ āĻāĻŦāĻ āĻāĻ¸āĻžāĻā§: āĻāĻ āĻāĻŋāĻāĻŦ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (3) Number Properties āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã2ãFactors and multiplies: LCM,GCF āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã3.2.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã3.2.aãāĻ˛āĻ¸āĻžāĻā§ āĻāĻŦāĻ āĻāĻ¸āĻžāĻā§: āĻāĻ āĻāĻŋāĻāĻŦ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ Factors and Multiples Factors and Multiples are opposite of each other. Factor āĻšāĻ˛ā§ āĻāĻāĻāĻŋ positive integer āĻ¯āĻž āĻĻāĻŋā§ā§ āĻ āĻ¨ā§āĻ¯ āĻā§āĻ¨ integer āĻā§ āĻāĻžāĻ āĻāĻ°āĻž āĻ¯āĻžā§āĨ¤ [latex]1, 2, 4[latex] and [latex]8[latex] […]
ã3.1.aãāĻŦāĻŋāĻāĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻ¸āĻāĻā§āĻ¯āĻž, āĻ¸ā§āĻĨāĻžāĻ¨ā§ā§ āĻŽāĻžāĻ¨ āĻāĻŦāĻ āĻāĻŋāĻā§ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (3) Number Properties āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã1ãTypes of Numbers āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã3.1.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã3.1.aãāĻŦāĻŋāĻāĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻ¸āĻāĻā§āĻ¯āĻž, āĻ¸ā§āĻĨāĻžāĻ¨ā§ā§ āĻŽāĻžāĻ¨ āĻāĻŦāĻ āĻāĻŋāĻā§ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ āĻāĻ āĻ¨āĻāĻ°ā§ āĻāĻ āĻ āĻ§ā§āĻ¯āĻžā§ā§āĻ° āĻ¸ā§āĻ¤ā§āĻ°āĻ¸āĻŽā§āĻš: āĻ¯ā§ āĻĄāĻŋāĻāĻŋāĻ āĻĒāĻ°ā§āĻ¯āĻ¨ā§āĻ¤ rounding up āĻāĻ°āĻ¤ā§ āĻšāĻŦā§ āĻ¤āĻžāĻ° āĻ āĻŋāĻ āĻĒāĻ°ā§āĻ° āĻĄāĻŋāĻāĻŋāĻā§āĻ° āĻĻāĻŋāĻā§ āĻ¨āĻāĻ° āĻĻāĻŋāĻ¤ā§ āĻšāĻŦā§āĨ¤ āĻ¯āĻĻāĻŋ āĻ¸ā§āĻāĻž [latex]4[latex] āĻŦāĻž āĻ¤āĻžāĻ° āĻāĻŽ āĻšā§, āĻ¤āĻžāĻšāĻ˛ā§ āĻ¸ā§āĻāĻžāĻā§ […]
ã3.4.aãāĻ§āĻžāĻ°āĻžāĻŦāĻžāĻšāĻŋāĻ āĻ¸āĻāĻā§āĻ¯āĻž, āĻ¤āĻžāĻĻā§āĻ° āĻā§ āĻ āĻŽāĻ§ā§āĻ¯āĻŽāĻž āĻ¨āĻŋāĻ°ā§āĻŖā§ āĻāĻŦāĻ āĻ āĻ¨ā§āĻ¯āĻžāĻ¨ā§āĻ¯
 [Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (3) Number Properties āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã4ãConsecutive Number āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã3.4.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã3.4.aãāĻ§āĻžāĻ°āĻžāĻŦāĻžāĻšāĻŋāĻ āĻ¸āĻāĻā§āĻ¯āĻž, āĻ¤āĻžāĻĻā§āĻ° āĻā§ āĻ āĻŽāĻ§ā§āĻ¯āĻŽāĻž āĻ¨āĻŋāĻ°ā§āĻŖā§ āĻāĻŦāĻ āĻ āĻ¨ā§āĻ¯āĻžāĻ¨ā§āĻ¯ âĸ Consecutive multiplies āĻā§āĻŦāĻ˛āĻŽāĻžāĻ¤ā§āĻ° integer āĻĻā§āĻŦāĻžāĻ°āĻž āĻāĻ āĻŋāĻ¤ āĻšā§āĨ¤ âĸ The arithmetic mean (average) and median and equal to the element in the set can be found by figuring out the […]
ã3.6.aãāĻ¸āĻāĻā§āĻ¯āĻžāĻ° āĻŦāĻŋāĻāĻžāĻā§āĻ¯āĻ¤āĻž āĻāĻŦāĻ āĻāĻāĻ āĻ¸ā§āĻĨāĻžāĻ¨ā§ā§ āĻŽāĻžāĻ¨ āĻ¨āĻŋāĻ°ā§āĻŖā§ā§āĻ° āĻĒāĻĻā§āĻ§āĻ¤āĻŋ
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (3) Number Properties āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã6ãDivisibility, Last digit āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã3.6.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã3.6.aãāĻ¸āĻāĻā§āĻ¯āĻžāĻ° āĻŦāĻŋāĻāĻžāĻā§āĻ¯āĻ¤āĻž āĻāĻŦāĻ āĻāĻāĻ āĻ¸ā§āĻĨāĻžāĻ¨ā§ā§ āĻŽāĻžāĻ¨ āĻ¨āĻŋāĻ°ā§āĻŖā§ā§āĻ° āĻĒāĻĻā§āĻ§āĻ¤āĻŋ āĻĻā§āĻāĻāĻŋ integer āĻāĻ° āĻ¯ā§āĻāĻĢāĻ˛ āĻŦāĻž āĻŦāĻŋā§ā§āĻāĻĢāĻ˛ āĻ¸āĻŦ āĻ¸āĻŽā§ āĻāĻ°ā§āĻāĻāĻŋ integer āĻšā§āĨ¤ āĻĻā§āĻāĻāĻŋ integer āĻāĻ° āĻā§āĻŖāĻĢāĻ˛ āĻ¸āĻŦāĻ¸āĻŽā§ āĻāĻ°ā§āĻāĻāĻŋ integer āĻšā§āĨ¤ āĻĻā§āĻāĻāĻŋ integer āĻāĻ° āĻāĻžāĻāĻĢāĻ˛ āĻ¨āĻ¤ā§āĻ¨ āĻāĻāĻāĻŋ integer āĻšāĻ¤ā§ āĻĒāĻžāĻ°ā§ āĻāĻŦāĻžāĻ° āĻāĻāĻāĻž fraction (āĻāĻā§āĻ¨āĻžāĻāĻļ) āĻšāĻ¤ā§ […]
ã3.6.a2ãāĻĻāĻļāĻŽāĻŋāĻāĻ¯ā§āĻā§āĻ¤ āĻ¸āĻāĻā§āĻ¯āĻžāĻ° āĻ¸āĻžāĻšāĻžāĻ¯ā§āĻ¯ā§ āĻ āĻ¨ā§āĻĒāĻžāĻ¤ āĻ āĻāĻžāĻāĻļā§āĻˇ āĻ¨āĻŋāĻ°ā§āĻŖā§
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (3) Number Properties āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã6ãDivisibility, Last digit āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã3.6.a2ãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] Rule: āĻā§āĻ¨ āĻ¸āĻāĻā§āĻ¯āĻžāĻā§ ([latex]p[latex]) āĻāĻ°ā§āĻāĻāĻŋ āĻāĻ¨ā§āĻāĻŋāĻāĻžāĻ° ([latex]d[latex]) āĻĻāĻŋā§ā§ āĻāĻžāĻ āĻāĻ°āĻ˛ā§ āĻāĻžāĻāĻļā§āĻˇ āĻŦāĻž remainder āĻšāĻŋāĻ¸āĻžāĻŦā§ [latex]r[latex] āĻāĻ° āĻŽāĻžāĻ¨ āĻ¸āĻ°ā§āĻŦāĻ¨āĻŋāĻŽā§āĻ¨ [latex]0[latex] āĻāĻŦāĻ āĻ¸āĻ°ā§āĻŦā§āĻā§āĻ [latex](d-1)[latex] āĻĒāĻ°ā§āĻ¯āĻ¨ā§āĻ¤ āĻšāĻŦā§āĨ¤ [latex]r[latex] āĻāĻ° āĻŽāĻžāĻ¨ [latex]d[latex] āĻŦāĻž āĻ¤āĻžāĻ° āĻŦā§ āĻšāĻ¤ā§ āĻĒāĻžāĻ°āĻŦā§ āĻ¨āĻžāĨ¤ āĻāĻĻāĻžāĻšāĻ°āĻŖ āĻ¸ā§āĻŦāĻ°ā§āĻĒ, āĻā§āĻ¨ āĻ¸āĻāĻā§āĻ¯āĻžāĻā§ [latex]13[latex] āĻĻāĻŋā§ā§ āĻāĻžāĻ āĻāĻ°āĻ˛ā§ āĻāĻžāĻāĻļā§āĻˇ […]
ã3.5.aãāĻ¸ā§āĻāĻ āĻāĻŦāĻ āĻŦāĻ°ā§āĻāĻŽā§āĻ˛ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻāĻ˛ā§āĻāĻ¨āĻž
 [Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (3) Number Properties āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã5ãExponents and roots āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã3.5.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã3.5.aãāĻ¸ā§āĻāĻ āĻāĻŦāĻ āĻŦāĻ°ā§āĻāĻŽā§āĻ˛ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻāĻ˛ā§āĻāĻ¨āĻž Increasing power cause positive fraction to decrease. āĻ§āĻ¨āĻžāĻ¤ā§āĻŽāĻ āĻāĻā§āĻ¨āĻžāĻāĻļāĻā§ āĻ¯āĻ¤ āĻā§āĻ power āĻ āĻāĻ¨ā§āĻ¨ā§āĻ¤ āĻāĻ°āĻž āĻšā§ āĻ¤āĻžāĻ° āĻŽāĻžāĻ¨ āĻ¤āĻ¤ āĻŦā§ āĻšā§ āĻāĻŦāĻ āĻŦā§ āĻšāĻ¤ā§ āĻšāĻ¤ā§ āĻ¸ā§āĻāĻŋ āĻ¸āĻ°ā§āĻŦā§āĻžāĻā§āĻ āĻĒāĻ°ā§āĻ¯āĻ¨ā§āĻ¤ āĻ¯ā§āĻ¤ā§ āĻĒāĻžāĻ°ā§ āĻāĻŋāĻ¨ā§āĻ¤ā§ āĻāĻŋāĻā§āĻ¤ā§āĻ […]
ã4.1.aã āĻ āĻ¨ā§āĻĒāĻžāĻ¤, āĻ¸āĻŽāĻžāĻ¨ā§āĻĒāĻžāĻ¤ āĻāĻŦāĻ āĻļāĻ¤āĻāĻ°āĻž āĻŦāĻŋāĻˇā§āĻ āĻāĻ˛ā§āĻāĻ¨āĻž
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (4) Decimals, Fraction, Percentage āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã1ãRatio, Proportion, Percent āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã4.1.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã4.1.aã āĻ āĻ¨ā§āĻĒāĻžāĻ¤, āĻ¸āĻŽāĻžāĻ¨ā§āĻĒāĻžāĻ¤ āĻāĻŦāĻ āĻļāĻ¤āĻāĻ°āĻž āĻŦāĻŋāĻˇā§āĻ āĻāĻ˛ā§āĻāĻ¨āĻž Ratios āĻŦāĻž āĻ āĻ¨ā§āĻĒāĻžāĻ¤āĻ A ratio expresses a particular relationship between two or more quantities. Here are some examples of ratios: The two partners spend time working in the ratio […]
ã4.4.aãāĻ˛āĻžāĻ āĻ āĻā§āĻˇāĻ¤āĻŋ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻāĻ˛ā§āĻāĻ¨āĻž
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (4) Decimals, Fraction, Percentage āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã4ãProfit loss āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã4.4.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã4.4.aãāĻ˛āĻžāĻ āĻ āĻā§āĻˇāĻ¤āĻŋ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻāĻ˛ā§āĻāĻ¨āĻž Selling price with profit included: If buying price is [latex]B[latex] and you want to make [latex]P[latex]% profit, then selling price [latex]S[latex] would be: [latex]S=B+(P[latex]% of [latex]B)=B+BP/100=B(100+P/100)[latex] For loss, the âplus signâ will […]
ã4.2.aãāĻāĻā§āĻ¨āĻžāĻāĻļ (āĻšāĻ°-āĻ˛āĻŦ āĻ¨āĻŋā§āĻŽ, āĻ¯ā§āĻ, āĻŦāĻŋā§ā§āĻ, āĻā§āĻ¨ āĻ āĻāĻžāĻ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ)
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (4) Decimals, Fraction, Percentage āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã2ãFractions āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã4.2.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã4.2.aãāĻāĻā§āĻ¨āĻžāĻāĻļ (āĻšāĻ°-āĻ˛āĻŦ āĻ¨āĻŋā§āĻŽ, āĻ¯ā§āĻ, āĻŦāĻŋā§ā§āĻ, āĻā§āĻ¨ āĻ āĻāĻžāĻ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ) Decimals are one way of expressing the numbers that fall in between the integers. Another way of expressing these numbers is fractions. For example, the fraction [latex]9/2[latex] which equals […]