2nd Grading Period Chapter Test Name:Airis Ragub Date Submitted: Oct. 20 2014 Section: 7- Lily QUESTION: What are the lessons that we have discussed during the 2nd Grading Period? Enumerate and tell something about each topic. (50pts.) We discussed about the Measurement, it guises a number to a particular characteristics of a person, an object or a concept. A digit is the thickness or width of indexfinger. A foot is the length of a foot. A cubit is the distance from the tip of the middle finger of the out stretched hand to the front of the elbow. The inch, foot and yard are said to be based on the cubit . they are the basic units of length of the English system of measurement. Since the inch and foot are both units of length, each can be converted into the other. Conversion Factor : 1 foot = 12 inches 1 yard = 3 feet 1 mile = 1,760 yards = 5,280 feet Example of English System of Measurement: 1. Convert 48 inches into feet : 48 inches x 1 foot /12 inches = 4 feet 2. Convert 5 yards to feet : 5 yards x 3 feet/1 yard = 15 feet 3. Convert 40 feet to yard: 45 feet x 1 yard/3 feet = 15 yards 4. Convert 5 miles into inches: 5 miles x 5,280 feet/1 miles x 12 inches/1 foot =5x5,280x12inches/1x1 = 316,800 inches We also discussed about the Metric System of Measurement, is easier to use than the English System since its conversion factors would be in the decimal system, unlike the English System of Measurement where units of lengths have different conversion factors. Meter is the basic unit for Length Conversion Factor: 1. 1.5 m to mm =1500 mm 2. 400 hm today =4000 00 dm 3. 0.125 km to m =125 m 4. 0.125 cm tom = 0.00.12 m Examples of Metric System of measurement: 1. Convert 5 km to m : 5 km x 1,000 m 1 km = 5,000 m 2. Convert 10, 000 mm to m : 10,000 mm x 1m 1,000 mm = 10 m 3. Convert 10 Mm to mm : 10 Mm x 1,000,000 m 1 Mm x 1,000 mm 1m = 10,000,000,000 mm 4. Convert 1,000dam to Gm : 1000 dam x 10 m 1 dam x 1 Gm 1,000,000,000 m = 1. 100 000 Gm = ).00001 Gm 5. Convert 100 Hm to Tm : 100 Hm x 100m 1 Hm x 1 Tm 1. 000 000 000 000 m = 100 000 000 Tm Measuring Mass and Weight : Mass and Weight are often used interchangeably although weight is the more popular term. However, mass and weight are two different measurements. The Mass of an object is the amount of matter it contains while weight is the gravitational force acting on an object. Examples: 1 TON = 1000kg 2 800 kg to tons 2 800 kg 1 ton 1000 kg = 2 800 kg ( 1 Ton ) 1000 = 2 800 Ton 1000 = 2.8 ton 10 = 2.8 tons 1 kg = 2.2 punds (LBS) 7.5 Lbs to kg 7.5 Lbs ( 1Kg 2.2 Lbs ) = 7.5 (1kg) 2.2 =7.5 kg 2.2 7.5 LBS = 3.409 kg 1. 250 g to kg = 0.250 kg x P 150 = P 37.50 2. 1 Ton = 1000kg 8.25 tons (1000kg 1 ton) = 8.25 (1000kg ) = 8 250 kg 8 2.5 ton = 8250 kg Measuring Volume and Capacity: Volume is the amount of space an object contains or occupies. The volume of a container is said to be the capacity of the container. This is measured by the number of cubic units or the amount of fluid it can contain and hot the amount of space the container occupies the base SI unit for volume is the cubic meter (m3 ) A side from cubic meter, another commonly used metric unit for volume of solids is the cubic centimeter (cmo or cc) while the commonly used metric units for volume of fluids are the liter (L) and the Milliliter (mL) Volume, capacity and mass are related in the metric system. One cm3 holds one mL of water which weight one gram. Examples: 1. Cylinder V= r2 H = (3.14) (5cm) 2 (6cm) = (3.14) (25cm2) (6cm)=V=471cm 2. Cone V= 13 r2h =13 (3.14) (4m)2 (9m) = 13 (3.14) (16m2) (9m)=150.72 m3 Volume. Amount of space an object contain or occupies cm3 km Basic. Unit for Volume is cubic meter (m3) Capacity, Amount of fluid that contains in a container ml L Cubic. Container (cm3 or cc) Liters or Milliliter for fluid Measurement of an Angle: A protractor is an instrument used for measuring angles. It has a semicircular shape which is divided into 180 equal units. Each unit is one degree. Angles are classified according to their measures : A Cute angle- it measures greater than 00 but less than 900 Right angle – measures 900 Obtuse angle- measures greater than 900 but less than 1800 Examples: 1. Complementary – 2 that measures 900 450 cord 450 100 and 800 650 and 250 400 cord 500 350 and 550 150 and 750 Time and Speed: The concept of time is very basic and is integral in the discussion of other concepts such as speed. Currently, there are two types of notation in stating time, the 12- hour notation (standard Time) or the 24-hour notation (Military or astronomical Time) Examples: 2 Hour Notation 1. 12 Hour am ( a tec meridian) PM (Post Meridian) 2. 24 Hour military Time 3. 1 Hour = 60 Minutes 4. 1 min = 60 seconds 5. 1 day = 24 Hours 6. 1 score = 20 Years 7. 1 year = 365 days 8. 1 century = 100 years 9. 1 Decade = 10 Years 10. 1 millenion = 1000 years Speed Late of an objects change in position rate of the distance travelled by the spent Average Speed- Distance Travelled Time Spent Units of Temperature: There are two units being used to measure the temperature, both named after their instrument makers: Examples: -Normal Today Temperature 370c -Normal room temperature 200c -Hot Day Temperature 300c -Cold day Temperature 100c -Building Point of water 1000c -Freezing Point of Water 00c 2 Temperature Scales: 1. Degree Fahrenheit (0F) – Gabriel D. Pahrenheit Girman Physicist 170005 212 0F – Building Pt Of H20 320F – Freezing Pt Of H20 2. Degree Celcus (0c) Centigrade – Andres Calcius Awedist astronomer 1742 1000c – Boiling Pt Of H20 o0c –Freezing Pt Of H20 Evaluating Algebraic Expressions by Substitution: Constants: Are numbers that have fixed values EX: 14, 100 Variables: Are Symbols or Letters which may represent a value or a number EX.a,x or y Term: is a number, a variable or a product of numbers and variables. The terms number part is called the (numerical coefficient) while the Literal coefficient is the variable including its exponent. The word coefficient alone is referred to as the numerical coefficient. Examples: 125xy2 - 125 is the numerical coefficient - x and y2 are Literal coefficient 1. 5-x , 2a + 3b, 10ab – 3xy = An Algebraic Expression 2. 3x and 8x are similar, 3x2 and 8x are not = Similar Terms Definition of Polynomials: An expression whose terms are product of a constant and a variable and its exponent are positive number: 1. 2x, 3x3, 5x + 3y –Z2 Not a Polynomial If: 1. The Exponentof the variables is not a positive whole number Ex. 3x+ 2x2y 14 x As 2. The Variable is inside the radical Sign Ex. 3x = 3x 12 3. The Variable is in the Dendminator Ex.3x 5y + 1x Kinds of Polynomial According to number is terms: 1. Monomial- One term Ex. 6x 1.3x 2x+5 3, 8abc 2. Bonimial- Two Terms Ex. 6x+5y 13 x – 5y 2x 15 _3 -2y, 8abc -3 3. Trinomial- Three terms Ex. 6x+5y + 72 13x -5y+ 6x 2x+5 3 -2y+x 8abc 3+ 5yz 4. Polynomial- Four or More Terms Ex. 6x3+ 52 + 8y- 9xy 13 x -5y + 6x + 923 -2x2 Kinds of Polynomials Accdig Degree 1. Constant-Degree is Zero Ex. 2x0 = 1 =2 (1) =2 4x2y0 = 4x2(1) 24x2 a0=1 2. Linear-Degree is One Ex. a Degree is one Zx 3. Quadratic-Degree is two Ex. a2, Xy, 5ab,3xy 5 4. Cubic- Degree is Three Ex. x3, abc, 3xy2, 4a2b 5. Quadratic- Degree is Five Ex. ab3 , 2x2y2, xy3, x2yz, 4abcd 6. Quintic- Degree is Five Ex. 2x2b3 , abcde, abc3 Laws of Exponents: Product of a power, Quotient of a power, Power of Powers, Zero Exponent, Negative Exponent: Examples: 1. 3x2 (4x4) = 3.4.x2 . x4 = 12x6 2. -5a5 (7a8) = -5.7.a5.a8 =-35a13 3. (2a)-2 = 1 (2a)2 = 1 4a2 Laws of Exponents: 1. Product of a Power Ex. a3 = a0 a0 a 2a2 b3 = 20a0a0 b0b0b 2. Power of the same base Ex. ax = a3 = ax + y x2. x3 = x2.x3= x2+3=x5 (4a2b) (2a3b2) = (4) (2) a2+3 b1+ 2 = 8a5b3 3. Quatient of a Power Ex. ax ay = ax-y x6 x2 = x6 2 = x4 6a4b5 3ab2 = 63 a4-1 b 5-2 = 2a3b3 4. Powers of Powers Ex. (ax)y=ax-y (x2)3=92-3=a6 (2a2b3) 3 = 2 1-3 a2-3 b3-8 = 2a2ba =8acba 5. Zero Exponent Ex. ax ax = ax –x = a=1 X4 x4 = x4-4 =x0 =1 A3 b4 a3 b2 a 3-3 b4-2 = a0b2= (1) b2 = b2 6. Negative Exponent Ex. a-11 = 1a n x-2 1x2 5x3= 5x3 (2a) -2 = 1 = 1 2 = 1 (29) 2 22 92 4a2 Addition of Polynomials: Combine similar terms – With the samc= Literal Cafficients Examples: 1. 29 + 3b + 49 + 2bt 3a 2a + 3b 4a + 2b = 9a + 5b 2. 7x7 4y – 10 + (-4x+Sy-6) -4 x + 8y -6 3x + 12y -16 3. 7a 3a 12g 22a 4. 9x 4x 5x 18 x 5. 2m 7m 15m 24m 6. 12a + 6b -10a -3b 7. 20x -7y -6x -5y 14 x -12y 8. 15ab – 10a + 5b –ab 14 ab -10a + 5b 9. 10x2y -5x2y 2x2y 7x2y 10. 12ab + 3xy 10ab 7xy 2ab -4xy
Posted on: Mon, 20 Oct 2014 06:51:06 +0000
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