Exercise 1 Real numbers Name………………………………………………………………..No……... Check in the box following each match type. That the correct number. No Number Real numbers Numeral Integ er numbe r Negat ive numbe r Ration al number Irrati onal number 1 -8 2 0.3 ¿ 3 − 13 2 4 125 5 √ 3 6 1.41 7 15 3 8 √ 4× √ 2 9 0.23 ¿ 4 ¿ 10 ( √ 6 ) 2 Score = ………………………… Examiner ………………………………….. ……./……………./…………….. คคคคคคคคคคคคค คคคคคคคค
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Exercise 1 Real numbersName………………………………………………………………..No……...
Check in the box following each match type. That the correct number.
Exercise 2 Property of equalityName………………………………………………………………..No……...
Put the properties of equality in each of the following correctly.No
.Number Property of equality
1 8 = 8 Reflexive Property2 9 = 93 100 = 1004 If 6 = 5 + 1 then 5 + 1 = 6 Symmetric Property5 If 8 = 3 + 5 then 3 + 5 = 86 If 10 = 7 + 3 then 7 + 3 =
107 If 42 = 16 then 16 = 7 + 9
แล้�ว 42 = 7 + 9Transitive Property
8 If 52 = 25 then 25 = 20 + 5 แล้�ว 52 = 20 + 5
9 If 72 = 49 then 49 = 40 + 9 แล้�ว 72 = 40 + 9
10 If 4 5 = 20 then (4 5) + 3 = 20 + 3
Addition Property
11 If (2 6) = 12 then (2 6) + 2 = 12 + 2
12 If 3 2 = 6 then (3 2) + 5 = 6 + 5
13 If (4 3) = 12 then (4 3) Multiplication
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5 = 12 5 Property14 If (5 2) = 10 then (5 2)
6 = 10 615 If
82 = 4 then
82 4 = 4
6
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If a, b, c is numbers then property of equality is
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CONC
Exercise 3 Property of equality ConceptName………………………………………………………………..No……...
Students to summarize the content on the properties of equality
If a, b, c is real number 1. a = a ex. 10 = 10 is ………………………………………………………2. if a = b then b = a ex. 6 = 3 + 3 then 3 + 3 = 6 is ……………….3. if a = b แล้ะ b = c then a = c ex. 102 = 100 and 100 = 60 + 40 then
102 =60 + 40 is ………………………………………………………………4. if a = b then a + c = b + c ex. 5 2 = 10 and c = 6 then (2 5) + 6 = 10 + 6 is ………………………………………………………………………………..
5. if a = b then ac = bc ex. 102 = 5 and c = 4 then (
102
) 4 = 5 4is ………………………………………………………………………………..
6. from 1 - 5 summarize the content on the properties of equality is
ExplanationStudents to put the answer correctly complete
No.
Word Property
1 if 5, 3 R then 2 5 R
Closure Property
2 7 2 = 2 7 Commutative Property of multiply
3 5 (4 3) = (5 4) 3
Associativity
4 1 8 = 8 = 8 1 Multiplicative identity5 1
3 3 = 1 = 3 13
inverse property of multiply
6 10 3 = 3 107 if 6, 7 R then 7 6
R8 1 10 = 10 = 10
19 1
5 5 = 1 = 5 15
10 if -2, 7 R then (-2) 7 R
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11 15 3 = 3 1512 7 (2 3) = (7 2)
313 1 20 = 20 = 20
114 6 (4 5) = (6 4)
515 10 5 = 5 10
Concept If a, b, c is real number Multiplication property have 1. . …………………………………………………………………………….. 2. ……………………………………………………………………………… 3. ……………………………………………………………………………… 4. ……………………………………………………………………………… 5. ………………………………………………………………………………
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Exercise 6 Use real numbers to solving quadraticName…………………………………………………………No……... Class……Explanation : students solve factorization of polynomials, 1-8 by the following example.
EX. Be factorization of polynomials.1. 3x2 + 62. 4x3 + 8x2 - 12x
Concept factorization of polynomials used by. ………………………………………………………………..…………………………………..
………………………………………………………………………………………………….
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Exercise 7 Use real numbers to solving quadratic ax2 + bx + c
Name…………………………………………………………No……... Class……Explanation : students solve factorization of polynomials, ax2 + bx + c when a, b, c is Real number and a 0 by the following example
Ex. Be factorization of polynomials of x2 + 5x + 6
Solution Find two numbers multiply is 6 and sum is 5 2 3 = 6 and 2 + 3 = 5 x2 + 5x + 6 = (x + 2)(x + 3)
Exercise 12 QUADRATIC WORD PROBLEMSName………………………………………………………………………………………No……... Class……- We want a single equation that we can solve for the zeros.
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- At times, we may need to start with two equations if there are two distinct variables. If this happens, rearrange one equation and substitute it into the other so we are left with a single equation.- Solve the equation by factoring or using the Quadratic Formula.
1. When the square of a certain number is diminished by 9 times the number the result is 36. Find the number.2. A certain number added to its square is 30. Find the number.3. The square of a number exceeds the number by 72. Find the number.4. Find two positive numbers whose ratio is 2:3 and whose product is 600.5. The product of two consecutive odd integers is 99. Find the integers.6. Find two consecutive positive integers such that the square of the first is decreased by 17 equals 4 times the second.7. The ages of three family children can be expressed as consecutive integers. The square of the age of the youngest child is 4 more than eight times the age of the oldest child. Find the ages of the three children.8. Find three consecutive odd integers such that the square of the first increased the product of the other two is 224.9. The sum of the squares of two consecutive integers is 113. Find the integers.10. The sum of the squares of three consecutive integers is 302. Find the integers.11. Two integers differ by 8 and the sum of their squares is 130.12. rectangle is 4 m longer than it is wide, its area is 192 m2. Find the dimensions of the rectangle.13. right triangle has a hypotenuse of 10 m. If one of the sides is 2 m longer than the other, find the dimensions of the triangle.14. The sum of the squares of three consecutive even integers is 980. Determine the integers15. Two integers differ by 4. Find the integers if the sum of their squares is 250.16. Find three consecutive integers such that the product of the first and the last is one less than five times the middle integer.17. A rectangle is three times as long as it is wide. Its area has measure equal to ten times its width measure plus twenty-five. What is the width?18. Richie walked 15 m diagonally across a rectangular field. He then returned to his starting position along the outside of the field. The total distance he walked was 36 m. What are the dimensions of the field?
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19. A square picture with sides of length 20 cm is to be mounted centrally upon a square frame. If the area of the border of the frame equals the area of the picture, find the width of the border of the frame to the nearest millimetre.20. A square lawn is surrounded by a walk 1 m wide. The area of the lawn is equal to the area of the walk. Find the length of the side of the lawn to the nearest tenth of a metre.21. A picture 20 cm wide and 10 cm high is to be centrally mounted on a rectangular frame with total area three times the area of the picture. Assuming equal margins for all four sides, find the width of the margin.22. A fast food restaurant determines that each 10¢ increase in the price of a hamburger results in 25 fewer hamburgers sold. The usual price for a hamburger is $2.00 and the restaurant sells an average of 300 hamburgers each day. What price will produce revenue of $637.50?23. George operates his own store, George’s Fashion. A popular style of pants sells for $50. At that price, George sells about 20 pairs of pants a week. Experience has taught George that for every $1 increase in price, he will sell one less pair of pants per week. In order to break even, George needs to produce $650/week. How many pairs of pants does George need to sell to break even?24.A biologist predicts that the deer population, P, in a certain national park
can be modelled by where x is the number of years since 1999.a) According to the model, how many deer were in the park in 1999.b) Will the deer population ever reach zero?c) In what year will the population reach 1000?25. A t-ball player hits a baseball from a tee. The flight of the ball can be modelled by where h is the height in metres, and t is the time in seconds.a) How high is the tee?b) How long does it take the ball to land?c) When does the ball reach a height of 4.5 m?