1. Exercise 1 Real numbers<br />Name………………………………………………………………..No……...<br />Check in the box following each match type. That the correct number.<br />NoNumberReal numbersNumeralIntegernumberNegative numberRational numberIrrational number1-8234125561.4178910<br />303784016065500<br />-1162054953000<br /> Score = …………………………<br /> Examiner ………………………………….. <br /> ……./……………./……………..<br />Exercise 2 Property of equality<br />Name………………………………………………………………..No……...<br />Put the properties of equality in each of the following correctly.<br />No.NumberProperty of equality1 8 = 8Reflexive Property2 9 = 93 100 = 1004If 6 = 5 + 1 then 5 + 1 = 6Symmetric Property5If 8 = 3 + 5 then 3 + 5 = 86If 10 = 7 + 3 then 7 + 3 = 107If 42 = 16 then 16 = 7 + 9 แล้ว 42 = 7 + 9Transitive Property8If 52 = 25 then 25 = 20 + 5 แล้ว 52 = 20 + 59If 72 = 49 then 49 = 40 + 9 แล้ว 72 = 40 + 910If 4 5 = 20 then (4 5) + 3 = 20 + 3Addition Property 11If (2 6) = 12 then (2 6) + 2 = 12 + 212If 3 2 = 6 then (3 2) + 5 = 6 + 513If (4 3) = 12 then (4 3) 5 = 12 5Multiplication Property 14If (5 2) = 10 then (5 2) 6 = 10 615If = 4 then 4 = 4 6-390525118746Concept00Concept If a, b, c is numbers then property of equality is<br />Exercise 3 Property of equality Concept<br />Name………………………………………………………………..No……...<br />Students to summarize the content on the properties of equality<br />If a, b, c is real number <br />1.a = a ex. 10 = 10 is ………………………………………………………<br />2.if a = b then b = a ex. 6 = 3 + 3 then 3 + 3 = 6 is ……………….<br />3.if a = b และ b = c then a = c ex. 102 = 100 and 100 = 60 + 40 then <br />102 =60 + 40 is ………………………………………………………………<br />4.if a = b then a + c = b + c ex. 5 2 = 10 and c = 6 then (2 5) + 6 = 10 + 6 is ………………………………………………………………………………..<br />5.if a = b then ac = bc ex. = 5 and c = 4 then () 4 = 5 4<br />is ………………………………………………………………………………..<br />6.from 1 - 5 summarize the content on the properties of equality is<br />6.1……………………………………………………………………………………<br />6.2……………………………………………………………………………………<br />6.3……………………………………………………………………………………<br />6.4……………………………………………………………………………………<br />6.5……………………………………………………………………………………<br /> <br />Exercise 4 Addition property<br />Name………………………………………………………………..No……...<br />ExplanationStudents to put the answer correctly complete<br />No.Word property1if 2, 6 R Then 2 + 6 RClosure Property27 + 3 = 3 + 7Commutative Property of Addition33 + (5 + 4) = (3 + 5) + 4associativity4Real number 0 so 0 + 3 = 3 = 3 + 0Additive identity5(-7) + 7 = 0 = 7 + (-7)inverse property of addition66 + 3 = 3 + 6710 + (2 + 8) = (10 + 2) + 88if 4, -3 R then 4 + (-3) R90 + 8 = 8 = 8 + 010(-15) + 15 = 0 = 15 + (-15)<br />Exercise 5 Multiplication property<br />Name………………………………………………………………..No……...<br />ExplanationStudents to put the answer correctly complete<br />No.Word Property1if 5, 3 R then 2 5 RClosure Property27 2 = 2 7Commutative Property of multiply35 (4 3) = (5 4) 3Associativity41 8 = 8 = 8 1Multiplicative identity5 3 = 1 = 3 inverse property of multiply610 3 = 3 107if 6, 7 R then 7 6 R81 10 = 10 = 10 19 5 = 1 = 5 10if -2, 7 R then (-2) 7 R1115 3 = 3 15127 (2 3) = (7 2) 3131 20 = 20 = 20 1146 (4 5) = (6 4) 51510 5 = 5 10-7239011176000 Concept If a, b, c is real number Multiplication property have 1. . …………………………………………………………………………….. 2. ……………………………………………………………………………… 3. ……………………………………………………………………………… 4. ……………………………………………………………………………… 5. ………………………………………………………………………………<br />Exercise 6 Use real numbers to solving quadratic<br />Name…………………………………………………………No……... Class……<br />Explanation : students solve factorization of polynomials, 1-8 by the following example.<br />-3803654254500<br />EX. Be factorization of polynomials.<br />1.3x2 + 6<br />2.4x3 + 8x2 - 12x<br />Solution1.3x2 + 6 =3(x2 + 2)<br />2.4x3 + 8x2 - 12x=4x(x2 + 2x - 3)<br />-914405588000<br />1)3x2 + 6x2= ……………………………………………………………………….<br />2)2x2 - x= ……………………………………………………………………….<br />3)4x3 - 16x2 - 8x= ………………………………………………………………<br />4)5x3 + 15x2= ……………………………………………………………………….<br />5)6x3 - 12x2 - 18x= ………………………………………………………………<br />6)7x2 - 14x= ……………………………………………………………………….<br />7)9x4 + 18x3 + 27x2= ………………………………………………………<br />8)10x2 - 30x= ……………………………………………………………………….<br />1905020891500<br />Concept factorization of polynomials used by.<br /> ………………………………………………………………..…………………………………..<br />………………………………………………………………………………………………….<br />Exercise 7 Use real numbers to solving quadratic ax2 + bx + c <br />Name…………………………………………………………No……... Class……<br />Explanation : students solve factorization of polynomials, ax2 + bx + c when a, b, c is Real number and a 0 by the following example<br />-1485904254500<br /> Ex. Be factorization of polynomials of x2 + 5x + 6<br />Solution Find two numbers multiply is 6 and sum is 5<br /> 2 3 = 6 and 2 + 3 = 5<br /> x2 + 5x + 6 = (x + 2)(x + 3)<br />-914405588000<br />1)x2 + 7x + 10= ……………………………………………………………….<br />2)x2 + 8x + 10= ……………………………………………………………….<br />3)x2 + 7x + 12= ………………………………………………………………<br />4)x2 + 9x + 8 = ………………………………………………………………<br />5)x2 - 10x + 24 = ………………………………………………………………<br />6)x2 - 4x - 12= ……………………………………………………………….<br />7)x2 + 3x + 2= ………………………………………………………………<br />8)x2 - x - 6= ………………………………………………………………<br />1905020891500<br />Concept factorization of polynomials used by <br />…………………………………………………………………………………………………………<br />………………………………………………………………………………………………….<br />………………………………………………………………………………………………….<br />Exercise 8 Use real numbers to solving quadratic <br />Name…………………………………………………………No……... Class……<br />students solve factorization of polynomials, ax2 + bx + c when a, b, c is Real number and a 0 by the following example<br />Ex.factorization of polynomials 25x2 + 15x + 2<br />Solution 1.Find a polynomial second degree polynomials multiply like 25x2 ex. (25x)(x) or (5x)(5x)<br />We can write polynomials is <br />(25x )(x ) or (5x )(5x )<br />2.Find two numbers to multiple are equal. 2 is (2)(1) or (-2)(-1)<br />Writing a term of two polynomials in the back of Item 1 <br />(25x + 2)(x + 1)or(5x + 2)(5x + 1)<br />(25x - 2)(x - 1)or(5x - 2)(5x - 1)<br />3.Find the middle term of the polynomial. From the multiplication of polynomials, each pair in 2 equal to the sum. 15x will be.<br />158305524447500166497024447500 10x<br />177546020637500123253522542500From multiply (5x + 2)(5x + 1) middle term is 15x<br /> 5x<br /> <br />polynomials is 25x2 + 15x + 2 = (5x + 2)(5x + 1)<br />-9144011239500<br />1)3x2 + 10x + 3 = …………………………………………………………….<br />2)2x2 + x - 6= ……………………………………………………………<br />3)8x2 - 2x - 3= ……………………………………………………………<br />4)4x2 + 5x - 9= ……………………………………………………………<br />5)3x2 + 4x - 15= ……………………………………………………………<br />6)2x2 - x - 1= ……………………………………………………………<br />factorization of polynomials 1 - 8 <br />Exfactorization of polynomials x2 + 6x + 9 and x2 - 8x + 16<br />Solutionx2 + 6x + 9 =x2 + 2(3)x + (3)2<br /> = (x + 3)2<br />x2 - 8x + 16 =x2 - 2(4)x + (4)2<br /> = (x - 4)2<br />-914405588000<br />1)x2 + 10x + 25= ……………………………………………………………….<br />2)x2 - 4x + 4= ……………………………………………………………….<br />3)x2 + 16x + 64= ………………………………………………………………<br />4)x2 - 12x + 36 = ………………………………………………………………<br />5)x2 - 14x + 49 = ………………………………………………………………<br />6)x2 + 22x + 121= ……………………………………………………………….<br />7)x2 - 24x + 144= ……………………………………………………………….<br />8)x2 + 30x + 225= ……………………………………………………………….<br />-336558953500<br /> Concept Second degree polynomial factorization and factor polynomials have a unique <br /> degree. Called. …………………………………………………………………………….<br />And write a formula is.<br />x2 + 2ax + a2 =………………………………………………………<br />x2 - 2ax + a2 =………………………………………………………<br />Exercise 9 Solving quadratic by perfect square. <br />Name…………………………………………………………No……... Class……<br />factorization of polynomials <br />1.7x2 - 14x + 28 =……………………………………………………………..<br />2.x2 - 78x + 77 =……………………………………………………………..<br />3.a2b - 12ab + 27b =……………………………………………………………..<br />4.7x2 - 2x – 5 =……………………………………………………………..<br />5.13m2 + 21m – 10 =…………………………………………………………….. <br />Students of polynomial factorization is made ​​by Perfect square from 1 to 5.By the following example.<br />Ex.factorization of polynomials x2 - 6x - 2<br />Solutionx2 – 6x – 2=(x2 – 6x) – 2 <br />=(x2 – 2(3)x + 32) – 2 – 32 <br />=(x2 – 6x + 9) – 2 – 9<br />=(x – 3)2 – 11 <br />=(x – 3)2 – ()2<br />=(x – 3 + )(x – 3 - )<br />914409398000<br />1.x2 + 8x – 5=……………………………………………………………..<br />2.x2 + 8x + 14=……………………………………………………………..<br />3.x2 – 10x + 7=……………………………………………………………..<br />4.x2 + 7x + 11=……………………………………………………………..<br />5.-3x2 + 6x + 4=……………………………………………………………..<br />Exercise 10 Solving quadratic by perfect square. <br />Name…………………………………………………………No……... Class……<br />Show solution <br />-1270011176000<br />1.factorization of polynomials <br />1.1x2 – 8x + 16<br />1.2x2 + 50x + 125<br />2.factorization of polynomials by perfect square <br />2.1x2 – 6x + 7<br />2.22x2 + 7x – 3 <br />2.3x2 + 14x – 1 <br />Solution<br />Exercise 11 Find answer of quality <br />Name…………………………………………………………No……... Class……<br />find the answer of quality<br />No.qualityanswer of quality1 x2 + 8x + 12 = 02 x2 – 6x = 163 2x2 + 7x + 3 = 04 7x2 + 3x – 4 = 05 4x2 + 8x + 3 = 06 x2 – 2x – 10 = 2x + 117 3x2 + 2x – 3 = 08 2x2 + 3x – 7 = 09 10x2 – 20x – 30 = 010 –5x2 – 2x + 17 = 0<br /> show solution in your note book<br />-952510541000<br />1.Find answer by factorization<br />1.1x2 – 8x + 12 = 0<br />1.25x2 + 13x + 6 = 0<br />2.Find answer by perfect square <br />2.1x2 + 10x + 3 = 0<br />2.2x2 – 6x + 4 = 0<br />3.Find answer by formula x = <br />3.12x2 = -4x + 1<br />3.2x2 – 4x = 21<br />Exercise 12 QUADRATIC WORD PROBLEMS<br />Name………………………………………………………………………………………No……... Class……<br />- We want a single equation that we can solve for the zeros.<br />- 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.<br />- Solve the equation by factoring or using the Quadratic Formula.<br />1. When the square of a certain number is diminished by 9 times the number the result is 36. Find the number.<br />2. A certain number added to its square is 30. Find the number.<br />3. The square of a number exceeds the number by 72. Find the number.<br />4. Find two positive numbers whose ratio is 2:3 and whose product is 600.<br />5. The product of two consecutive odd integers is 99. Find the integers.<br />6. Find two consecutive positive integers such that the square of the first is decreased by 17 equals 4 times the second.<br />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.<br />8. Find three consecutive odd integers such that the square of the first increased the product of the other two is 224.<br />9. The sum of the squares of two consecutive integers is 113. Find the integers.<br />10. The sum of the squares of three consecutive integers is 302. Find the integers.<br />11. Two integers differ by 8 and the sum of their squares is 130.<br />12. rectangle is 4 m longer than it is wide, its area is 192 m2. Find the dimensions of the rectangle.<br />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.<br />14. The sum of the squares of three consecutive even integers is 980. Determine the integers<br />15. Two integers differ by 4. Find the integers if the sum of their squares is 250.<br />16. Find three consecutive integers such that the product of the first and the last is one less than five times the middle integer.<br />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?<br />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?<br />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.<br />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.<br />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.<br />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?<br />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?<br />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.<br />a) According to the model, how many deer were in the park in 1999.<br />b) Will the deer population ever reach zero?<br />c) In what year will the population reach 1000?<br />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.<br />a) How high is the tee?<br />b) How long does it take the ball to land?<br />c) When does the ball reach a height of 4.5 m?<br />Exercise 13 QUADRATIC INEQUALITY <br />Name………………………………………………………………………………………No……... Class……<br />To solve a QUADRATIC of inequality. or find the answer to inequality will require.Properties are not equal. The following example.Example 1 Find the answers to the following inequality. by the set.1. 2x + x <10.2. 4x - 4 2x + 4.solution : 2x + 2 < 10. 2x + 2 + (-2) < 10 + (-2). 2x < 8. (2x) < (8). x < 4.Set answer 2x + 2 <10 is {x | x <4}.<br />2.4x – 4 2x + 4<br /> 4x – 4 + 4 2x + 4 + 4<br /> 4x 2x + 8<br /> 4x + (-2x) 2x + (-2x) + 8<br /> 2x 8<br /> (2x) (8)<br />x 4<br /> Set answer 4x – 4 2x + 4 is {x | x 4}<br />Example 2 Solve the following. And show you the line number.<br />1.-x + 4 < -12<br />2.-x + 7 4<br />Solution 1.-x + 4 < 12<br />Plus on both sides of the inequality with a -4 <br />-x + 4 + (-4) < -12 + (-4)<br /> -x < -8<br /> x > 8 (multiply both sides by -1)<br /> Set of inequalities is the answer. The set of real numbers greater than 8, or {x | x> 8}.<br /> -1 0 1 2 3 4 5 6 7 8 9 10<br />2.-x + 7 4<br />Plus on both sides of the inequality with a -7.<br />-x + 7 + (-7) 4 + (-7)<br /> -x -3<br /> x 3<br /> set of inequalities is the answer. The set of real numbers less than or equal to 3 or {x | x 3}<br /> -3 -2 -1 0 1 2 3 4 5 <br />No.inequality1Find the answers to the following inequality. by the set.1.1 x + 3 < 61.2 2x + 4 101.3 3x – 7 51.4 -4 + 4x 81.1 …………………….1.2 …………………….1.3 …………………….1.4 …………………….2Solve the following. And show you the line number.2.1 -3x -62.2 -5x – 1 -112.3 -8x + 6 > -102.4 -5 – 5x > -2x - 8<br />Exercise 14 QUADRATIC INEQUALITY <br />Name………………………………………………………………………………………No……... Class……<br />Example Solve x2 + x – 6 > 0 and show you the number line.<br />Solution x2 + x – 6 > 0<br /> (x + 3)(x – 2) > 0<br />Consider value of x in the interval (-, -3), (-3, 2) and (2, )<br />By choosing the value of x in the interval<br />Intervalx(x + 3)(x – 2) (x + 3)(x – 2)(-, -3)-5(-2)(-7) = 14Positive(-3, 2)14(-1) = -4Negative(2, )4(7)(2) = 14Positive<br />When the value of x in the increase is that (x + 3) (x - 2) is positive orGreater than zero on the x in range (-, -3) and (2, )<br />Show the answer <br /> -5 -4 -3 -2 -1 0 1 2 3 4<br /> Solve inequity and show answer by number line<br />1.x2 – 9 < 0<br />2.x2 – 4x – 5 < 0<br />3.x2 + 6x + 9 > 0<br />4.x2 + 4x -4<br />5.x2 – 9x < 10<br />Exercise 15 Interval <br />Name………………………………………………………………………………………No……... Class……<br />The table shows the different types of interval.<br />The elements as the set of real numbers and a, b R by a < b<br />intervalsymbolicmeaninggraph on a number lineexampleopen(a, b){x | a < x < b}(2, 4)close[a, b]{x | a x b}[3, 6]Half-open half-closed,[a, b)(a, b]{x | a x < b}{x | a < x b}[2, 5)(2, 5]Infinite(a, )[a, )(-, a)(-, a]{x | x > a}{x | x a}{x | x < a}{x | x a}(3, )[3, )(-, 5)(-, 5]<br />Exercise <br />No.interval meaninggraph on a number line1(1, 6)2[2, 7]3(3, 6]4[-3, 2)5(3, ) 6[3, )7(-, 4)8(-, 6]9(4, 9)10[6, 10]<br />