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Student Name: ID: Teacher: Group: This paper is part of the 50% of

The score will be obtained in relation with the following

It must be handwritten (writing clarity and spelling). 2.

1 Student Name: ID: Teacher: Group: This paper is part of the 50% of your score. The score will be obtained in relation with the following statements: 1. It must be handwritten (writing clarity and spelling). 2. It must be completely and correctly answered. 3. Identification data. 4. It must be turned at the beginning of the exam to the established teacher. 5. THE TASKS MUST BE COMPLETED WITH PENCIL. NOTE: Plagiarism and Trade related to the academic contents of this portfolio will be sanctioned in accordance to the Academic Legislature.

2 MES Leticia A. Castañeda Bermea Página 2

3 STAGE 1: OPERATIONS WITH POLYNOMIALS I.-Write into Symbolic Language the following expressions: a) The third part of a number w b) 8 times the price x c) The quotient of two numbers is 25 II.-Translate into Common Language the following symbolic expressions: a) (n 1 ) b) (x ) III.- Complete the reduction of like terms: 4( a + y ) 8( a + y ) 6xy + 3xy + 15x 3x + 8x + xy Write the polynomial in ascendant order 8x 2 5x 3-2x 6 + x 4 22x + 4 IV.- Perform the following addition of polynomials: (4a 3b + 6c -11); (2a +8b 11c) ; ( -a +2b + c +14) (2wx 4w 2 x 8wx 2 ); (3wx 9w 2 x + 2wx 2 ); (-5wx + 7w 2 x + 7wx 2 ) V.- Perform the following subtraction of the given polynomials: Subtract the second polynomial from the first: (6x 6y + 6z ) ; (-3x + 10y z) Subtract the result of (12a + 3b 4c) and (6a- 8b + 5c) from (4a- 10b 5c) VI.- Perform the indicated operations in each problem: 11x 4 y 6 c 2 (28xy x 2 y -10 +y 9 c 10 )= MES Leticia A. Castañeda Bermea Página 3

4 (4x 2 1)(6x 2 9)= (4x 5y)(16x xy + 25y 2 )= 36a 6 b 10 9a 2 b 5 = 30x 2 y 4 45x 2 y 3 z 15x 2 y 3 = (2x 4 11x 3 + 3x x +4 ) ( x + x 2 2)= VII.-Simplify and delete the following grouping symbols. -(7 + 3ax) - {( 2 ax ) (4 x + ax) (4x 4ax)} = { 2( 3 + x ) - [ 4 (x + 1)] } - [(2 + x) (x 2)] = MES Leticia A. Castañeda Bermea Página 4

5 STAGE 2: SPECIAL PRODUCTS AND FACTORING OF POLYNOMIALS I.-Find the Greatest Common Factor (GCF) of the following expressions 8x 5 y xy 3 2xy 6xy 2 10x 2 y x 3 y + 30x 4 y 5 56d 2 7d 9 21d 4 II.-Obtain the products of the following conjugated binomials. (8 4xy)(8 + 4xy) = (9a x)(9a + x) = III.-Factor each differences of squares. 4x 2 16 = 16p = 36a 2 16b 2 = IV.-Multiply the following bonimials. (w 8)(w 4) = (2x + 5)(x + 4) = V.- Factor the following quadratic trinomials. x 2 8x + 12 = r 2 4r 12 = u 2 + u 72 = 3x x + 10 = 2x x 90 = MES Leticia A. Castañeda Bermea Página 5

6 VI.- Perform by the square binomial formula. (a + 10) 2 = (2b 4) 2 = VII.-Write the following trinomials as a square binomial x 2 + 6x + 9 = x 2 8x + 16 = x 2 30x = VIII.-Factor completely the following additions or cubes differences (a 3 27) = (x 3 + 1) = IX.-Identify and perform the type of factorization. (x 3 64) = (x 2 64) = (3a + 4b 6a 2 8ab) = I.- Simplify the following expressions. (2x 7)(x 8) (8 x)(2x 7) = STAGE 3: RATIONAL ALGEBRAIC EXPRESSIONS x 2 + 2x 3 x 2 + 7x + 12 = x 2 2x 35 x x + 30 = 2x 2 5x 3 2x 2 3x 2 = MES Leticia A. Castañeda Bermea Página 6

7 II.- Perform the indicated operation and simplify 32x 33y 44x 8y = 8 4x 25 x x 4 x 2 = a 2 + 4a 45 3a 3 4a 20 a 2 81 = 2a + 3 4a + 6 4a + 5 2a + 3 8a a + 3 = III.-Find the Least Common Multiple (LCM) 55x 3, 5a 2 x 2,10a 4 15r 3, 21r 2 s 3, 35s 4 2a 4 b, 12a 3 b 2, 18a 2 b 4 IV.-Perform the following operations and simplify the answers. x x + 1 = 6 MES Leticia A. Castañeda Bermea Página 7

8 1 4m + 1 2m 2 3m = x + x + 5 x 5 = h 2 h h 10 = x 2 y2 y x + x y = m 6 m 1 m 9 m 3 = STAGE 4: LINEAR AND FRACTIONAL EQUATIONS Ì.-Evaluate the expressions and substitute the given values of the variable (x-2) If x=6 If x=4 MES Leticia A. Castañeda Bermea Página 8

9 3(w 9 ) + ( w + 5 ) If w=10 If w=3 If w=5 II.-Solve the following equations and show the steps in each transformation. 5x 2(x + 3 ) = 90 5n + 3( n + 4 ) = 28 III.-Solve the equations and prove the solutions. If it is an identity or the equations do not have solutions, write the appropriate conclusion. 9x 6 = 8x 10x + 24 = 8 + 8(x + 2) + 2x IV.-Solve the following equations and approximate the answer to two decimals 0.5(2.1x 3) = 0.6 (3.1x + 8) MES Leticia A. Castañeda Bermea Página 9

10 When a taxi driver starts, its taximeter displays $6.50. Once the taxi starts its travel, the amount increases at a ratio of $3.00 per kilometers travelled. Supposing that X is the number of kilometers travelled: a) Write an expression for the amount to pay after x kilometers. b) How much will you pay after 8 km? c) How much will you pay after 24 km? V.-Evaluate the formula for the given values of the literal constants. P = 50 t, t = 140 y v = 25 v A = 1 2 (b 1 + b 2 )h, b 1 = 12, b 2 = 8, h = 30 VI.-Solve the following application problem. Certain day the temperature in Monterrey is 39 C and it is descending at speed of 1.3 C per hour. That same day, the temperature in Saltillo is 24 C and it is descending at speed of 1.2 C per hour. a) Write an expression that represents the temperature in each city after x hours. b) Write an equation expressing both places have the same temperature. VII.- Solve the following equations and discard any extraneous root. 3x 8 x = 13 x MES Leticia A. Castañeda Bermea Página 10

11 3 2a = 5 a 7 VIII.-.Solve the following problems. The ratio of two integers is 17:13. Its addition is 390. Find the two integers. Mr. Gonzalez regularly gives $ per month for charity and $ per month to his grandchildren. a) What is the ratio of these two numbers in its minimun expression? b) Mr. Gonzalez testament specifies his inheritance will be divided in the same ratio. If his inheritance has $ , how much money will be for charity and how much for his grandchildren? The sides of a triangle are in a ratio of 7:10:11; its perimeter is 112 m. What is the length of each side? Clara is 31 years old and her sister Helena is 47. When will their ages be in a ratio of 4:5? I.- Evaluate x= 9, y=7 7-3(x + 2y) to:: STAGE 5: SYSTEM OF LINEAR EQUATIONS x=18, y= - 9 x= - 4, y= - 11 MES Leticia A. Castañeda Bermea Página 11

12 II.-Respresent the following ordinate pairs in the Cartesian plane and identify in a clear way each one. Then, identify the quadrant they are localed in. Point Quadrant Point Quadrant a) (4,2) f) (-2,3) b) (-3,7) g) (2,-6) c) (-3,-9) h) (-4,-7) d) (-2,-5) i) (3,-8) e) (0,1) j) (4,0) MES Leticia A. Castañeda Bermea Página 12

13 III.-Draw the graphs of the following equations. Make the corresponding line and, in the intersection point, write the correct coordinates Example#1 2x 4y =4 3x 6y =6 MES Leticia A. Castañeda Bermea Página 13

14 Example #2 2x + 3y = 18 x y = 5 IV.- Solve the following equations by the Substituting Method. y=2x 3x + y =10 x + 2y =2 5x 3y =-29 MES Leticia A. Castañeda Bermea Página 14

V.-Solve by substituting, draw the graph for both equations by the previous technique and show both graphs are intersected in the calculated point.

15 V.-Solve by substituting, draw the graph for both equations by the previous technique and show both graphs are intersected in the calculated point. 3x + y =1 x y = 7 Solution Proving Graph: VI.- Solve the following equations system by Addition and Subtraction method. x 4y =23 3x + y = 13 MES Leticia A. Castañeda Bermea Página 15

16 3x + 5y = 17 2x + 3y = 11 VII.- Solve the following application problems where the mathematical method is a system of lineal equations. The tickets for a show were sold in $400 numbered and $275 general and, they were sellout. Calculate how many tickets of each section were sold if the theater capacity is 1600 seats and the income was $552, 500. In the Automatic Teller Machine were deposited 967 bills, some of $20 and other of $50. The total amount of money is $37,970. How many bill were deposited of each quantity? MES Leticia A. Castañeda Bermea Página 16

MATH Spring 2010 Topics per Section

MATH Spring 2010 Topics per Section MATH 101 - Spring 2010 Topics per Section Chapter 1 : These are the topics in ALEKS covered by each Section of the book. Section 1.1 : Section 1.2 : Ordering integers Plotting integers on a number line