**and** Skew-Symmetric Matrices. Transposition gives rise to two useful **classes** of matrices. Symmetric matrices are square matrices whose transpose equals the matrix itself. Skew-symmetric matrices are square matrices whose transpose equals minus the matrix. Both cases are defined in (11) **and** illustrated by Example **8**/ respect to the two **algebraic** operations (addition **and** scalar multiplication) defined **for** the vectors of V.”/zero. In particular, a determinant with two **identical** rows or columns has the value zero./

NOR, **and** NAND? **For** example, implementing X **and** Y is/**expression** that is true when the variables X **and** Y have the same value **and** false, otherwise X, Y are Boolean **algebra** variables CS 150 - Spring 2008 – Lec #3: Combinational Logic - 7 Axioms **and** Theorems of Boolean **Algebra** **Identity**/ Y) • Z = X • (Y • Z) CS 150 - Spring 2008 – Lec #3: Combinational Logic - **8** Axioms **and** Theorems of Boolean **Algebra** (cont’d) Distributivity: **8**. X • (Y + Z) = (X • Y) + (X • Z) 8D. X + (Y •/the scope of this **class**) Can identify non-/

partition is to be installed so that 2 **classes** can use it. The area of the smaller classroom is 38x. How can the area of the larger classroom be **expressed** in terms of x? Correct Answer - D Spring 2003 #19 A(b)(3) Foundations **for** functions. The student understands how **algebra** can be used to **express** generalizations **and** recognizes **and** uses the power of symbols to represent/

**and** y’s do not make the connections **and** cannot apply the techniques learned in math **classes** when other letters arise in other disciplines. Should x Mark the Spot? Kepler’s third law **expresses** the relationship between the average distance of a planet from the sun **and**/ exponential function. T = **8**.6 + 35.439(0.848) t. Integrating Statistics in College **Algebra** The normal distribution function is It makes **for** an excellent example involving both stretching **and** shifting functions **and** a composite function. Match /

support such as ICT **8**. listen to **and** deal with unpredictable **and** less familiar language 9. listen to **and** talk about past, present **and** future actions **and** events 10. use what they hear to develop their own productive language 11. adapt **and** vary previously learned language to suit context, audience **and** purpose **for** reuse in speech 12. **express** **and** justify personal opinions **and** feelings 13. use language creatively **and** imaginatively. Skills Modern Foreign/

**for** the desired binomial by substituting **for** “a” **and** “b” –Simplify the result Homework Problems Section: Page: Problems:Binomial Worksheet There is no MyMathLab Homework Assignment that corresponds with these problems Binomial Expansion Worksheet Use the Binomial Theorem to expand **and** simplify each of the following: 1. 2. 3. 4. 5. 6. 7. **8**. Equation a statement that two **algebraic** **expressions**/ classified as a “contradiction” **and** has “no solution” **Identity** Solve: x – (2 /**for** a grade on the date of our next **class**/

**expression** **for**. Answer: the quotient of **8** times x squared **and** 5 Example 1-4b Answer: the difference of y to the fifth power **and** 16 times y Write a verbal **expression** **for**. Example 1-4c Write a verbal **expression** **for** each **algebraic** **expression**/Answer:Additive **Identity** Property Example/**and** the number of cars sold. Example **8**-4d Answer: Example **8**-5a Mr. Mar is taking his biology **classes** to the zoo. The zoo admission price is $4 per student, **and** at most, 120 students will go. Identify a reasonable domain **and** range **for**/

**identical** twin) = Simplify. The probability that a child is not an **identical** twin is. 249 250 P(not an **identical** twin) + P(**identical** twin) = 1 Write an equation. Probability PRE-**ALGEBRA**/**8**% of Earth’s surface. What is the approximate surface area of Earth? 1,128 200 214% about 511,000,000 km 2 6-6 Percents **and** Equations PRE-**ALGEBRA** LESSON 6-7 6-7 Match each **expression** in Column 1 with an equivalent **expression**/ he make on the sale of a car **for** $35,000? Percents **and** Equations PRE-**ALGEBRA** LESSON 6-7 c = 0.065 35,/

**8**, 2012 COMMUNITY COLLEGE RESEARCH CENTER Concepts of Numbers: A Case Study **for** Scaling Meaningful **and** Sustainable Reform SCALING INNOVATION / NOVEMBER **8**, 2012 **8** COMMUNITY COLLEGE RESEARCH CENTER The success rates* **for** the past eight years in our arithmetic **classes**/integers **algebraic** **expressions** Application of the addition concept (perimeter, money problems) **Identity** element, commutative & associative properties, **and** binary operation concepts are introduced Unit 4: Addition SCALING INNOVATION / NOVEMBER **8**, /

**algebra** how to efficient programs could be generated automatically taught me how to think about ASD Modularity15-21 ASD MODULARITY DIAGRAMS – PART 1 Modularity15-22 UML **Class** Diagrams Allow designers to **express** relationships among program entities declarative in that they can be implemented in LOTS of ways Modularity15-23 In Automated Design Different entities **and**/**for** Modular Relationship Commuting diagram Defines compositional equivalences (**algebraic** **identities**) No implementation or language is perfect **for**/**8**/

A.PA.07.11 Understand **and** use basic properties of real numbers: additive **and** multiplicative **identities**, additive **and** multiplicative inverses, commutativity, associativity, **and** the distributive property of multiplication/. 36 minutes GLCE: D.AN.07.03 Calculate **and** interpret relative frequencies **and** cumulative frequencies **for** given data sets. State Results District Results A6% / A. n + **8** B. n – **8** C. 8n D. **8** - n A.FO.06.06 Represent information given in words using **algebraic** **expressions** **and** equations. (Core) /

**expressed** another way as “**for** each thing, if it is worth doing then cynics are wrong” Go forward to see that way. Problem 19107 If something is worth doing then cynics are wrong. FET:if it is worth doing then cynics are wrong. Let’s pick a specific thing worth doing, like “**Algebra** Go forward to see the FET fall of **and**/We might need **identity** **for** this. Let us use the universal form **and** try to represent that. Think about the symbols **and** then go / ready. Problem **8** with identity369 There are at most three things /

2. –Path **expressions** are a side effect of the definitions. Dependent join q 1 join q 2 –**For** each element e/**8** name ”Lee” i 9 born 1951 i 128 i 16 Emp i 17 sal 1500 i 18 worksIn i 19 Student i 20 studentNo 223344 i 21 faculty ”Physics” K.Subieta. SBA **and** SBQL, slide 69 Sept. 2006 SBQL semantics **for** M2 Changes concern only ENVS **and** non-**algebraic** operators –The order of sections of roles **and** **classes**/migration: An object can change its **classes** without changing its **identity**. Temporal properties: Roles can represent/

) | = | **8** | = **8**. ? Ex: A combination of variables **and** numbers using the operations of addition, subtraction, multiplication, or division, as well as powers or roots, is called an **algebraic** **expression**. Note: there is NO EQUAL SIGN, **and** we can only SIMPLIFY, not SOLVE! Here are some examples of **algebraic** **expressions**: x + 6, x – 6, 6x, x/6, 3x + 5. **Algebraic** **Expressions** Note: In none of these cases can you SOLVE **for** the/

will be completed together in **class** during review time. Students are not expected to complete every single problem in the packet. They should complete several problems from each page-- in addition to studying the notes **and** past quizzes– in order to be fully prepared **for** test. Topics: Order of Operations Evaluating **Algebraic** **Expressions** Verbal Math Sentences (translating) Properties Commutative Associative Distributive **Identity** Inverse Zero Property Sequences/

**Algebra** 1(A/B) Mr. Valdez Fall 2012 **Class** Schedule **Class** Announcements Quiz 2.5-2.6 today! Chapter 2 Test on Monday, October 1 st Warm-Up Homework Check/Questions Color Card Review Lesson Recap Quiz 2.5-2.6 Warm-Up 1) Simplify: (-**8**/ of the **expression** when x = 3? a) 72w 2 b) 36w 3 c) -36w 3 d) -72w 3 e) -72w 2 a)Commutative b) **Identity** c) Associative d) Distributive e) Inverse a) **8** b) 10/ of everything except **for** a pencil You may use a multiplication table You must remain quiet until all /

**Algebra** logical not ( ~ ) not B also ~B This is the negation or the opposite of B. Venn Diagram #6 not (A **and** B) ~(A * B) This is the opposite of (A **and** B). Venn Diagram #7 not (A or B) ~(A + B) This is the opposite of (A or B). Venn Diagram #**8** not A **and** not B ~A * ~B This is **identical**/(x == 5); System.out.println(); } Output **for** the next 3 programs… // Java1003.java // This program shows a boolean **expression** being used in a while statement. public **class** Java1003 { public static void main (String args[]) /

The relational model has rigorously defined query languages that are simple **and** powerful q Relational **algebra** is operational; useful as internal representation **for** query evaluation plans q Projection, selection, cross-product, difference **and** union are the minimal set of operators with which all operations of the relational **algebra** can be **expressed** q Several ways of **expressing** a given query; a query optimizer should choose the most efficient/

**algebra** is like ordinary **algebra** except that variables stand **for** bits, + means “ or ”, **and** multiplication means “ **and** ”. See chapter 10 **for**/**for** logical **expressions**. Ex: since p / p p, q / ( p / p) q / p Topic #1.1 – Propositional Logic: Equivalences The Foundations Transparency No. 1-40 Equivalence Laws - Examples **Identity**/#Students ; #sons + #sons = 2 #sons ( #students / #**classe**) + ( #students / #**classe**) = 2 * + ( #students / #**classe**) ( x – z = 5) + (x – z + 5)/ earlyPremise #4. **8**. earlyModus ponens on 6/

an equivalent **algebraic** **expression**. a. -3(m – 4) -3(m – 4) = -3m – (-3)(4) = -3m + 12 b. 9(-3n – 7y) 9(-3n – 7y) = 9(-3n) – (9 ∙ 7y) = -27n – 63y 8m + 24n -3y + 30 6a + 24 On a school visit to Washington D.C., Daniel **and** his **class** visited the Smithsonian Air **and** Space Museum. Tickets to the IMAX movie cost $**8**.99. Find the total cost/

product of a number multiplied by 0 is 0. Multiplicative **Identity** The product of a number multiplied by 1 is the/156 Copyright © 2011 Pearson Education, Inc. Example **8** Bruce has the following test scores in his biology **class**: 92, 96, 81, 89, 95, 93/**and** quotient indicate the answer **for** their respective operations. sum of x **and** 3 x + 3 difference of x **and** 3 product of x **and** 3quotient of x **and** 3 x – 3 x 3 x 3 Slide 1- 167 Copyright © 2011 Pearson Education, Inc. Example 1 Translate to an **algebraic** **expression**/

a(bc) ›**Identity** a + 0 = a, 0 + a =a a.1 = a, 1. a = a ›Inverse a + (-a) = 0 a. 1/a = 1, a /= 0 ›Distributive a(b + c) = ab + ac **ALGEBRA** 2; AGENDA/ 44 (even) & 45-55 (all) › Home Learning: Vocabulary W/S Today!! (Due **8**/28/15) **ALGEBRA** 2; AGENDA; DAY 6; MON. AUG. 31, 2015 (1 st 9-Weeks) ›SEE /**and** show procedure **for** solving such items. ›ACTIVITIES: Solve complex numbers **and** Rational **expressions**. › HOME LEARNING: Complete worksheet if you did not complete in **class**. Assignment on KHAN ACADEMY (PROBABILITY). **ALGEBRA**/

**and** generate one output signal. Binary Logic The binary logic system is one of a **class** of mathematical systems referred to as Boolean **Algebra**. In digital electronics, Boolean variables 0 **and** 1 correspond to binary 0 **and** 1. Input **and**/**for** the following Boolean **algebraic** **expressions**: x+yx+y (x+y)x(x+y)x x+yx+y (x+y)x(x+y)x Circuit-to-Truth Table Example OR A Y NOT **AND** B C 2 # of Inputs = # of Combinations 2 3 = **8**/ the following **identity** of each of the following Boolean equations using **algebraic** manipulation: a/

**algebra** is like ordinary **algebra** except that variables stand **for** bits, + means “ or ”, **and** multiplication means “ **and** ”. See chapter 10 **for**/**for** logical **expressions**. Ex: since p / p p, q / ( p / p) q / p Topic #1.1 – Propositional Logic: Equivalences The Foundations Transparency No. 1-40 Equivalence Laws - Examples **Identity**/#Students ; #sons + #sons = 2 #sons ( #students / #**classe**) + ( #students / #**classe**) = 2 * + ( #students / #**classe**) ( x – z = 5) + (x – z + 5)/ earlyPremise #4. **8**. earlyModus ponens on 6/

by a number is the sum of the product of each addend **and** the number. **Identity** Property of Addition 0 + a = a **Identity** Property of Multiplication 1 x a = a Inverse Property of Addition /**AND** SIT IN YOUR ASSIGNED SEAT. -FILL OUT YOUR AGENDA **AND** HAVE IT OUT **FOR** ME TO SIGN. -COMPLETE THE FOLLOWING WARM-UP: Classwork: **8**.4 Understanding **Algebra** Word Problems Pg. 104 - 105 Homework: VOCAB QUIZ TUESDAY! **Algebra** Word Problems **8**.4 (pg. 104) 1.Read the problem CAREFULLY. 2.Decide what is known. These terms are **expressed**/

**Algebra** –Section 2.1 of Katz’s Textbook –In-**class** Activity #2 2 Recap XYX ORY 0 0 1 1 0 1 0 1 0 1 1 1 Z = X + Y OR XYXY Z Binary Octal Decimal Hex 3 You already know the rules **for** decimal addition **and** subtraction (how to handle sums, carries, differences, **and**/ the **AND**-OR Two bubbles cancel each other out 23 DeMorgans Law Examples: Use to convert **AND**/OR **expressions** to OR/**AND** **expressions** 24 / (1) X (1) = X **identity** (1D) distributive law (**8**) **identity** (2) **identity** (1) Proving Theorems 26 Other Useful Functions/

6.Acceptance 7.Ada Lovelace **8**.**Algebraic** numbers 9.Algorithms 10./**classes** 70.Complexity gaps 71.Complexity Zoo 72.Compositions 73.Compound pendulums 74.Compressibility 75.Computable functions 76.Computable numbers 77.Computation **and**/**identities** 328.Ramsey theory 329.Randomness 330.Rational numbers 331.Real numbers 332.Reality surpassing Sci-Fi 333.Recognition **and** enumeration 334.Recursion theorem 335.Recursive function theory 336.Recursive functions 337.Reducibilities 338.Reductions 339.Regular **expressions**/

**expression** is often used even when R 1 R 2 –see Example 6.7 **and** Example 6.**8**/**Algebra** Boolean Constants –these are ‘0’ (false) **and** ‘1’ (true) Boolean Variables –variables that can only take the vales ‘0’ or ‘1’ Boolean Functions –each of the logic functions (such as **AND**, OR **and** NOT) are represented by symbols as described above Boolean Theorems –a set of **identities** **and** laws – see text **for**/ Limited 2004 OHT 1.615 **Classes** of Amplifier **Class** A –active device conducts **for** complete cycle of input signal/

(s.toDouble)) def application: Parser[Application] = **ident**~"("~repsep(expr, ",")~")" ^^ { case f~"("~ps~")"/**expression** **and** its resulting value (Int) an equals sign (=) the value resulting from evaluating the **expression** (3) 66 More features Supports lightweight syntax **for** anonymous functions, higher-order functions, nested functions, currying ML-style pattern matching Integration with XML –can write XML directly in Scala program –can convert XML DTD into Scala **class** definitions Support **for** regular **expression**/

**Algebra** logical not ( ~ ) not B also ~B This is the negation or the opposite of B. Venn Diagram #6 not (A **and** B) ~(A * B) This is the opposite of (A **and** B). Venn Diagram #7 not (A or B) ~(A + B) This is the opposite of (A or B). Venn Diagram #**8** not A **and** not B ~A * ~B This is **identical**/: Everything shaded only once. // Java1001.java // This program demonstrates a boolean **expression** being used in an if statement. public **class** Java1001 { public static void main(String args[]) { System.out.println(" JAVA1001./

Rationality Rational **Expressions** 3 About the LDIAG Hopf **algebra** In a relatively recent paper Bender, Brody **and** Meister (*) introduce a special Field Theory described by a product formula (a kind of Hadamard product **for** two exponential /**8** 23 24 We could check that this law is associative (now three independent proofs). **For** example, direct computation reads 25 26 This amounts to use a monoidal action with two parameters. Associativity provides an **identity** in an **algebra** which acts on a diagram as the **algebra**/

Week 3 Day 1 Bring every assignment to next **class** **for** a progress report. Chapter 1 Fundamental Concepts 1.6 **Algebraic** **Expressions** Add **and** Subtract 1.7 Exponents **and** Radicals 1.**8** Multiplication of **Algebraic** **Expressions** 1.9 Division of **Algebraic** **Expressions** 1.10 Linear Equations 1.13 Applications Involving Linear Equations 1.14 Ratio **and** Proportions 1.11 **and** 1.12 previously covered. 1.6 **ALGEBRAIC** **EXPRESSIONS** page21 Definitions help when later you read how/

**identity** element **for** **and** A + 0 = A0 is the **identity** element **for** or ~(~A) = ADouble negative law Basic Laws of Boolean **Algebra** - 3 A + ~A = 1Law of Complement **for** or A * ~A = 0Law of Complement **for** **and** ~(A + B) = ~A * ~BDeMorgans Law ~(A * B) = ~A + ~BDeMorgans Law The Law of Absorption presents the following two **expression**/ or false. Boolean variables adds readability to programs. import java.util.Scanner; public **class** Java1002 { public static void main (String args[]) { System.out.println(" JAVA1002.JAVA/

**for** the tightest possible integration of OOP **and** FP in a statically typed language. This continues to have unexpected consequences. Scala unifies –**algebraic** data types with **class**/**expressions**, stats: cond ? expr1 : expr2 // **expression** if (cond) return expr1; // statement else return expr2; switch (expr) { case pat 1 : return expr 1 ;... case pat n : return expr n ; } // statement only 39 Scala cheat sheet (3): Objects **and** **Classes** Scala **Class** **and** Object **class**/Parser[Application] = **ident**~"("~repsep(expr, /

**and** experiences of faculty **and** students Current system not structured to encourage pedagogical improvement Causes **for** Concern at MCCC The success rates* **for** the past eight years in our arithmetic **classes**/Subtraction Unit 6: Multiplication Unit 7: Division Unit **8**: Combinations Unit 1: History of Numbers In understanding / fractions integers **algebraic** **expressions** Application of the addition concept (perimeter, money problems) **Identity** element, commutative & associative properties, **and** binary operation concepts/

information about facts. Interrogative: get information from others. **Expressive**: **express** feelings **and** attitudes of the speaker. Evocative: create certain feelings / two words fall into different categories, the **class** of the second or final word will be/**algebra** alcohol Loss of words Words can be lost from a language as time goes by. The following words, taken from Romeo **and**/**identical** part of culture between two societies owing to some similarities in the natural environment **and** psychology of human beings. **For**/

b in place of a ÷ b ● coefficients written as fractions rather than as decimals ● brackets A2 substitute numerical values into formulae **and** **expressions**, including scientific formulae A3 understand **and** use the concepts **and** vocabulary of **expressions**, equations, formulae, **identities**, inequalities, terms **and** factors A4 simplify **and** manipulate **algebraic** **expressions** by: ● collecting like terms ● multiplying a single term over a bracket ● taking out common factors ● expanding products of two or more/

b in place of a ÷ b ● coefficients written as fractions rather than as decimals ● brackets A2 substitute numerical values into formulae **and** **expressions**, including scientific formulae A3 understand **and** use the concepts **and** vocabulary of **expressions**, equations, formulae, **identities**, inequalities, terms **and** factors A4 simplify **and** manipulate **algebraic** **expressions** by: ● collecting like terms ● multiplying a single term over a bracket ● taking out common factors ● expanding products of two or more/

**8** ¼ inches ¾ + 5/4 = **8**/4 3(x + 1) + 5(x+1) = **8**(x+1) Students’ expertise in whole number arithmetic is the most reliable expertise they have in mathematics It makes sense to students If we can connect difficult topics like fractions **and** **algebraic** **expressions** to whole number arithmetic, these difficult topics can have a solid foundation **for**/ b = b + a 2 + 3 = 3 + 2 Additive **identity** property of 0 a + 0 = 0 + a = a 3 + 0 = 0 + 3 = 3 Existence of additive inverses **For** every a there exists –a so that a + (–a) = /

involving the calculation of percentages [**for** example, of measures, **and** such as 15% of 360] **and** the use of percentages **for** comparison solve problems involving similar shapes where the scale factor is known or can be found solve problems involving unequal sharing **and** grouping using knowledge of fractions **and** multiples. **Algebra** use simple formulae generate **and** describe linear number sequences **express** missing number problems **algebraically** find pairs of numbers that/

6.46ms + (**8**.33ms * (16/4)) = 39.8ms (1 average seek) (time per rotation) (# rotations) Objectives **for** instruction **and** expected results **and**/or skills developed from learning. 24 Mirroring Disks Mirroring Disks – having 2 or more disks hold **identical** copied of data./ the conversion, we need rules **for** replacing two-argument selection with a relational **algebra** **expression** Different rules depending on the nature of the sub query Here is shown an example **for** IN operator **and** uncorrelated query (sub query computes a/

Bit-level manipulations Boolean **algebra** **Expressing** in C Representations of Integers Basic properties **and** operations Implications **for** C 15-213 F’07 class02.ppt 15-213 “The **Class** That Gives CMU Its/ double888 long double–10/1210/12 char *448 »Or any other pointer – **8** – 15-213: Intro to Computer Systems Fall 2007 © Byte Ordering How should/w (t, UMult w (u, v)) = UMult w (UMult w (t, u ), v) 1 is multiplicative **identity** UMult w (u, 1) = u Multiplication distributes over addtion UMult w (t, UAdd w (u, v)) = UAdd/

languages is **identical**. Relational Completeness : A relational query language L is relationally complete if we can **express** in L any query that can be **expressed** in the relational calculus (or **Algebra**). Most relational query languages are relationally complete More **expressive** power is provided by operations such as aggregate functions, grouping **and** ordering . Capter 9 ER- **and** EER-to-Relational Mapping, **and** Other Relational Languages Functional Dependencies **and** Normalization **for** Relational/

numbers »characters **and** strings »Instructions Bit-level manipulations Boolean **algebra** **Expressing** in C 15-213 F’03 class02.ppt 15-213 “The **Class** That Gives/ Linux P Linux Address Hex: B F F F F **8** D 4 Binary: 1011 1111 1111 1111 1111 1000 1101 /**identity** **for** sum 1 is **identity** **for** product – 24 – 15-213, S’04 Boolean **Algebra** {0,1}, |, &, ~, 0, 1 forms a “Boolean **algebra**” Or is “sum” operation **And** is “product” operation ~ is “complement” operation (not additive inverse) 0 is **identity** **for** sum 1 is **identity** **for**/

+ (**8**.33ms * (16/4)) = 39.8ms (1 average seek)(time per rotation)(# rotations) CS 257 Database Principles Mirroring Disks Mirroring Disks – having 2 or more disks hold **identical** copied /**for** replacing two-argument selection with a relational **algebra** **expression** Different rules depending on the nature of the sub query Here is shown an example **for** IN operator **and**/ databases this layer is often defined by a collection of **classes** CS 257 Database Principles Heterogeneity Problem What is Heterogeneity Problem /

into matrix A’, then use Tools/Matrix **Algebra** to multiply this pair of matrices in a specific order. 1 2 3 4 5 6 7 **8** 9 10 AP CO DE HP IB/. Words with **identical** matrices or images are equivalent, **and** the set of all words with **identical** images comprise an equivalence **class**. **For** Krackhardt’s high/**for** the A&F role table permutes **and** partitions the 5x5 table into two groups that produce “nearly **identical** results”: {1,3} **and** {2,4,5} which have the word equivalences {A,AF} **and** {F,FA,FF}. The reduced matrix **expresses**/

**and** check the answers. Use correct **algebraic** terminology, such as variable, equation, term, coefficient, inequality, **expression**, **and** constant. Evaluate numerical **expressions** **and** simplify **algebraic** **expressions** by applying the correct order of operations **and** the properties of rational numbers (e.g., **identity**, inverse, commutative, associative, **and** distributive properties). Justify each step in the process. Solve an equation or formula with two variables **for**/ tells the **class** that they are going to play a guessing /

**8**(x+1) Unitizing links fractions to whole number arithmetic Students’ expertise in whole number arithmetic is the most reliable expertise they have in mathematics It makes sense to students If we can connect difficult topics like fractions **and** **algebraic** **expressions** to whole number arithmetic, these difficult topics can have a solid foundation **for** students Operations **and**/ **identity** property of 0 a + 0 = 0 + a = a 3 + 0 = 0 + 3 = 3 Existence of additive inverses **For** /**class** in questions Object **and** focus is **for**/

fraction that is below the line Factor: one of two or more numbers, **algebraic** **expressions**, multiplied together produce a given product; a divisor Example 1: Step 1: Factor completely the numerator **and** denominator. Look **for** common factors. Step 2: 3 is a common factor. Cross both 3’s out **and** replace them **for** 1’s. Simplify 3a+6 3a+3b 3(a+2) 3(a+b/

**for** weak students of **Class** X **and** XII Unit Tests on every Monday in all schools **for** all subjects in rotation Preparation **and** distribution of Question Banks to students (Free of cost) Stress on proper correction **and** application based assignments Results of unit tests to be monitored **and**/ I. **Algebra** 26 (**8**) 1. Linear Equations 7 (2)11- 2. Polynomials 3 (1)1-- 3. Rational **Expression** 3 (/. Students should be made to learn the basic **identities** thoroughly Diffi - cult 2.Complementary angles (Internal /

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