(Division of Aakash Educational Services Ltd.) Regd. Office : Aakash Tower‚ Plot No.-4‚ Sec-11‚ MLU‚ Dwarka‚ New Delhi-110075 Ph.: 011-47623456 Fax : 011-47623472 Admission-cum-Scholarship Test (Sample Paper) (First Step for IIT-JEE 2012-2014) (Syllabus of the Test : Mathematics of Class IX & X) Roll No.: __________________ Test Booklet Code: Time : 1½ Hrs. A Max.Marks : 150 INSTRUCTIONS TO THE CANDIDATES 1. The initial 10 minutes are earmarked for the candidates to carefully
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Real number Irrational numbers π ‚ √�� Rational numbers Integers Whole Natural 3 5 1 2 4 2 2 3 Rational Like: Integers {…‚ -3‚ -2‚ -1‚ 0‚ 1‚ 2‚ 3…….} Whole {0‚ 1‚ 2‚ 3…} Natural {1‚ 2‚ 3…} ‚ ‚ ‚ Properties of real numbers 1234- Reflexive property a=a Symmetric property a = b then b = a Transitive property a = b and b = c then a = c Principle of substitution if a = b then we can substitute b for a in any expirations Commutative properties a+b=b+a ‚ a.b=b.a Associative properties
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Contents Preface xiii To the Student xxi Calculators and Calculations xxii 1 Fundamentals ■ 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 Chapter Overview 1 Real Numbers 2 Exponents and Radicals 12 Algebraic Expressions 24 ● DISCOVERY PROJECT Visualizing a Formula 34 Rational Expressions 35 Equations 44 Modeling with Equations 58 ● DISCOVERY PROJECT Equations through the Ages 75 Inequalities 76 Coordinate Geometry 87 Graphing Calculators; Solving Equations and Inequalities
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What is irrational and rational decision making? Well first to understand what each on is individually‚ I believe that you should know what each word means separately. So according to meriam-webster.com‚ rational means‚ “having reason or understanding” (Rational‚ 2009) while irrational means‚ “not endowed with reason or understanding.” (Irrational‚ 2009). Lastly but not least‚ from the Encarta.msn.com/dictionary‚ decision making‚ is “the process of making choices or reaching conclusions‚ especially
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TMA 01 Answer Sheet Student name: Student PI number: Module year and month (e.g. ‘2012 February’): 2012 February Question number Answer 1 i. A 1 ii. B 1 iii. C 2. The author suggests the results to the studies mean that desirable approaches to studying can be brought about by appropriate course design‚ appropriate teaching methods or appropriate forms of assesments. 3 i. 2 3 ii. 4 3 iii 1 3 iv. 3 4. D 5. C 6. A 7. B 8 i. Course Experience Questionnaire (CEQ)
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Buried treasure. Ahmed has half of a treasure map‚ which indicates that the treasure is buried in the desert 2x - 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure‚ one must get to Castle Rock‚ walk x paces to the north‚ and then walk 2x - 4 paces to the east. If they share their information then they can find x and save a lot of digging. What is x? Given this scenario the Pythagorean Theorem would be the strategy we use to solve for x
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9 Mathematics Learner’s Material Module 4: Zero Exponents‚ Negative Integral Exponents‚ Rational Exponents‚ and Radicals This instructional material was collaboratively developed and reviewed by educators from public and private schools‚ colleges‚ and/or universities. We encourage teachers and other education stakeholders to email their feedback‚ comments‚ and recommendations to the Department of Education at action@deped.gov.ph. We value your feedback and recommendations. Department of Education
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ALWAYS‚ SOMETIMES‚ OR NEVER Chapter 9 Tell whether each statement is always‚ sometimes‚ or never true. 1. The graph of a quadratic function is a straight line. 2. The range of a quadratic function is the set of all real numbers. 3. The highest power in a quadratic function is 2. 4. The graph of a quadratic function contains the point (0‚ 0). 5. The vertex of a parabola occurs at the minimum value of the function. 6. The graph of a quadratic function that has a minimum
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tive if there existed a decline in population. Otherwise‚ r can be found as a ratio of the birth rate to the death rate. If we let 1 + r = b‚ the base of the exponential expression‚ the function becomes p = p 0bt. An alternative version of this relation describes the time it would take for the population to reach a given amount p: t = logb( p / p0). Students will use both functions to predict the future global population‚ provided the current growth rate or 1.3% (Abbott‚ 2004). This relation will
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Week Three Written Assignment mustangsallygt08 MAT126 February 18‚ 2013 Week Three Written Assignment The steps that are being followed to solve quadratic equations that came from India‚ and the steps are: (a) Move the constant tern to the right side of the equation. (b) Multiply each term in the equation by four times the coefficient of the x2 term. (c) Square the coefficient of the original x term and add it to both sides of the equation. (d) Take the square root of both
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