Review of Algebra 2 s REVIEW OF ALGEBRA Review of Algebra q q q q q q q q q q q q q q q Here we review the basic rules and procedures of algebra that you need to know in order to be successful in calculus. Arithmetic Operations The real numbers have the following properties: a b b a ab a b c a b ab c ab ac In particular‚ putting a b and so b c b c ba c (Commutative Law) (Associative Law) (Distributive law) ab c a bc 1 in the
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inflexion point. 2. People use differential equations to predict the spread of diseases through a population. Populations usually grow in an exponential fashion at first: However‚ populations do not continue to grow forever‚ because food‚ water and other resources get used up over time. Differential equations are used to predict populations of people‚ animals‚ bacteria and viruses that are being affected by external events. The logistic equation (developed in the mid-19th century) allows for
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apart. Many enduring substances such as rock and water are highly stable. One molecule of methane and two molecules of oxygen yield one molecule of carbon dioxide. Chemists summarize chemical reactions using formulas called chemical equations. Chemical equations generally show the product formed when the
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of tree growth rate and the current height and the difference between the maximum height and its current height is k. Model building and solving According to the analysis of the problem and the assumptions made above‚ we obtain the following equation: Where the proportional constant k
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LAB REPORT 6 – IONIC REACTIONS No credit will be given for this lab report if the Data section is not completely filled out. OBJECTIVES 1. Study the nature of ionic reactions 2. Write balanced equations 3. Write net ionic equations for precipitation reactions PROCEDURE Please complete the entire experiment as instructed in the lab manual except for any modifications noted below. Fill out the report below‚ insert your digital photographs into the report‚ and submit it me electronically
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write a word equation? To write a word equation‚ write the names of the reactants separated by plus signs followed by an arrow‚ and followed by the names of the products separated by plus signs. 8. How do you write a skeleton equation? To write a skeleton equation‚ write the formulas of the reactants to the left of the arrow and the formulas of the products to the right of the arrow. 9. Describe the steps in writing a balanced chemical equation. To write a balanced chemical equation‚ first write
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Partial Fractions A way of "breaking apart" fractions with polynomials in them. What are Partial Fractions? We can do this directly: Like this (read Using Rational Expressions to learn more): 2 + 3 = 2·(x+1) + (x-2)·3 x-2 x+1 (x-2)(x+1) Which can then be simplified to: = 2x+2 + 3x-6 = 5x-4 x2+x-2x-2 x2-x-2 ... but how do we go in the opposite direction? That is what we discover here: How to find the "parts" that make the single fraction (the "partial fractions")
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place‚ creating a distinct root or two of the same root. For PROOF 1‚ the equation y=a(x-b)2 is used. PROOF 1 y = 3 (x – 2)2 = y = 3 (x2 – 4x + 4) = y = 3x2 – 12x + 12 ^ = b2 – 4ac = (-12)2 – 4 x 3 x 12 = 144 – 144 = 0 The discriminant is equal to zero. The parabola touches the x-axis at (2‚ 0) and as a in the equation is a positive value‚ the parabola curves upwards. For PROOF 2‚ the equation y=-a(x-b)2 is used. PROOF 2 y = -3(x - 2)2 = y = -3 (x2- 4x + 4) = y
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Student Name/Number:___________________ Teacher Name:__________________________ 2011 MID COURSE EXAMINATION Preliminary - YEAR 11 Mathematics Time allowed – Two hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Attempt ALL questions. ALL questions are of equal value. All necessary working should be shown in every question. Marks may be deducted for careless or badly arranged work. Board-approved calculators may be
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MATHEMATICS CURRICULUM FOR SECONDARY COURSE RATIONALE Mathematics is an important discipline of learning at the secondary stage. It helps the learners in acquiring decision- making ability through its applications to real life both in familiar and unfamiliar situations. It predominately contributes to the development of precision‚ rational and analytical thinking‚ reasoning and scientific temper. One of the basic aims of teaching Mathematics at the Secondary stage is to inculcate the skill
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