EUROPEAN SCHOOL Mathematics Higher Level Portfolio Type 1 SHADOW FUNCTIONS Candidate Name: Emil Abrahamyan Candidate Number: 006343-021 Supervisor: Avtandil Gagnidze Session Year: 2013 May Candidate Name: Emil Abrahamyan Candidate Number: 006343-021 Mathematics Higher Level Type 1: Shadow Functions SHADOW FUNCTIONS The Aim of the Investigation: The overall aim of this investigation is to investigate different polynomials with different powers and create shadow function
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Sullivan’s Handbags marks up their bags at 45% of the selling price. Pat Sullivan saw a bag at a trade show that she would sell to her customers for $85. What is the most she could pay for the bag and still retain the 45% markup of the selling price? 6. Jeff Jones earns $1‚200 per week. He is married and claims four withholding allowances. The FICA rate is as follows: Social Security rate is 6.2% on $97‚500; Medicare rate is 1.45%. To date his cumulative wages are $6‚000. Each paycheck‚
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1. Solve a. e^.05t = 1600 0.05t = ln(1600) 0.05t = 7.378 t = 7.378/.05 t = 147.56 b. ln(4x)=3 4x = e^3 x = e^3/4 x = 5.02 c. log2(8 – 6x) = 5 8-6x = 2^5 8-6x = 32 6x = 8-32 x = -24/6 x = -4 d. 4 + 5e-x = 0 5e^(-x) = -4 e^(-x) = -4/5 no solution‚ e cannot have a negative answer 2. Describe the transformations on the following graph of f (x) log( x) . State the placement of the vertical asymptote and x-intercept after the transformation. For example‚ vertical shift
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Treasure Hunt: Finding the Values of Right Angle Triangles This final weeks course asks us to find a treasure with two pieces of a map. Now this may not be a common use of the Pythagorean Theorem to solve the distances for a right angled triangle but it is a fun exercise to find the values of the right angle triangle. 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
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Module 8 Business Decisions Capital Gains Page 705‚ question 30 30A- How much tax will you have saved by waiting? $1‚250 $25‚000 X .10 = $2‚500 $25‚000 X .15 = $3‚750 $3‚750 - $2‚500 = $1‚250 30B- How much would you save in 36% bracket? Between $2‚000 to $4‚400 $25‚000 X .20 = $5‚000 $25‚000 X .28 = $7‚000 to $9‚900 $7‚000 - $5‚000 = $2‚000 $9‚900 - $5‚000 = $4‚400 Interpreting the numbers Page 743‚ Question 20 2‚300 2‚430‚ 2‚018‚ 2‚540‚ 2‚675‚ 4‚800
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Understanding What You Read – Week 3 Week 3- Chapter 5- Understanding Your Customer 1. Identify demographic trends that are occurring in the United States‚ related to (a) number of single-person households‚ (b) median age for marriage‚ (c) birthrate‚ (d) U.S. population growth‚ and (e) number of male homemakers. Single person households are showing the greatest increase in numbers and that trend is projected to continue. Birthrate has remained relatively stable in the United States since
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1998 9 14 1. 1.1 Markov Property 1.2 Wiener Process 1.3 2. 2.1 2.2 2.3 2.4 2.5 2.6 Taylor Expansion 2.7 3. Stochastic 3.1 3.2 SDE(Stochastic Differential Equation) 4. Stochastic 4.1 Stochastic integration 4.2 Ito Integral 4.3 Ito Integral 4.4 5. Ito’s Lemma 5.1 Stochastic 5.1.1 5.1.2 5.1.3 First Order Term Second Order Term Cross Product Terms “ ” – Ito Integral Riemann (Ordinary Differential Equation) (Chain rule) 5.2 Ito’s Lemma 6. 6.1 6.1.1 6.1.2 Closed-Form Solution Numerical Solution
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let f(x) be a quadratic polynomial such that that f(2)= -3 and f(-2)=21‚ then the co-efficient of x in f(x) is a. -3 b. 0 c. -6 d. 2 1. if f(x) =x3 +ax+b is divisible by (x-1) 2 ‚then the remainder obtained when f(x) is divided by (x+2) is ; a. 1 b . 0 c. 3 d. -10 3. the remainder when x1999 is divided
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Discuss the cause of the Tacoma bridge disaster‚ in terms of waves‚ vibrations‚ and resonance. Elaborate the effects with relevant equations and formulae. The Tacoma bridge collapse can be attributed to the waves caused by the buildup of energetic vibrations. These energetic vibrations were built up from the bridge “taking energy from the steadily blowing wind” (Crowell). Eventually enough of these energetic vibrations built up to cause resonance within the system‚ causing the wave-like motion
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Mathematics is highly valued in our society but for many students the thought of learning mathematics is daunting. Learning mathematics in primacy school may have been a positive experience but it may have also been filled with frustration and anxiety. If a teacher has a negative view of mathematics then their students will adopt this view. Students must be shown the relevance and purpose of mathematics in a real life and meaningful way. There is no doubt that mathematics is an indispensable tool
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