Centre Number For Examiner’s Use Candidate Number Surname Other Names Examiner’s Initials Candidate Signature Pages General Certificate of Secondary Education Foundation Tier November 2013 Mark 2–3 4–5 6–7 Mathematics 43601F Unit 1 Wednesday 6 November 2013 9.00 am to 10.00 am For this paper you must have: l mathematical instruments. 10 – 11 12 – 13 14 – 15 16 – 17 a calculator l F 8–9 TOTAL Time allowed l 1 hour Instructions
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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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2008 H I G H E R S C H O O L C E R T I F I C AT E E X A M I N AT I O N Mathematics General Instructions • Reading time – 5 minutes • Working time – 3 hours • Write using black or blue pen • Board-approved calculators may be used • A table of standard integrals is provided at the back of this paper • All necessary working should be shown in every question Total marks – 120 • Attempt Questions 1–10 • All questions are of equal value 212 BLANK PAGE – 2 – Total marks – 120
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A P P E N D I X E S Tables and Data Sets A Areas under the Normal Curve B Student’s t Distribution C Data Set 1 — Real Estate D Data Set 2 — Major League Baseball E Data Set 3 — OECD F Data Set 4 — Northwest Ohio School Districts G Critical Values of the F Distribution H Critical Values of Chi-Square I Binomial Probability Distribution J Factors for Control Charts K Poisson Distribution L Table of Random Numbers M Wilcoxon T Values N Banking Data Set — Case 262 Appendixes Appendix A Areas
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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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Brief Introduction: AJ Davis is a department store chain‚ which has many credit customers and want to find out more information about these customers. AJ Davis has complied a sample of 50 credit customers with data selected in the following variables: Location‚ Income (in $1‚000’s)‚ Size (Number of people living in the household)‚ Years (number of years the customer has lived in the current location)‚ and Credit Balance (customers current credit card balance on the store’s credit car‚ in $)
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Puzzle: Who Got More? Mrs Mess was buying a set of garden furniture. The bill was seventy rupees. She gave the attendant what she thought were two ₹50 notes‚ (actually two ₹100 notes). The attendant was sleepy and didn’t notice either‚ so he gave Mrs Mess what he thought were three ₹10 notes (actually three ₹50 notes). Who ended up better off than they should? Solution: Mrs Mess comes away better off than she should‚ by ₹20 in fact. Despite the warning in the title‚ Mrs Mess did pay
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Cause and Effect Essay Topics A cause and effect essay aims at explaining the reasons and results of an event or situation. • It is one the most popular essay types in the academic world. • It is beneficial for a student to write a cause and effect essay because it propels him to think of the situation in depth to come up with the reasons for the birth of that situation and its eventual impact on everything it affects. • It encourages the mind to think analytically and investigate a situation
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Causes of the Civil War The Civil War is an immense part of American history. It grasped battles all over the States with the Union against the Confederates‚ both fighting for the morals they believed were correct. Slavery was a big factor in the Civil War‚ with triggers that took a part in sparking the War such as‚ the Dred Scott v. Sanford case‚ the election of Abraham Lincoln‚ and the battle of Fort Sumter‚ which was the first battle of the Civil War. All of these events hold a special place
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