March 2018 Undergrad Admissions Assessment: Test 1 - English & Math Abilities, Study notes of Economics

Download March 2018 Undergrad Admissions Assessment: Test 1 - English & Math Abilities and more Study notes Economics in PDF only on Docsity! Undergraduate Admissions Assessment March 2018 TEST 1 - (Sections A, B1 and D). Three Hour Assessment. The UG Admissions Assessment (UGAA) gives Admissions Tutors the opportunity to see a sample of the applicant's original work, produced under examination conditions, and seeks to assess applicants from a variety of backgrounds in a fair and equitable manner. The assessment has three sections: comprehension exercises (Section A); essay questions (Section B); and mathematical problems (Section C or D). The purpose is to assess the applicant’s English language and mathematics abilities. It is not an assessment of general knowledge. The following criteria are of particular importance: • Clarity and precision of language • Sophisticated vocabulary • Logical structure and argument • Mathematical accuracy, techniques and conceptual understanding Before beginning the assessment, please read the following guidance and instructions carefully. Depending on the course to which you have applied, you have been entered for Test 1 or 2. Before beginning the assessment please check that you have received the correct paper. A list of courses and corresponding papers can be found overleaf. The assessment lasts three hours and all three sections must be completed. The marks for each section are weighted according to the paper. More time should be spent completing the sections with more marks attached. However, please note that to pass the UGAA a minimum grade in all three sections is required, as well as a good grade overall. Test 1: Section A (25%), Section B1 (25%), Section D (50%) Test 2: Section A (25%), Section B2 (50%), Section C (25%) Answer Booklets You must use the BLUE booklet for Sections A and B (English Sections) and the CREAM booklet for Sections C or D (Maths Sections). When answering the maths questions, you must show your working out, as well as your final answer. • Dictionaries may NOT be used • Hand-held calculators MAY be used. If a calculator is used please indicate on the answer booklet the type used (e.g. TI.500) TEST 1 TEST 2 BSc Actuarial Science (N321) BSc Economics (L101) BSc Economics with Economic History (L1V3) BSc Econometrics and Mathematical Economics (L140) BSc Economic History with Economics (VL31) BSc Economics and Economic History (V3L1) BSc Environmental Policy with Economics (F9L1) BSc Finance (N300) BSc Financial Mathematics and Statistics (GN13) BSc Government and Economics (LL12) BSc Accounting and Finance (NN34) BA Anthropology and Law (ML16) BSc Economic History (V300) BSc Economic History and Geography (V3L7) BSc Environment and Development (FK84) BA Geography (L702) BSc Government (L230) BSc Government and History (LV21) BA History (V146) BSc International Relations (L250) BSc International Relations and History (VL12) LLB Law (M100) BSc Philosophy, Logic, and Scientific Method (V503) BSc Politics and Philosophy (LV25) BSc Politics and International Relations (L290) BA Social Anthropology (L601) BSc Social Anthropology (L603) BSc Social Policy (L400) BSc Social Policy with Government (LL42) BSc Social Policy and Sociology (LL34) BSc Sociology (L301) BSc Geography with Economics (L7L1) BSc Management (N200) BSc Mathematics and Economics (GL11) BSc Mathematics with Economics (G1L1) BSc Mathematics, Business, and Statistics (G0N0) BSc Philosophy and Economics (LV15) BSc Philosophy, Politics and Economics (L0V0) BSc Social Policy and Economics (LLK1) BSc Statistics with Finance (G3N3) Please check you have received the correct paper. If you think you have received the wrong paper please notify the invigilator immediately. Test Papers Section A • All candidates should complete this section. • This section has one question only. • The marks achieved in this section account for 25% of your final exam result. Please turn over for Section B. Instructions: Write a summary (précis) of the following passage, in not more than 150 of your own words. You must write a summary, not a discussion of the passage. No credit will be given for answers made up of sentences extracted from the original passage. President Trump, whose first year in office saw near-constant turmoil and division, claimed Tuesday that he has ushered in an ebullient “new American moment” and issued a summons for “the unity we need to deliver for the people we were elected to serve.” The conciliatory tone of Trump’s first State of the Union address was sharply at odds with the combative manner in which he has conducted his presidency — and with the tension evident between Republicans and Democrats in the Capitol, where he spoke…. The president set an ambitious agenda for his second year in office, from a $1.5 trillion plan to rebuild the nation’s crumbling infrastructure to a four-pronged immigration package to a pledge to reduce prescription drug prices. His one-hour, 20-minute speech was the longest since Bill Clinton’s State of the Union address in 2000. The president laid out details of his immigration package, offering citizenship for undocumented immigrants brought to the United States as children, who are known as “dreamers,” in return for increased spending on border security, including for his promised wall at Mexico’s border; an end to the visa lottery; and limits on family reunification policies. Trump used some of his most polarizing language when lamenting crime from MS-13 and other gangs, which he blamed on “open borders.” He sought to repurpose the term “dreamer” by saying American citizens have seen their economic prospects dimmed and personal safety put at risk because of illegal immigration. “Trump calls for unity, pushes GOP agenda in State of the Union speech,” Washington Post, 30 January 2018 This page is left intentionally blank. Section B1 • Complete Section B1 ONLY if you are completing Maths Section D. • The marks achieved in this section account for 25% of your final exam result. Instructions: Write ONE essay from the following three choices: 1. ‘The voting age should be reduced to sixteen.’ Discuss. • What are the strengths and weaknesses of reducing the voting age? 2. ‘Ever since the advent of nuclear weapons, World War III between the great powers has been unthinkable.’ Discuss. • Have nuclear weapons produced peace between the great powers? 3. ‘Multinational corporations enjoy more power than states.’ Discuss. • Are states able to control multinational corporations? The light on a lighthouse is rotating at 3 revolutions per minute. a) What is the rate of rotation in radians per second (give your answer in terms of π) b) The lighthouse L is 2km from the centre of a straight breakwater AB as shown. i) Find an expression for the speed of the light 𝑑𝑥 𝑑𝑑 in m/s as it passes along the breakwater, where x is the distance along the breakwater from the closest point on the breakwater. Give your answer in terms of θ. ii) Evaluate your expression to find the speed of the light when it passes the closest point to the lighthouse, giving your answer exactly. A B θ L 2 km Question 4 a) Sketch the curve 𝑓(𝑥) = 𝑎𝑥 + 6 𝑎𝑥 − 2 ,𝑤ℎ𝑠𝑒𝑠 𝑎 > 0 Show the equations of any asymptotes and the coordinates of the points of intersection with the axes clearly on your sketch. (5 marks) b) Write 𝑎𝑥+6 𝑎𝑥−2 in the form 𝐴 + 𝐵 𝑎𝑥−2 where A and B are integers to be determined. (3 marks) c) Hence find the area fully enclosed by the curve f(x) and the x and y axes giving your answer in the form 𝐶 ln 2 + 𝐷 𝑎 where C and D are integers to be determined. (6 marks) Total 14 marks Question 5 (1 mark) (3 marks) (1 mark) Total 5 marks x Question 6 In this question give your numerical answers to an appropriate degree of accuracy. Jamil is saving money. At the start of each month he puts £50 into a savings account. At the end of each month the savings account adds 0.5% interest to his account. a) If he starts saving by putting £50 in his account at the start of January 2018 how much money will he have in his savings account at the end of the 2nd month i.e. February 2018, after the interest has been added? (2 marks) b) Derive a single expression in terms of n for the amount of money he will have in his account at the end of the nth month. (2 marks) c) Hence calculate how much money he will have at the end of December 2018. (3 marks) d) Use your answer to b) to find out the number of years it would take Jamil to have £1 million in his savings account if he continues saving in this way. (5 marks) Total 12 marks Question 7 a) Differentiate the following expressions with respect to x and simplify your answers: i) 𝑠(−𝑥2) ii) 𝑥𝑠𝑥 iii) 𝑥 𝑒𝑥 iv) 𝑥 𝑒(𝑥2) (7 marks) b) Find the following indefinite integrals: i) ∫ 𝑠−𝑥 𝑑𝑥 ii) ∫ 𝑥𝑠−𝑥 𝑑𝑥 iii) ∫𝑥𝑠(−𝑥2) 𝑑𝑥 (6 marks) c) On the same axes sketch 𝑦 = 𝑠−𝑥 and 𝑦 = 𝑥𝑠−𝑥for 𝑥 𝜖 ℝ showing the intercepts with the axes and any points of intersection of the curves clearly. (3 marks) d) i) Find an expression for the area between the curves from x = 1 to x = n giving your answer in terms of n, where n > 1. (4 marks) ii) Explain why the area you have found can never exceed 1/e (2 marks) e) On the same axes sketch 𝑦 = 𝑥𝑠−𝑥 and 𝑦 = 𝑥𝑠(−𝑥2)for 𝑥 ≥ 0 showing the intercepts with the axes, any turning points and any points of intersection of the curves clearly. (5 marks) f) Calculate the area fully enclosed between the curves giving your answer exactly. (3 marks) Total 30 marks Question 8 The outside of this lighthouse (excluding the light) can be modelled by the following curve: 5𝑥2 4 − 𝑦2 15 = 9 10 for −11 2 ≤ 𝑦 ≤ 3 2 a) Find x when y = - 5.5 (2 marks) b) Find the volume of revolution of the curve when rotated by 2π radians about the y- axis. Show a full algebraic method and give your final answer to 3 sf. (4 marks) c) The radius of the base is 4m, use this and your answer to b) to calculate the volume of the lighthouse giving your answer to 3 sf. (3 marks) Total 9 marks End of Test