Math assignment
Microsoft Word - Assignment A 4 Assignment File Unit 2 Assignment (54 marks) Chapter 3 1. Find a general linear equation (Ax+By+C = 0, with A,B,C integers) of the straight line which passes through (5, 2) and (6,−8), and sketch the line. (4 marks) 2. Find the slope, y-intercept, and x-intercept of the line given by x − 9 = 5y + 3 and sketch its graph. (4 marks) 3. An oil producer will place 1.5 million barrels of oil per week on the market when the price is $75 per barrel, and 2.5 million barrels of oil per week when the price is $90 per barrel. (a) Find the supply equation (giving price as a function of quan- tity), assuming that price p and quantity q are linearly related. (3 marks) (b) According to this model, how much will this producer supply if the price of oil goes to $110 per barrel? (2 marks) 4. Sketch of a graph of the function f(x) = −3x2 + 18x + 7. State the vertex and y-intercept of the graph of the function. (4 marks) 5. The demand function for an office supply company’s line of fuzzy pen- cils is p = 23−2q, where p is the price per box of pencils when q boxes are demanded (per week) by consumers. Find the level of production that will maximize the manufacturer’s total revenue, and determine this revenue (assuming all boxes produced are sold). (4 marks) 6. Solve the system of equations { 3x + 5y = 14 2x − y = −8 (4 marks) 7. Solve the system of equations { x2 − y = 11 x − 4y = 11 (5 marks) 8. The supply and demand equations for a certain product are supply: p = (q + 5)2 demand: p = 440 − 19q TRU-Open Learning Math 1071 Fundamentals of Mathematics for Business and Economics 5 where p is the price per unit and q is the number of units sold per month. (a) Sketch a graph showing the equilibrium point. (2 marks) (b) Find the equilibrium quantity and price (round to 2 decimal places). (4 marks) Chapter 4 9. Suppose $4000 is invested for 3 years at 6% compounded monthly. (a) Find the accumulated amount. (3 marks) (b) Find the amount of interest earned in part (a). (1 mark) 10. Evaluate: (3 marks) (a) log8 64 (b) log4 64 (c) log2 64 11. Simplify by writing as a single logarithm: (4 marks) 3 ( 4 log x + 2 log y ) − 4 log z 12. Solve for x: (3 marks) log5 125 = 3x + 2 13. Solve for x: (4 marks) log(x − 3) + log(x − 5) = 1 TRU-Open Learning Microsoft Word - Assignment A ii Assignment File Assignment Guidelines and Strategies ALWAYS show all work clearly and in a logical order. Your work should justify your answers. This simply means that you should write down all steps of relevant mathematical reasoning, sketch relevant graphs, etc. It may be helpful for markers if you: • Clearly mark the question number (for example, “3. (a)”). • Copy down the question. • Organize your work so that the marker can follow your reasoning. Don’t leave miscellaneous calculations scattered across the page — you will no doubt have to do this kind of work, but do it on scrap paper or leave it on your rough draft. Include all steps required, in a logical order, to show how you obtained your solution and why your solution is correct. • Circle, underline, or draw a box around your final answers. Answer in a sentence or phrase where appropriate. This way it is absolutely clear what your answer is. • Make marking your paper easy for marker — a happy marker is a generous marker! If the marker has to search for your final answer or can’t follow your reasoning step by step, you are unlikely to get full marks, even if you have the correct answer somewhere on the page. On graphing • when asked to sketch a graph, this means sketch a graph — an exact to scale diagram is not expected (nor possible) • sketches of graphs should show an accurate general shape of the graph – is it a straight line, a curve, asymptotic, bounded, unbounded? • and any relevant points – such as: x-intercepts, y-intercepts, maximum values, minimum values, vertices, “corners”, breaks in the graph, where the graph “stops” or changes direction, . . . TRU-Open Learning Math 127 Fundamentals of Mathematics for Business and Economics iii On calculators You will also need a scientific calculator; one which has operations for performing calculations with exponents and logarithms. These buttons have symbols like: “ex”, “log” and “ln”. Almost any scientific calculator will have these functions. Programmable calculators which enable you to store notes, or anything with a qwerty keyboard, will not be permitted to be used during the final exam — in particular, the graphing calculators so popular in high schools are not permitted. Your calculator is your friend! Use the same calculator for assignments which you will use for the final exam, so that you become familiar with its use. TRU-Open Learning