ECON 1111 Quantitative Methods for Business and Economics 1 20 marks 10 marks each item In this question your goal is to divide two polynomials and simplify your solution the furthest you can cid 19 2 x y2 cid 32 cid 18 x cid 18 y x2 y2 x2 2xy y2 cid 33 cid 19 cid 18 x 1 cid 19 2 cid 19 cid 18 x y y x y 2 20 marks 10 marks each item Rearrange the following equations to identify the slope and intercept of the function y Then state whether the function is downward or upward sloping and calculate the point at which it crosses the x axis Hint this is the horizonal not vertical axis 3 20 marks 10 marks each item Use a line to represent the range of values of x that In case your solution is a fraction indicate its two satisfy the following inequalities closest integers on the line 4 20 marks 10 marks each item Find out if the following systems of equations have a unique solution infinite solutions or no solution at all In case there is a unique solution calculate it a b a b a 2x 3y 14 b 9x 5y 90 a 4 x b x2 4 8 5x 9 x 2 9x 8 5 20 marks 10 marks each item In a family of four people find the age of each person a If we multiply the age of the mother by two and add the age of her son the sum is 61 Moreover if we multiply the age of the son by three and add the age of his mother the sum is 43 b Half the age of the father minus the age of his daughter is 8 The father s age is 4 times his daughter s age cid 26 3x 9y 6 cid 26 2x 10y 2 4x 12y 8 5x 25y 3 3 ECON 1111 Quantitative Methods for Business and Economics 1 30 marks 10 marks each Using the rules of indices simplify the following expressions 2 30 marks 10 marks each Write down the following expressions as a single log a b c a b c a b a b x6 8 8 cid 112 x2y6 cid 112 x6y8 x15 5 y 10 z0 5 y 10 3 logb x logb y log2 4 logb x cid 19 cid 18 10 logb x logb y 1 2 8 4 logb y logb y2 2x2 3x 1 0 x2 2x 3 0 y 3x2 4x 5 y 2x2 8x 8 3 20 marks 10 marks each Solve the following inequalities 4 10 marks 5 marks each For each of the following quadratic functions state its number of roots and whether it has a u shape or an inverted u shape Explain how you find your answers 5 10 marks 5 marks each Considering the rules of derivatives below calculate the derivatives of the following functions cid 136 When f x xn f x nxn 1 cid 136 When h x af x h x af x cid 136 When h x f x g x h x f x g x cid 136 When h x f x g x h x f x g x a f x x3 4 2 b f x 1 x 2x 3 ECON 1111 Quantitative Methods for Business and Economics 1 40 marks 10 marks each Calculate the derivative of the following functions and simplify your answer the furthest you can a b c d a b f x f x 5 cid 112 x3 2 x 1 x2 4x 7 f x x6 x 2x 1 f x 5x4 9x3 8 f x x3 3x2 8 x 3 2 2 20 marks 10 marks each Find the stationary points of the following functions and classify them as maximum minimum or none of those 3 10 marks The owner of a shop reports the following revenue in a period of four years Year Revenue 86 Inflation 2020 2021 2022 2023 106 52 2 4 6 74 Calculate the value of each year s revenue in prices of year 2020 and identify the year with the highest value of real revenue 4 10 marks Company A has a policy of paying a base wage and add a percentage of this base wage depending on the workers performance Company A s employee received an hourly wage of 87 4 in January after a percentage increase of 15 How much has this employee received in February when the percentage increase was equivalent to 12 5 10 marks Which of the following payment methods would you choose for the same service considering an interest rate of 2 that is compounded monthly a Immediate payment of 4 500 b Three installments of 1 550 each paid one month apart starting next month 6 10 marks If a machine depreciates at an annual rate of 2 what was its value two years ago if it is currently sold at 8 643 60 3