Math5900 Final Exam Spring, 2006 Kelly MacArthurName____________________________ Date________________Instructions: Please show all your work, as partial credit will be given where appropriate. If there is no work shown, you may not get any points for an answer, even if it’s correct. Please put your answer in the designated place. Each question is worth 10 points.1. Solve this quadratic equation. x−32−25=0 x = ______________________2. Solve this linear equation (i) using a diagram and (ii) with algebra notation. 2(-x + 1) – 3x = 3x – 6x = __________________13. Solve these systems of linear equations.(a) x3y=−7−2x−4y=8Answer 3(a): _________________________(b) y=4x−32x−12y=32Answer 3(b): __________________________24. A grocer wants to mix candy corn and jelly beans together to sell. Candy corn sells for $1.75 per pound and the jelly beans are $3.20 per pound. She wants 25 pounds of candy mix that costs $2.33 per pound. How many pounds of each type of candy is in the mixture?# pounds of jelly beans = _________________# pounds of candy corn = _________________5. Convert these numbers to a different base as indicated.(a) 7618to base 10 = _________________(b) 4444 to base 4 = ____________________(c) 111001012to base 10 = __________________36. Convert all these numbers (as necessary) to fractions, order these numbers and then place them on a number line. (No calculator allowed, i.e. I want to see all your work.)(a) 64% = _________(b) 13(c) 29(d) 516(e) 310(f) 0. 9= _________(g) 0.61 = ____________(h) 910(i) 47% = ___________(j) 0. 65= _____________ <------------------------------------------------------------------------------------------------------>7. A 51-row auditorium seats 20 people in the first row, 21 in the second row, 22 in the third row and so on. Use short-cuts to find the total number of seats in the auditorium.# seats = ___________________48. The product of two numbers is 792 and their difference is 9. What are the two numbers?________________ and ______________9. For the sequence 5, 13, 21, 29, ... (a) Find a formula to give the nth term of the sequence.Formula: ______________________________(b) What is the 200th term?200th term = ____________________510. Draw a Venn Diagram for all the number systems (including fractions) and place these numbers in the proper place in the Venn Diagram.(a) -5.1(b) 27(c) 6.34(d) 0(e) 11.343343334...(f) 21.9 87(g) 5(h) 153(i) -9(j) 0. 9611. Perform the following arithmetic operations. For part (a), use two methods, and for (b) & (c) use one method to show your work. (You cannot choose the standard algorithm for (b) or (c)!) (a) 236÷7= ____________ (Use one partitive method and one measurement method.)(b) 4231 x 5= _______________(c) 16 – 19 = ______________712. Find the GCF and LCM of the following pair of numbers. (You can leave your answers in factored form, if you'd like.)(a) GCF(980, 1750) = _______________(b) LCM(980, 1750) = ________________13. Simplify.14366234÷2⋅2512= ________________814.A young man spent 14of his allowance on a movie. He spent 1118of the remainder on after-school snacks. Then from the money remaining, he spent $3.00 on a magazine, which left him 124of his original allowance to put into savings. How much of his allowance did he save?Answer 14: ______________________15. An airline passenger fell asleep halfway to her destination. When she awoke, the distance remaining was half the distance traveled while she slept. How much of the entire trip was she asleep?Answer 15: ______________________916. Barry said that to find 13of a number, he just had to multiply by 0.3, so that 13of 54, for example, would equal 16.2. Do you agree with Barry? Explain your reasoning.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________17. Maria multiplied 157and 149and got 21063. She says that the answer in simplest form is 103. Karl disagrees with Maria and says that the answer in simplest form is 313. Who is correct (or are they both correct or both incorrect)? Explain your reasoning.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________10Choose one of the following three questions to answer. Indicate clearly which one you are answering!!! A. In your own words, what is a definition of algebraic thinking?B. What is the essence of mathematics? Explain why underlying mathematical skills are important in daily life.C. Explain why 0 and 1 are such “powerful”