MAT 1033A

1. MAT 1033A Final Exam Review and Practice Test Solutions Part I

2. Information about the Final Exam Length: 25 questions (not multiple−choice). Each question is worth 4 points. If you miss the test: Students who do not take the final exam will receive a zero on the final exam unless prior arrangements have been made for a rare incomplete. If you miss the final and do not email me by the day of the exam, I will assume you wish to take a zero on your final exam. Question Order: The questions on the final exam will be scrambled. The order will NOT necessarily be the same as it appears on this review. Calculator Policy: Calculators are not permitted in this course.

3. How to Study for the Exam • Review your notes. Set up a study system to review important definitions, procedures, and notation. • Complete the practice test questions and be prepared to go over the answers in class on the date of the final exam review. • Continue to review by working the suggested textbook problems and checking your answers with the key at the back of the book. • Review the corresponding questions from the tests. • Redo the sample questions (especially the ones you missed).

8. Final Exam Practice Solutions (Test 1 Material)

9. 1) Solve. Write your answer in interval notation. Switch the sign when dividing or multiplying both sides by a negative.

10. 2) How many hits does Ricardo need in his fifth game to average at least 2 hits per game if in his first four games he had the following number of hits: 1, 0, 5, 3? At least 1 hit. “at least” → “at most” →

11. 3) Determine if is a solution of Substitute the first coordinate for and the second for .

12. 4) Determine the x and y intercepts of Graph the line. y X intercept – set y equal to zero Y intercept – set x equal to zero

13. 5) Graph each line.a) b)

14. 6) Find the slope of the line between the points and (5, 1).

15. 7) Find the slope and y intercept of

16. 8) Find the equation of the line with slope that contains the point Write your answer in slope-intercept form. OR OR

17. 9) Find the equation of the line through the points . Write your answer in slope-intercept form. OR Find the slope first, then use point – slope or y = mx+b

18. 10) Determine if the two lines are parallel, perpendicular or neither. parallel Solve for y first. Slopes equal → parallel Slopes negative reciprocals → perpendicular

19. 11) Write the equation of the line parallel to through the point (2, 9). Write your answer in slope – intercept form. OR Find the slope of the given line, use the same for parallel and the negative reciprocal for perpendicular Write the equation using point slope or y = mx+b

20. 12) Graph the linear inequality 1) Graph the line 2) Test 3) Shade the region that has Graph the line (dashed or solid), test a point, shade a side

21. 13) Consider the relation{(1, 3), (2, 4), (, 5), }. a) What is the domain of the relation? b) What is the range of the relation? c) Is the relation a function? Domain: first coordinate Range: second coordinate It’s a function if every x goes to one and only one y

22. 14) Is the relation graphed below a function? Use the vertical line test. It’s not a function because a vertical line intersects the graph in more than one point. no

23. 15) Suppose . Complete the function table. Substitute the values in the left hand column into the function to get the values in the right hand column.

24. 16) Find the domain and range of the function graphed below. Be sure to write the domain and range in interval notation. Domain: x’s - least (left most) to greatest (right most) Range: y’s – least (lowest) to greatest (highest) Domain: Range:

25. 17) Find the domain (in interval notation) of . For now, exclude where the denominator is zero.

26. 18) Which ordered pair solves the system? The point must work for BOTH lines. A) B) A

27. Substitution: Solve for one variable in one equation and place that into the other equation. Elimination: Multiply one equation by a number so that when you add the equations, one variable goes to zero. Solve for the other. Back substitute. 19) Solve the system Substitution Elimination

28. 20) The Cabana Hotel has 51 rooms. There are rooms with two queen beds and rooms with 1 king bed. There are three more rooms with 1 king bed than there are with two queen beds. How many of each type of room are at the hotel? Be sure to let the variables be what the problem asks for.

29. Final Exam Practice Solutions (Test 2 Material)

30. 1) Simplify.

31. 2) Simplify. a) b) Multiply – add the exponents, Divide – subtract Negative exponent – switches between numerator/denominator

32. 3) Simplify. Power to a power – multiply the exponents

33. 4) Convert between scientific and decimal notation. “Big” numbers have positive exponents. “Small” numbers have negative exponents. a) Convert to scientific notation. i) 0.0511 = ii) 7, 289,561 b) Convert to decimal notation. i) ii) =

34. 5) Find the degree of the polynomial. The degree is the largest degree of any one monomial.

35. 6) Add or subtract as indicated. Be sure to distribute the negative when subtracting.

36. 7) Multiply. a) b) c) d) First, Outside, Inside, Last Distribute twice.

37. 8) Multiply. a b) c)

38. 9) Divide. Divide each term of the polynomial by the monomial.

39. 10) Divide. Use either polynomial division or synthetic division. 3 Answer:

40. 10) Divide. Use either polynomial division or synthetic division. Answer: Synthetic – change the sign of the constant divisor.

41. 11) Factor completely. GCF – GCF of the coefficients times the highest power of the variable

42. 12) Factor completely. Grouping: GCF of the first two terms, GCF of the second two terms, Factor out the common binomial

43. 13) Factor completely.

44. 14) Factor completely. Use those two numbers to separate the middle term and factor by grouping.

45. 15) Factor completely.

46. 16) Factor completely. Remember SOAP : Same, Opposite, Always Positive

47. 17) Factor completely GCF, then factor by terms, then factor again if necessary, then check

48. 18) Solve. Set the factors equal to zero. Write the solutions inside a set.

49. 19) Solve. Get everything on the left and a zero on the right. Factor. Set the factors equal to zero. Write the solutions inside a set.

50. 20) The length of a dining room table is three more than the width. If the area is 70 square feet, find the length and width. Let the variable be what the problem asks for.