MAT 1033A

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

2. Final Exam Extra Practice (Test 1 Material)

3. 1) Solve. Write your answer in interval notation.

4. 1) Solve. Write your answer in interval notation. Switch the sign when dividing or multiplying both sides by a negative. You didn’t do that here because you didn’t multiply or divide both sides by a negative number.

5. 2) Carla kept track of the rainfall in Destin over a six day period. The totals (in inches) were: 1, 2, 1.5, 2.5, 0, and 2. How much rain must fall on the seventh day to average at least 1.5 inches of rain for the week?

6. 2) Carla kept track of the rainfall in Destin over a six day period. The totals (in inches) were: 1, 2, 1.5, 2.5, 0, and 2. How much rain must fall on the seventh day to average at least 1.5 inches of rain for the week? At least 1.5 inches of rain must fall. “at least” → “at most” →

7. 3) Determine if is a solution to

8. 3) Determine if is a solution to Substitute the first coordinate for and the second for .

9. 4) Determine the x and y intercepts of Graph the line.

10. 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

11. 5) Graph each line.a) b) 7

12. 5) Graph each line.a) b) 7

13. 6) Find the slope of the line between the points and (9, ).

14. 6) Find the slope of the line between the points and (9, ).

15. 7) Find the slope and y intercept of

16. 7) Find the slope and y intercept of

17. 8) Find the equation of the line with slope that contains the point

18. 8) Find the equation of the line with slope that contains the point OR OR

19. 9) Find the equation of the line through the points . Write your answer in slope-intercept form.

20. 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

21. 10) Determine if the two lines are parallel, perpendicular or neither.

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

23. 11) Find the equation of the line perpendicular to through . Write your answer in slope – intercept form.

24. 11) Find the equation of the line perpendicular to through . 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

25. 12) Graph the linear inequality

26. 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

27. 13) Consider the relation a) What is the domain of the relation? b) What is the range of the relation? c) Is the relation a function?

28. 13) Consider the relation 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

29. 14) Is the relation below a function?

30. 14) Is the relation below a function? Use the vertical line test. It is a function because a vertical line intersects the graph in at most one point. yes

31. 15) Suppose . Complete the function table.

32. 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.

33. 16) Find the domain and range of the function graphed below. Be sure to write the domain and range in interval notation.

34. 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:

35. 17) Find the domain (in interval notation) of .

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

37. 18) Which ordered pair solves the system? A) B)

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

39. 19) Solve the system

40. 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

41. 20) The sum of two numbers is 15. The difference when the second is subtracted from the first is 9. Find the two numbers.

42. 20) The sum of two numbers is 15. The difference when the second is subtracted from the first is 9. Find the two numbers. Be sure to let the variables be what the problem asks for.

43. Final Exam Extra Practice (Test 2 Material)

44. 1) Simplify.

45. 1) Simplify.

46. 2) Simplify. a) b)

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

48. 3) Simplify.

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

50. 4) Convert between scientific and decimal notation. a) Convert to scientific notation. i) 0.077 ii) 8, b) Convert to decimal notation. i) ii)