1. In the figure below, C is on BD, ∠BAC measures 40°, and ∠ABC measures 110°. What is the measure of ∠ACD?
2. For what value of a is the equation _1_a+10 =6 true?
3. What is the least common denominator of the fractions _4__, _1__, and _3_?
4. ⎪5 −3⎪−⎪1 −6⎪=?
5. In the trapezoid below, AB is parallel to DC. What is the measure of ∠C?
6. Gao earns his regular pay of $12 per hour for up to 40 hours of work per week. For each hour over 40 hours of work per week, Gao is paid 1_1_ times his regular pay. How much does Gao earn in a week in which he works 56 hours?
7. On the first day of school, Ms. Dubacek gave her third-grade students 6 new spelling words to learn. On each day of school after that, she gave the students 3 new spelling words. How many new spelling words had she given the students by the end of the 21st day of school?
8. What is the value of the expression __8_!__?
9. Right triangle nABC and its side lengths given in inches are shown below. What is sin,B?
10. (6a3−5ac2+12c) −(4c−3a3−2ac2) is equivalent to:
11. Which of the following (x,y) pairs is the solution for the system of equations x+2y=2 and −x+y=7?
12. Tim’s flight was originally scheduled to depart at 4:51p.m., but it was delayed 563 minutes. What time did Tim’s flight eventually depart?
13. A circle with the equation x^2+y^2=144 is graphed in the standard (x,y) coordinate plane. At what points does the circle intersect the x-axis?
14. Given that x^2−5x−36 factors into 2 binomial factors with integer coefficients, which of the following binomials is 1 of those factors?
15. Two vectors are shown in the standard (x,y) coordinate plane below. One of the following vectors in the standard (x,y) coordinate plane is the sum of these 2 vectors. Which one?
16. A square and a rectangle have the same area. The length of the rectangle is 196 centimeters, and the width of the rectangle is 4 centimeters. What is the length, in centimeters, of a side of the square?
17. Valentina has N dollars with which to purchase T-shirts. After she purchases the maximum number she can, Q T-shirts, she has R dollars left. For all possible choices of D and N, which of the following equations models a correct relationship between D, N, Q, and R?
18. How many customers ordered a vegetarian sandwich on wheat bread?
19. What is pˆ, the sample proportion, for this sample?
20. √•2 +√•8 +√•1•8 =?
21. Which of the following inequalities is equivalent to 3 −2x>7 −x?
22. Let a be positive and b be negative. If it can be determined, in which quadrant of the standard (x,y) coordinate plane is the point (−a,b^2) located?
23. rst reached 10 milligrams?
24. One day will be randomly selected from the 7 days in a week. Then 1 month will be randomly selected from the 12 months in a year. What is the probability that the selected day will be Tuesday and the selected month will be January?
25. The average weight of Juan, Jim, and Malik is exactly 160 pounds. The average weight of Juan, Jim, Malik, and Harry is exactly 150 pounds. How many pounds does Harry weigh?
26. What is the value of the expression _log (36)+_log (9)+?
27. Each of 2 identical number cubes has a different integer, 1 through 6, on each face. Consider the sample space determined by rolling these number cubes and adding the 2 integers on the faces that land on top. What is the positive difference between the greatest sum and the least sum in this sample space?
28. What angle measure, in radians, is equal to 30°?
29. Hannah recorded the following temperatures, in degrees Fahrenheit, so she could investigate the difference between the high and low temperature each day. To the nearest degree, what was the mean of the differences in daily high and low temperatures for these 5 days?
30. What fractional part of their weekly income is left for unbudgeted items?
31. What is the 322nd digit after the decimal point in the repeating decimal 0.1357?
32. How many seconds after you first started pouring the water into the bucket will it contain 24 ounces of water?
33. What is the probability that a piece drawn randomly from the package is red?
34. Which of the following intervals is the range of the function f(x) =−(x−3)2+4?
35. What is the length, in centimeters, of the longer side of the classroom in Anoki’s scale drawing?
36. What is the area of ABCD, in square feet?
37. The first number is what percent of the third number?
38. How much monthly rent is charged for this store?
39. What percent of the science final semester grade is the final exam grade?
40. Which of the following CANNOT be the perimeter, in inches, of the rectangle?
41. What is the positive difference, in dollars, of the 2 list prices?
42. Which one of the following comparisons is true regarding price per square foot?
43. What is the assessed value of Condo X?
44. In the complex plane, consider the segment whose endpoints are the points corresponding to −6+3i and 2 − 7i. The midpoint of this segment corresponds to which of the following complex numbers?
45. In the standard (x,y) coordinate plane, the 3 lines with equations y= _3_x−3, y=−_2_x+2, and x=0 bound a triangular region. What is the area, in square coordinate units, of that triangular region?
46. In square ABC D shown below, AC is a diagonal and the length of BC is 75 feet. Which of the following quantities is NOT a rational number?
47. The volume of a solid object is equal to the volume of water it displaces when completely submerged in water. A solid object will be placed in a rectangular tank that has a base of 35 cm by 30 cm and is filled with water to a uniform depth of 13 cm. When the object is completely submerged, the new depth of the water in the tank is 15 cm. What is the volume, in cubic centimeters, of the object?
48. What is the x-coordinate of B?
49. A 3rd circle, not shown, is the image resulting from applying the 1st transformation listed below to the smaller circle and then applying the 2nd transformation listed below to the result of the 1st transformation. 1st: A dilation with center O and scale factor 2 2nd: A translation of 8 coordinate units to the right The 3rd circle has how many points in common with the larger circle?
50. What is the area, in square coordinate units, of the region that is outside the smaller circle and inside the larger circle?
51. Which of the following is an equation of OB?
52. A sequence is given by s = 4 and s = 2s − 3 for n≥1. What is s?
53. In the figure below, the distances between 2 pairs of cities are shown, as well as the angle formed at Ewing, which has a measure of 127°. Which of the following values is closest to the distance, in miles, from Deerborn to Fergus?
54. Which of the following expressions is equivalent to __1___ − __1___ ?
55. One of the following equations represents the ellipse shown below in the standard (x,y) coordinate plane. Which one?
56. One of the following equations is that of a parabola with x-intercepts −5 and _3_ in the standard (x,y) coordinate plane. Which equation?
57. There are 100 fractions in the following set. Each fraction after the first is found by adding 3 to the preceding fraction’s numerator and denominator. What is the product of these 100 fractions?
58. If 2x=7 and 2y=14, then x−y=?
59. The table indicates the grade (10 or 11) and high school (North or South) of the 270 students enrolled in Algebra II in the Green City School District. Suppose 2 of these students will be chosen at random to represent the Algebra II classes at a local STEM event. Which of the following expressions gives the probability that both chosen students will be from the same grade and the same high school?
60. A certain company has 120 employees, 85 of whom have business degrees. Of the employees with business degrees, 75 are certified public accountants (CPAs). There are 14 employees who are not CPAs and also do not hold a business degree. What is the probability that the selected employee will be a CPA?