| Questions: 1, 2, 3: 1. If \[x + \frac{2}{x} = 5 + \frac{2}{5}\], the \[x\] can equal which of the following? (A) \[\frac{1}{5}\] (B) \[\frac{4}{5}\] (C) \[1\] (D) \[\frac{5}{2}\] (E) \[5\]  2. In the right triangle above, if \[x = 3\], what is the value of \[y\]? (A) \[\sqrt{13} \] (approximately 3.61) (B) \[\sqrt{15} \] (approximately 3.87) (C) \[4\] (D) \[\sqrt{17} \] (approximately 4.12) (E) \[5\] 3. Which of the following numbers can be used to show that the statement above is FALSE? (A) 4 (B) 8 (C) 12 (D) 18 (E) 24  Questions: 4, 5, 6: 4. In the figure above, the circle is tangent to sides \[BC\] and \[AD\] of the 8-by-12 rectangle, \[ABCD\]. What is the area of the circle? (A) \[16\pi\] (B) \[20\pi\] (C) \[36\pi\] (D) \[64\pi\] (E) \[96\pi\]  5. On the disk shown above, a player spins the arrow twice. The fraction \[\frac{a}{b}\] is formed, where \[a\] is the number of the sector where the arrow stops after the first spin and \[b\] is the number of the sectors has an equal probability of being the sector on which the arrow stops. What is the probability that the fraction \[\frac{a}{b}\] is greater than \[1\]?
(A) \[\frac{15}{36}\] (B) \[\frac{16}{36}\] (C) \[\frac{18}{36}\] (D) \[\frac{20}{36}\] (E) \[\frac{21}{36}\] 6. Which of the following tables shows a relationship in which \[w\] is directly proportional to \[x\]? (A)
(B)
(C)
(D)
(E)
Questions: 7, 8, 9, 10: 7. Dwayne has a newspaper rote for which he collects \[k\] dollars each day. From this amount he pays out \[\frac{k}{3}\] dollars per day for the cost of the papers, and saves the rest of the money. In terms of \[k\], how many days will take Dwayne to save $1,000? (A) \[\frac{k}{1,500}\] (B) \[\frac{k}{1,000}\] (C) \[\frac{1,000}{k}\] (D) \[\frac{1,500}{k}\] (E) \[1,500k\]  8. Which of the lettered points on the number line above could represent the result when the coordinate of point \[P\] is multiplied by the coordinate of point \[Q\]? (A) \[A\] (B) \[B\] (C) \[C\] (D) \[D\] (E) \[E\] Student-Produced Response Questions: 9. If \[5y + 2x = 23\] and \[x = y + 1\], what is the value of \[y\]? 10. A company produced 300 appliances in the first week of the month. Because it received additional machinery, its production increased 50 percent from the first week to the second week. How many appliances did the company produce the second week?  Questions: 11, 12, 13, 14: 11. Each angle of \[\Delta ABC\] above has the same measure as an angle in \[\Delta XYZ\] (not shown). If the length of one side of \[\Delta XYZ\] is 24, what is one possible perimeter of \[\Delta XYZ\]? 12. The sum of 5 consecutive integers is 1,000. What is the value of the greatest of these integers?  13. The figure above shows the graph of \[y = g(x)\]. If the function \[h\] is defined by \[h(x) = g(2x) + 2\], what is the value of \[h(1)\]? 14. Exactly 4 actors try out for the 4 parts in a play. If each actor can perform any one part and no one will perform more than one part, how many different assignments of actors are possible?  Questions: 15, 16, 17: 15. In the figure above, \[\Delta PQR\] is equilateral and \[SR\] and \[TV\] intersect at point \[P\]. What is the value of \[y\]? 16. Let the operations  and  be defined for all real numbers a and b as follows.a b = a + 3ba b = a + 4bIf 4 (5y) = (5y)4, what is the value of \[y\]?17. In the \[xy\]-coordinate plane, the graph of \[x = y^2 - 4\] intersects line \[\ell \] at \[(0,p)\] and \[(5,t)\] . What is the greatest possible value of the slope of \[\ell\]? Question: 18: 18. Esther drove to work in the morning at an average speed of 45 miles for hour. She returned home in the evening along the same route and averaged 30 miles per hour. If Esther spent a total of one hour commuting to and from work, how many miles did Esther drive to work in the morning? |
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