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Practice Test 2 - ISEE Middle Level Mathematics Achievement

20 questions. Answer them in any order, then submit to see your score and every explanation.

  1. Sports: P(Tigers win)=710P(\text{Tigers win})=\frac{7}{10} and P(Lions win)=60%P(\text{Lions win})=60\%. Which is more likely?
  2. A piece of wire 60 inches long is bent to form a square. The same wire is then re-bent to form a rectangle with a length of 18 inches. What is the positive difference in area between the square and the rectangle?
  3. The temperature at 6:00 a.m. was -8°F. The temperature increased at a constant rate of 3°F per hour. Which equation can be used to find h, the number of hours it took for the temperature to reach 13°F?
  4. A piece of wood is 6 feet long. A carpenter needs to cut it into smaller pieces that are each 4124\frac{1}{2} inches long. How many full pieces can be cut from the piece of wood? (1 foot = 12 inches)
  5. Two fair six-sided dice are rolled. Let Event M be the event that the sum of the numbers on the two dice is 7. Let Event N be the event that the number on the first die is a 3. Compare the probabilities of Event M and Event N.
  6. What two-step rule with a constant operation is used to generate the sequence 124, 64, 34, 19, ...?
  7. A roll of ribbon contains 16 yards. A crafter needs to cut pieces that are each 34\frac{3}{4} of a yard long. After cutting as many full pieces as possible, what length of ribbon, in yards, will be left over?
  8. A fair six-sided die is rolled twice. What is the probability of rolling at least one 4?
  9. A number is randomly chosen from the set of all factors of 72. What is the probability that the chosen number is a multiple of 3?
  10. A recipe uses 1 2/31\ 2/3 cups sugar, then you add 1/31/3 cup more. What is the sum?
  11. A rectangular park measuring 0.5 miles wide and 0.8 miles long has 1,200 trees. A neighboring square-shaped forest preserve with sides of 2 miles has 18,000 trees. How much greater is the tree density, in trees per square mile, of the forest preserve than the park?
  12. A jar contains 5 red marbles, 4 blue marbles, and 3 green marbles. If two marbles are drawn from the jar at random without replacement, what is the probability that both marbles are blue?
  13. A recipe for 12 cookies requires 2 cups of flour. How many cups of flour are needed to make 90 cookies?
  14. Over three days, a cyclist rode a total of 30 miles. On the first day, she rode 9129\frac{1}{2} miles. On the second day, she rode 113511\frac{3}{5} miles. How many miles did she ride on the third day?
  15. An object consists of a cone with a radius of 3 cm and a height of 10 cm, topped with a hemisphere with the same radius. What is the total volume of the object in terms of π? (Formulas: V_cone = 13πr2h\frac{1}{3}\pi r^2h, V_sphere = 43πr3\frac{4}{3}\pi r^3)
  16. If x=4x=4 and y=−2y=-2, what is the value of the expression x2−(10−y)÷3x^2 - (10 - y) \div 3?
  17. A bag has P(red marble)=25P(\text{red marble})=\frac{2}{5} and another has P(blue marble)=12P(\text{blue marble})=\frac{1}{2}. Which is more likely?
  18. A graph shows a company's profit over five years. Year 1: $50,000, Year 2: $65,000, Year 3: $60,000, Year 4: $75,000, Year 5: $80,000. Which of the following statements is best supported by the data?
  19. If a point (x, y) is in Quadrant IV, which of the following points must be in Quadrant II?
  20. Mr. Ali records 10 test scores to check class average: 65, 70, 70, 75, 80, 80, 85, 90, 95, 100. What is the mean of the data set in the passage?

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