Grade 9 Math

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Grade 9 Math

• Problem of the Week

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Week 1 (Sept 21)

• How long will it take a mile-long train going 20
  miles per hour to get completely through a
  2-mile-long tunnel?

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Solution Week 2

• 9 minutes. If the train is going 20 mph, it will
  travel 1 mile in 3 minutes. It will take the
  engine 6 minutes to go through the tunnel, but it
  will take another 3 minutes for the caboose to go
  1 mile to clear the tunnel.

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Week 1 (Sept 18)

• A school has a hall with 500 lockers, all of
  which are closed. Five hundred students start
  down the hall. The first student opens every
  locker. The second student closes all the lockers
  that are multiples of 2. The third student
  changes (closes an open locker or opens a closed
  one) all multiples of 3. The fourth student
  changes all multiples of 4, and so on. After all
  students have finished with the lockers, which
  numbered lockers will be open? Describe the
  pattern.

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Solution Week 1

• 11.
• Lockers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100,
  121, 144, 169, 196, 225, 256, 289, 324, 361, 400,
  441, and 484 will be open. The pattern is that
  all locker numbers that are perfect squares will
  be open after all students pass. Using the
  strategy for problem number 6, the pattern
  indicates that all perfect squares less than or
  equal to 500 will be open after all students
  pass. Trial and error show that 232 529,
  whereas 222 484. Therefore, 22 lockers will be
  open, the squares of the numbers 122, which are
  1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144,
  169, 196, 225, 256, 289, 324, 361, 400, 441, and
  484.

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Week 3 (Oct 1)

• A princess is in love with a dashing knight.
  Unfortunately, the king prefers another suitor
  for his daughter. The king has locked her in the
  castles tower. The castle is surrounded by a
  moat that is 10 yards wide. The knight wants to
  cross the moat, but he has only two 9.75 yard
  planks and no way to fasten them together. How
  can the brave knight bridge the moat?

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Week (Oct 15)

• How much money would you make in 8 days if you
  made 8 dollars every time the hands of a clock
  formed a 90 degree angle?

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Week 4 (Oct )

• If A 1, B 2, C 3, . . . , and Z 26, find
  the spelling of a particular quadrilateral whose
  letters are all different and will sum to 114.

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Week 5 (October 1)

• We need more boys in the club, said Maryanne.
  Why? asked Patty. Well, we have 32 members
  now, and only 1/4 are boys, Maryanne explained.
  Thats not too good, Patty admitted. Youre
  right, said Maryanne. We have to get some more
  boys to join. At least 1/3 of the members must be
  boys. That would be a more balanced club,
  Patty agreed. How many more boys would they need
  if no more girls joined their club?

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Week 6 (October 23)

• What is the 99th letter in the pattern ABBCCCDDDD
  . . .

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Week 7 (October 30)

• How many triangles are in the figure below?