Ncl Research Paper
APRIL
A book is to have 250 pages that will be numbered with Arabic numerals. How many times will the digit 2 be used in numbering the pages?
John and a group of his friends took a bus trip. Each person paid the bus driver with the same combination of 9 coins. If the bus driver received $8.41 from the group, how many dimes did he receive?
A man walks 3 miles east, then 3 miles north, and then 2 miles northeast. How far is he from his starting point?
A culture of bacteria doubles in size twice every day. A dish with 1 million bacteria is full after 15 days. How long will it take for a dish with 2 million bacteria to fill?
1
Two clocks now indicate the true time. One gains a second every hour, and the other gains 3 seconds every 2 hours. In how many days will both clocks again indicate the true time?
2
In his last game, Joe bowled a 199, raising his average by one pin (one point in bowling) to 178. What must he bowl in his next game to raise his average to 179?
3 …show more content…
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SOLUTIONS to calendar
1. None. Since 841 = 292, John and 28 of his friends could only have been paid $8.41 in equal amounts by spending $0.29 each. The only combination of 9 coins that yields $0.29 is 4 pennies and 5 nickels. So the bus driver did not receive any dimes. 2. 2 + 312. As indicated in the first figure, the man is walking along a path from point A to point D, followed by point C and point B. The distance we are looking for is represented by AB. As shown in the second figure, ABE and CBF are isosceles right triangles. Since BC = 2,
CF = 1 2 1 2 .
Since AE = BE,
BE = 3 + 1 2
also. Therefore,
AB = 2 • AE 1 = 2 • 3 + 2 = 2 + 3
A book is to have 250 pages that will be numbered with Arabic numerals. How many times will the digit 2 be used in numbering the pages?
John and a group of his friends took a bus trip. Each person paid the bus driver with the same combination of 9 coins. If the bus driver received $8.41 from the group, how many dimes did he receive?
A man walks 3 miles east, then 3 miles north, and then 2 miles northeast. How far is he from his starting point?
A culture of bacteria doubles in size twice every day. A dish with 1 million bacteria is full after 15 days. How long will it take for a dish with 2 million bacteria to fill?
1
Two clocks now indicate the true time. One gains a second every hour, and the other gains 3 seconds every 2 hours. In how many days will both clocks again indicate the true time?
2
In his last game, Joe bowled a 199, raising his average by one pin (one point in bowling) to 178. What must he bowl in his next game to raise his average to 179?
3 …show more content…
www.nctm.org. All rights reserved. This material may not be copied or distributed electronically or in any other format without written permission from NCTM.
SOLUTIONS to calendar
1. None. Since 841 = 292, John and 28 of his friends could only have been paid $8.41 in equal amounts by spending $0.29 each. The only combination of 9 coins that yields $0.29 is 4 pennies and 5 nickels. So the bus driver did not receive any dimes. 2. 2 + 312. As indicated in the first figure, the man is walking along a path from point A to point D, followed by point C and point B. The distance we are looking for is represented by AB. As shown in the second figure, ABE and CBF are isosceles right triangles. Since BC = 2,
CF = 1 2 1 2 .
Since AE = BE,
BE = 3 + 1 2
also. Therefore,
AB = 2 • AE 1 = 2 • 3 + 2 = 2 + 3