This book is a rare resource consisting of problems and solutions similar to those seen in mathematics contests from around the world. It is an excellent training resource for high school students who plan to participate in mathematics contests, and a wonderful collection of problems that can be used by teachers who wish to offer their advanced students some challenging nontraditional problems to work on to build their problem solving skills. It is also an excellent source of problems for the mathematical hobbyist who enjoys solving problems on various levels.
Problems are organized by topic and level of difficulty and are cross-referenced by type, making finding many problems of a similar genre easy. An appendix with the mathematical formulas needed to solve the problems has been included for the reader's convenience. We expect that this book will expand the mathematical knowledge and help sharpen the skills of students in high schools, universities and beyond.
Contents:
Arithmetic and Logic
Algebra
Geometry
Trigonometry
Logarithms
Counting
Number Theory
Probability
Functional Equations
Readership: High school students, teachers and general public interested in exciting mathematics problems. Mathematical Problem-Solving;Math Contests;Differentiate Instruction;Advanced Learner
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Yes, you can access Mathematics Problem-solving Challenges For Secondary School Students And Beyond by David Linker, Alan Sultan in PDF and/or ePUB format, as well as other popular books in Biological Sciences & Science General. We have over one million books available in our catalogue for you to explore.
1.Four houses each have four floors. On each floor are four apartments, with four doors in each apartment. On each door are four hinges. How many of these hinges are there in the four houses?
2.The average of 50 test scores is 38. One of the scores is 45, while another is 55. If these papers are removed, compute the average of the remaining scores.
3.The average of Jeff’s nine test grades is 92. If his highest grade, 96, and his lowest grade are not counted, the average of the other grades is 94. Compute his lowest grade.
4.We have five quarts of a solution which is made of 60% acid and 40% water. If 5 more quarts of water are added to this solution, compute the percentage of water in the new solution.
5.A town is built on a grid system of two-way roads. North–south roads are numbered consecutively as streets (1st Street, 2nd Street, etc.), while east–west roads are numbered consecutively as avenues (1st Avenue, 2nd Avenue, etc.). Billy lives on the corner of 75th Street and 83rd Avenue, while Hope lives on the corner of 92nd Street and 65th Avenue. Compute the minimum number of blocks that Billy can drive to go from his house to Hope’s house, assuming he stays on the roads.
6.A clock gains five seconds per hour. Twenty-four hours after the clock is set correctly, it reads 5:58. What is the correct time?
7.Compute the smallest two-digit positive integer that is the sum of the cube of one of its digits and the square of the other digit.
8.In the addition of two four-digit numbers below, each different letter represents a different digit. Compute the value of the sum.
9.Compute the number of digits in the number 416 · 520.
Level 2
10.A train to Washington, D.C. leaves from New York at noon and travels at a constant rate of 70 miles per hour. Also at noon, a train to New York leaves from Washington, D.C. along an adjacent and parallel track traveling at a constant rate of 40 miles per hour. They will meet each other somewhere along the route. How far away from each other will they be 1 hour before they meet?
11.An urn contains 70 marbles which differ only in color. Of the marbles, 20 each are red, green, and blue. The remaining 10 are either black or white. Without looking, and without replacement, n marbles are removed from the urn. Find the smallest n that ensures that at least 10 marbles of the same color have been removed.
12.How many degrees are there in the angle formed by the hands of an analog clock at 7:20?
13.Compute how many different integers from 100 to 400 inclusive are perfect powers (perfect squares, perfect cubes, etc.).
14.There are 100 students in the sophomore class of Bawne High School. Of them, 43 students take biology, 35 take physics, 42 take chemistry, 12 take physics and chemistry, 15 take biology and physics, 17 take biology and chemistry, and 7 take all three courses. Find how many students take none of the courses.
15.Find the units digit of 1! + 2! + ··· + 14! + 15!.
16.Find the 1991st digit to the right of the decimal point in the decimal expansion of
17.In the table below, we begin writing the positive integers in row D and move to the right, writing each consecutive integer until we reach row G, then we continue writing consecutive integers in the next row moving left until we reach row A, and then continue writing in the next row moving right, and so on. Find the column that contains the number 1998.
18.A cubic block with 8-inch edges is painted and then cut into 1-inch cubes. Compute the number of cubes that have at least one face painted.
19.How many integers between 1000 and 5000 are perfect squares?
20.A train begins crossing a 450-meter-long bridge at noon, and clears the bridge completely 45 seconds later. A stationary observer notices that the train takes 15 seconds to pass him. Compute the speed of the train in meters per second.
21.The inhabitants of a certain kingdom will always tell the truth when asked when their birthday is, except if they are asked on their actual birthday. Mrs. Larken (one such inhabitant) was asked what her birthday was on both January 5th and January 6th. She replied, “It was yesterday,” both times. When is her birthday?
22.Find the sum of all the digits of the integers between 1 and 1000 inclusive.
23.Compute the sum of the positive integral divisors ...
