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Math Contest Newsletters 2017-2018 School Year
Grade 4-5-Algebra Newsletter April 2018
High School Newsletter April 2018
High School Newsletter March 2018
High School Newsletter February 2018
High School Newsletter January 2018
High School Newsletter December 2017
High School Newsletter November 2017
Math Contest Newsletters 2016-2017 School Year
Special: Selected Math League Rules 2016-2017
Grade 4-5 and Algebra Newsletter 2017
Grade School 6-7-8 Newsletter 2017
High School Newsletter April 2017
High School Newsletter March 2017
High School Newsletter February 2017
High School Newsletter January 2017
High School Newsletter December 2016
High School Newsletter November 2016
Math Contest Newsletters 2015-2016 School Year
Special: Selected Math League Rules 2015-2016
Grade 4-5 and Algebra Newsletter 2016
Grade School 6-7-8 Newsletter 2016
High School Newsletter April 2016
High School Newsletter March 2016
High School Newsletter February 2016
High School Newsletter January 2016
High School Newsletter December 2015
High School Newsletter November 2015
Math Contest Newsletters 2014-2015 School Year
Special: Selected Math League Rules 2014-2015
Grade 4-5 and Algebra Newsletter 2015
Grade School 6-7-8 Newsletter 2015
High School Newsletter April 2015
High School Newsletter March 2015
High School Newsletter February 2015
High School Newsletter January 2015
High School Newsletter December 2014
High School Newsletter November 2014
Math Contest Newsletters 2013-2014 School Year
Special: Selected Math League Rules 2013-2014
Grade School 4-5 and Algebra Newsletter 2014
Grade School 6-7-8 Newsletter 2014
High School Newsletter April 2014
High School Newsletter March 2014
High School Newsletter February 2014
High School Newsletter January 2014
High School Newsletter December 2013
High School Newsletter November 2013
Math Contest Newsletters 2012-2013 School Year
Special: Selected Math League Rules 2012
Grade School 4-5 and Algebra Newsletter 2013
Grade School 6-7-8 Newsletter 2013
High School Newsletter April 2013
High School Newsletter March 2013
High School Newsletter February 2013
High School Newsletter January 2013
High School Newsletter December 2012
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Math Contest Newsletters 2011-2012 School Year
Special: Selected Math League Rules 2011
Grade School 4-5 and Algebra Newsletter 2012
Grade School 6-7-8 Newsletter 2012
High School Newsletter April 2012
High School Newsletter March 2012
High School Newsletter February 2012
High School Newsletter January 2012
High School Newsletter December 2011
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Math Contest Newsletters 2010-2011 School Year
High School Newsletter April 2011
Grade School 6-7-8 Newsletter #1 2011
High School Newsletter March 2011
High School Newsletter February 2011
High School Newsletter January 2011
High School Newsletter December 2010
High School Newsletter November 2010
Math Contest Newsletters 2009-2010 School Year
Grade School 6-7-8 Newsletter #1 2010
High School Newsletter April 2010
High School Newsletter March 2010
High School Newsletter February 2010
High School Newsletter January 2010
High School Newsletter December 2009
High School Newsletter November 2009
Math Contest Newsletters 2008-2009 School Year
Math League News #1, Nov., 2008
Math League News #2, Dec., 2008
Math League News #3, Jan., 2009
Math League News #4, Feb., 2009
Math League News #5, Mar., 2009
Math League News #6, Apr., 2009
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Official Contest Dates 2008-2009 School Year | ||||
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Contest Level | Registration Deadline * | Shipping Date | Contest Date | Registration Fee (Prices include shipping) |
4th Grade | February 28, 2009 | March | April 15th or later | $30 per set of 30 |
5th Grade | February 28, 2009 | March | April 15th or later | $30 per set of 30 |
6th Grade | January 31, 2009 | January | 3rd Tues. in Feb. - February 17, 2009 or 4th Tues. in Feb. - February 24, 2009 | $30 per set of 30 |
7th Grade | January 31, 2009 | January | 3rd Tues. in Feb. - February 17, 2009 or 4th Tues. in Feb. - February 24, 2009 | $30 per set of 30 |
8th Grade | January 31, 2009 | January | 3rd Tues. in Feb. - February 17, 2009 or 4th Tues. in Feb. - February 24, 2009 | $30 per set of 30 |
Algebra Course 1 | February 28, 2009 | March | April 15th or later | $30 per set of 30 |
High School | October 15, 2008 | October | 6 Contests, Oct.-Mar. | $75 / 6 contests, 30 of each |
* Late registrations will be accepted. |
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Algebra Course 1 Contest
Math League's Algebra Course 1 Contests are a great way to motivate students learning algebra for the first time. The questions range from basic algebra skills, to more difficult problems, requiring creative solutions by applying algebra course 1 techniques. A wide variety of word problems are included on each contest, in addition to computational problems, to stress the value of applied algebra techniques. These contests are provided for intraschool competition, and come with certificates of merit for your school's high scoring students, and one of our High School Contest problem books for your school's top scorer. Here's a quote from one of last year's Algebra Course 1 students who participated in our contest: "I hope you keep making those tests. It really gets your brain to work" -Amber L. Contest Format: Each contest consists of 30 multiple-choice questions that you can do in 30 minutes. On each 3-page contest, the questions on the 1st page are generally straightforward, those on the 2nd page are moderate in difficulty, and those on the 3rd page are more difficult. The questions require no more knowledge than that of a first year high school algebra course. |
Sample Algebra 1 Contest (PDF - 195k) • Solutions (PDF - 208k) Dates / Fees • Register Online • Print Order Form Rules • FAQ • Check School Registration |
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6th, 7th, and 8th Grade Contests
Math League's 6th, 7th, and 8th grade contests challenge students and schools in interschool league competitions. Students in each league compete for the highest scores, while schools compete for the highest team score: the total of the top 5 scores in each school. Each contest's questions cover material appropriate to each grade level. Questions may cover: basic topics, plus exponents, fractions, reciprocals, decimals, rates, ratios, percents, angle measurement, perimeter, area, circumference, basic roots, patterns, sequences, integers, triangles and right triangles, and other topics, depending on the grade level. Detailed solution sheets demonstrate the methods used to solve each problem. These contests encourage a variety of problem-solving skills and methods, to improve students' abilities and understanding of mathematical connections, while having fun! Contest Format: Each contest consists of 35 multiple-choice questions that you can do in 30 minutes. On each 3-page contest, the questions on the 1st page are generally straightforward, those on the 2nd page are moderate in difficulty, and those on the 3rd page are more difficult. There is a 6th Grade Score Report, and a 7th and 8th Grade Score Report sent to schools in each league after the contest. |
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High School ContestsMath League's High School Contests are the best in high school mathematics competition. Students in each league compete for the highest scores, while schools compete for the highest team score: the total of the top 5 scores in each school. These contests consist of 6 High School Contests each year, with 6 questions per contest. There are 6 score reports per year for each league, showing each participating school's team scores, high scoring schools and students, and students with a perfect score. Each score report is accompanied by a newsletter, which includes comments and alternate solutions from teachers and students. All high school students in accredited schools are welcome to compete. Problems draw from a wide range of high school topics: geometry, algebra, trigonometry, logarithms, series, sequences, exponents, roots, integers, real numbers, combinations, probability, coordinate geometry, and more. No knowledge of calculus is required to solve any of these problems. Detailed solution sheets demonstrate the methods used to solve each problem, including various approaches where appropriate. Working through these problems and our contest problem books is excellent practice for the SAT and college-bound students. Contest Format: There are 6 High School Contests each year, with 6 questions per contest. There is a 30 minute time limit for each contest. On each contest, the last two questions are generally more difficult than the first four. The final question on each contest is intended to challenge the very best mathematics students. The problems require no knowledge beyond secondary school mathematics. No knowledge of calculus is required to solve any of these problems. Two to four of the questions on each contest only require a knowledge of elementary algebra. Starting with the 1992-93 school year, students have been permitted to use any calculator on any of our contests. |
Sample 05-06 High School Contest & Solutions (PDF) Dates / Fees • Register Online • Print Order Form Score Reports • Rules • FAQ • Check School Registration |
2010-2011 High School Contest Dates | |
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Contest # | Official Date* (Tuesdays) |
HS Contest 1 HS Contest 2 HS Contest 3 HS Contest 4 HS Contest 5 HS Contest 6 | October 19, 2010 November 16, 2010 December 14, 2010 Janaury 11, 2011 February 22, 2011 March 22, 2011 |
*Alternate contest dates may be scheduled one week before the contest dates, in the event of scheduling conflicts. |
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Positive and negative numbers
About positive and negative numbers
The number line
Absolute value of positive and negative numbers
Adding positive and negative numbers
Subtracting positive and negative numbers
Multiplying positive and negative numbers
Dividing positive and negative numbers
Coordinates
Comparing positive and negative numbers
Reciprocals of negative numbers
About Positive and Negative Numbers
Positive numbers are any numbers greater than zero, for example: 1, 2.9, 3.14159, 40000, and 0.0005. For each positive number, there is a negative number that is its opposite. We write the opposite of a positive number with a negative or minus sign in front of the number, and call these numbers negative numbers. The opposites of the numbers in the list above would be: -1, -2.9, -3.14159, -40000, and -0.0005. Negative numbers are less than zero (see the number line for a more complete explanation of this). Similarly, the opposite of any negative number is a positive number. For example, the opposite of -12.3 is 12.3.
We do not consider zero to be a positive or negative number.
The sum of any number and its opposite is 0.
The sign of a number refers to whether the number is positive or negative, for example, the sign of -3.2 is negative, and the sign of 442 is positive.
We may also write positive and negative numbers as fractions or mixed numbers.
The following fractions are all equal:
(-1)/3, 1/(-3), -(1/3) and - 1/3.
The following mixed numbers are all equal:
-1 1/6, -(1 1/6), (-7)/6, 7/(-6), and - 7/6.
The Number Line
The number line is a line labeled with positive and negative numbers in increasing order from left to right, that extends in both directions. The number line shown below is just a small piece of the number line from -4 to 4.
For any two different places on the number line, the number on the right is greater than the number on the left.
Examples:
4 > -2, 1 > -0.5, -2 > -4, and 0 > -15
Absolute Value of Positive and Negative Numbers
The number of units a number is from zero on the number line. The absolute value of a number is always a positive number (or zero). We specify the absolute value of a number n by writing n in between two vertical bars: |n|.
Examples:
|6| = 6
|-0.004| = 0.004
|0| = 0
|3.44| = 3.44
|-3.44| = 3.44
|-10000.9| = 10000.9
Adding Positive and Negative Numbers
1) When adding numbers of the same sign, we add their absolute values, and give the result the same sign.
Examples:
2 + 5.7 = 7.7
(-7.3) + (-2.1) = -(7.3 + 2.1) = -9.4
(-100) + (-0.05) = -(100 + 0.05) = -100.05
2) When adding numbers of the opposite signs, we take their absolute values, subtract the smaller from the larger, and give the result the sign of the number with the larger absolute value.
Example:
7 + (-3.4) = ?
The absolute values of 7 and -3.4 are 7 and 3.4. Subtracting the smaller from the larger gives 7 - 3.4 = 3.6, and since the larger absolute value was 7, we give the result the same sign as 7, so 7 + (-3.4) = 3.6.
Example:
8.5 + (-17) = ?
The absolute values of 8.5 and -17 are 8.5 and 17. Subtracting the smaller from the larger gives 17 - 8.5 = 8.5, and since the larger absolute value was 17, we give the result the same sign as -17, so 8.5 + (-17) = -8.5.
Example:
-2.2 + 1.1 = ?
The absolute values of -2.2 and 1.1 are 2.2 and 1.1. Subtracting the smaller from the larger gives 2.2 - 1.1 = 1.1, and since the larger absolute value was 2.2, we give the result the same sign as -2.2, so -2.2 + 1.1 = -1.1.
Example:
6.93 + (-6.93) = ?
The absolute values of 6.93 and -6.93 are 6.93 and 6.93. Subtracting the smaller from the larger gives 6.93 - 6.93 = 0. The sign in this case does not matter, since 0 and -0 are the same. Note that 6.93 and -6.93 are opposite numbers. All opposite numbers have this property that their sum is equal to zero. Two numbers that add up to zero are also called additive inverses.
Subtracting Positive and Negative Numbers
Subtracting a number is the same as adding its opposite.
Examples:
In the following examples, we convert the subtracted number to its opposite, and add the two numbers.
7 - 4.4 = 7 + (-4.4) = 2.6
22.7 - (-5) = 22.7 + (5) = 27.7
-8.9 - 1.7 = -8.9 + (-1.7) = -10.6
-6 - (-100.6) = -6 + (100.6) = 94.6
Note that the result of subtracting two numbers can be positive or negative, or 0.
Multiplying Positive and Negative Numbers
To multiply a pair of numbers if both numbers have the same sign, their product is the product of their absolute values (their product is positive). If the numbers have opposite signs, their product is the opposite of the product of their absolute values (their product is negative). If one or both of the numbers is 0, the product is 0.
Examples:
In the product below, both numbers are positive, so we just take their product.
0.5 × 3 = 1.5
In the product below, both numbers are negative, so we take the product of their absolute values.
(-1.1) × (-5) = |-1.1| × |-5| = 1.1 × 5 = 5.5
In the product of (-3) × 0.7, the first number is negative and the second is positive, so we take the product of their absolute values, which is |-3| × |0.7| = 3 × 0.7 = 2.1, and give this result a negative sign: -2.1, so (-3) × 0.7 = -2.1
In the product of 21 × (-3.1), the first number is positive and the second is negative, so we take the product of their absolute values, which is |21| × |-3.1| = 21 × 3.1 = 65.1, and give this result a negative sign: -65.1, so 21 × (-3.1) = -65.1.
To multiply any number of numbers:
1. Count the number of negative numbers in the product.
2. Take the product of their absolute values.
3. If the number of negative numbers counted in step 1 is even, the product is just the product from step 2, if the number of negative numbers is odd, the product is the opposite of the product in step 2 (give the product in step 2 a negative sign). If any of the numbers in the product is 0, the product is 0.
Example:
2 × (-1.1) × 5 (-1.2) × (-9) = ?
Counting the number of negative numbers in the product, we see that there are 3 negative numbers: -1.1, -1.2, and -9. Next, we take the product of the absolute values of each number: 2 × |-1.1| × 5 × |-1.2| × |-9| = 2 × 1.1 × 5 × 1.2 × 9 = 118.8
Since there were an odd number of numbers, the product is the opposite of 118.8, which is -118.8, so 2 × (-1.1) × 5 (-1.2) × (-9) = -118.8.
Dividing Positive and Negative Numbers
To divide a pair of numbers if both numbers have the same sign, divide the absolute value of the first number by the absolute value of the second number.
To divide a pair of numbers if both numbers have different signs, divide the absolute value of the first number by the absolute value of the second number, and give this result a negative sign.
Examples:
In the division below, both numbers are positive, so we just divide as usual.
7 ÷ 2 = 3.5
In the division below, both numbers are negative, so we divide the absolute value of the first by the absolute value of the second.
(-2.4) ÷ (-3) = |-2.4| ÷ |-3| = 2.4 ÷ 3 = 0.8
In the division (-1) ÷ 2.5, both number have different signs, so we divide the absolute value of the first number by the absolute value of the second, which is |-1| ÷ |2.5| = 1 ÷ 2.5 = 0.4, and give this result a negative sign: -0.4, so (-1) ÷ 2.5 = -0.4.
In the division 9.8 ÷ (-0.7), both number have different signs, so we divide the absolute value of the first number by the absolute value of the second, which is |9.8| ÷ |-0.7| = 9.8 ÷ 0.7 = 14, and give this result a negative sign: -14, so 9.8 ÷ (-0.7) = -14.
Coordinates
Number coordinates are pairs of numbers that are used to determine points in a grid, relative to a special point called the origin. The origin has coordinates (0,0). We can think of the origin as the center of the grid or the starting point for finding all other points. Any other point in the grid has a pair of coordinates (x,y). The x value or x-coordinate tells how many steps left or right the point is from the point (0,0), just like on the number line (negative is left of the origin, positive is right of the origin). The y value or y-coordinate tells how many steps up or down the point is from the point (0,0), (negative is down from the origin, positive is up from the origin). Using coordinates, we may give the location of any point in the grid we like by simply using a pair of numbers.
Example:
The origin below is where the x-axis and the y-axis meet. Point A has coordinates (2.3,3), since it is 2.3 units to the right and 3 units up from the origin. Point B has coordinates (-3,1), since it is 3 units to the left, and 1 unit up from the origin. Point C has coordinates (-4,-2.5), since it is 4 units to the left, and 2.5 units down from the origin. Point D has coordinates (9.2,-8.4); it is 9 units to the right, and 8.4 units down from the origin. Point E has coordinates (-7,6.6); it is 7 units to the left, and 6.6 units up from the origin. Point F has coordinates (8,-5.7); it is 8 units to the right, and 5.7 units down from the origin.
Comparing Positive and Negative Numbers
We can compare two different numbers by looking at their positions on the number line. For any two different places on the number line, the number on the right is greater than the number on the left. Note that every positive number is greater than any negative number.
Examples:
9.1 > 4, 6 > -9.3, -2 > -8, and 0 > -5.5
-2 < -13, -1 < -0.5, -7 < -5, and -10 < 0.1
Reciprocals of Negative Numbers
The reciprocal of a positive or negative fraction is obtained by switching its numerator and denominator, the sign of the new fraction remains the same. To find the reciprocal of a mixed number, first convert the mixed number to an improper fraction, then switch the numerator and denominator of the improper fraction. Notice that when you multiply negative fractions with their reciprocals, the product is always 1 (NOT -1).
Examples:
What is the reciprocal of -2/7? We just switch the numerator and denominator, and keep the same sign: -7/2.
What is the reciprocal of - 5 1/8? First, we convert to a negative improper fraction: -5 1/8 = - 41/8, then we switch the numerator and denominator, and keep the same sign: - 8/41.