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General Articles

Math Contest Newsletters 2017-2018 School Year

Grade 4-5-Algebra Newsletter April 2018

Grade School Newsletter 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

High School Newsletter November 2012

 

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

High School Newsletter November 2011

 

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

To view contest newsletters get Acrobat Reader (free)To view PDF files, download and install Acrobat Reader (free).

To report your school's scores, please follow the instructions on the outside of the white envelope that contained the contests. (For security purposes, that information is not listed here.) If you do not have your school account number, help is available at the Internet Scoring Center login screen.

 

If you have any questions, you can contact us.

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Official Contest Dates 2018-2019 School Year
Contest Level Registration Deadline* Shipping Date Contest Date Registration Fee (Prices include shipping)
4th Grade January 31, 2019 March April 15th or later $40 per set of 30
5th Grade January 31, 2019 March April 15th or later $40 per set of 30
6th Grade December 31, 2018 January 3rd Tues. in Feb. - February 19, 2019 or 4th Tues. in Feb. - February 26, 2019 $40 per set of 30
7th Grade December 31, 2018 January 3rd Tues. in Feb. - February 19, 2019 or 4th Tues. in Feb. - February 26, 2019 $40 per set of 30
8th Grade December 31, 2018 January 3rd Tues. in Feb. - February 19, 2019 or 4th Tues. in Feb. - February 26, 2019 $40 per set of 30
Algebra Course 1 January 31, 2019 March April 15th or later $40 per set of 30
High School September 30, 2018 October HS Contest 1 - October 16, 2018
HS Contest 2 - November 13, 2018
HS Contest 3 - December 11, 2018
HS Contest 4 - January 8, 2019
HS Contest 5 - February 12, 2019
HS Contest 6 - March 19, 2019

Alternate contest dates may be scheduled one week after the contest dates, in the event of scheduling conflicts.

$90 / 6 contests, 30 of each

* Late registrations will be accepted.

 Contest Results and Newsletters Previous Years (old site)

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Official Contest Dates 2008-2009 School Year
Contest LevelRegistration
Deadline
 *
Shipping DateContest Date Registration Fee
(Prices include shipping)
4th GradeFebruary 28, 2009MarchApril 15th or later $30 per set of 30
5th GradeFebruary 28, 2009MarchApril 15th or later $30 per set of 30
6th Grade

January 31, 2009

January3rd Tues. in Feb. - February 17, 2009
or 4th Tues. in Feb. - February 24, 2009
$30 per set of 30
7th GradeJanuary 31, 2009January3rd Tues. in Feb. - February 17, 2009
or 4th Tues. in Feb. - February 24, 2009
$30 per set of 30
8th GradeJanuary 31, 2009January3rd Tues. in Feb. - February 17, 2009
or 4th Tues. in Feb. - February 24, 2009
$30 per set of 30
Algebra Course 1February 28, 2009MarchApril 15th or later$30 per set of 30
High School

October 15, 2008

October6 Contests, Oct.-Mar.$75 / 6 contests, 30 of each

 * Late registrations will be accepted.


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


To best view sample contests get Acrobat Reader (free) 

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.


 

 Sample 6th Grade Contest (PDF - 240k) • Solutions (PDF - 256k) 
 
Sample 7th Grade Contest (PDF - 232k) • Solutions (PDF - 253k) 
 Sample 8th Grade Contest (PDF - 195k) • Solutions (PDF - 247k) 
Dates / Fees • Register Online • Print Order Form
 Score Reports • Rules • FAQ • Check School Registration

To best view sample contests get Acrobat Reader (free)

High School Contests

Math 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


To best view sample contests get Acrobat Reader (free) 



 


2010-2011 High School Contest Dates

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.

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.