G8 Gauss Algebra


Grade 8 Gauss Math Competition Categorized: Algebra This document consists of a collection of problems that appeared in the Grade 8 Gauss Contests from 2001 to 2010. All the problems are original ones found on CEMC’s website, where the solutions to these problems, along with other information, are also provided. This document is created by Jian Kang (MathEasy123.wordpress.com), who collected these contest problems and put them into categories solely for study and teaching purposes. The standard of categorization employed is by no means the only way there is, as problems are often comprehensive. One is encouraged to come up with his or her own version of categorization.

Algebra Categorized here are problems which involve algebraic techniques and concepts, both fundamental and/or advanced, including but not limited to: addition, subtraction, multiplication, division, ratios, exponential s, equations, number sequences, etc., without appealing to a real-world situation.

Contest Problems

Basic Calculation These questions are very straightforward calculations. Usually appearing in the first half of Part A, these ones are mostly for warm-up. Watch out for the order of computations and the signs. Be careful. Don’t ever make mistakes on these easiest ones!

2010, Q1

2009, Q1

2007, Q1

2006, Q1

2008, Q1

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2003, Q1

2005, Q1

2009, Q2

2005, Q2

2003, Q2

2002, Q2

2002, Q3

2001, Q3


2008, Q4

2003, Q4


Basic Fractions, Decimals and Ratios This subcategory of questions tests one’s knowledge of fractions, decimals and ratios. One is often required to perform tasks such as converting fraction to decimals and comparing and/or putting values in descending/ascending orders. Remember two things:

1. The “puff and shrink rule”: to increase the value of

, one can either increase or decrease ,

while all other conditions remain unchanged (to decrease the value, vice versa). 2. You are allowed to use calculators!

2004, Q1

2002, Q1

2007, Q2

2004, Q2

2009, Q5

2005, Q5


2010, Q6

2010, Q13

2005, Q14

2003, Q16

2008, Q17

2007, Q19


2005, Q19


Variables, Equations and Inequalities This subcategory of questions is designed to test one’s knowledge and skills on substituting numbers into

variables and solving equations, as well as solving very basic equations whose solutions are limited whole

numbers. Note that a symbol such as an empty square in 2010, Q4 is also considered a variable, just like x

and y.

Also, there are mini-word questions which typically involve operations of “one number” and “other

numbers”. These questions implicitly require one to use variables.

2001, Q2

2010, Q3

2004, Q3

2004, Q4

2010, Q4


2006, Q4

2002, Q4

2001, Q5

2003, Q6

2008, Q6

2005, Q6


2004, Q7

2008, Q8

2007, Q9

2009, Q10

2002, Q13

2007, Q15


2005, Q15

2004, Q17

2006, Q17

2007, Q18

2003, Q18

2001, Q19


2001, Q20

2004, Q24

2005, Q24


Parity, Divisors, Factors, Prime and Composite Numbers The questions in this subcategory require one to have a good understanding division techniques and the concept of prime numbers, which is one of the most important concepts in the whole mathematics. Parity (even and odd numbers) is tightly associated with prime, as even numbers are numbers who have factor 2, while odd numbers do not.

2006, Q2

2002, Q5

2006, Q6

2001, Q12

2002, Q15

2004, Q16


2005, Q17

2005, Q18


Ordering and Sequences A sequence is basically a string of numbers, placed in some order. In this subcategory of questions, one is often required to sort numbers in a sequence according their values. This procedure may require one to deal with numbers in various forms, such as decimal form, fraction form, square roots, exponential, etc. Here one should proceed with caution and patience. 2008, Q5

2003, Q8

2004, Q12

2006, Q14


Max/Min Problems This subcategory consists of problems which require one to find the maximum or the minimum value of a specific expression. In most cases, the value is restricted in whole numbers, where there are only finitely many different choices. This kind of questions is not frequent in Gauss contests, but when they appear, they are very often more challenging than most other questions. Note that it is beneficial to one if he/she has some background knowledge of some most famous inequalities (The Arithmetic and Geometric Mean Inequality, for example).

2004, Q10

2005, Q12

2009, Q21

2010, Q22


Functions and More Complicated Problems Listed here are questions involving more advanced concepts such as functions (exponential functions, in particular). Here one can also find some more challenging and more comprehensive questions, which are difficult to be put into other subcategories. 2002, Q17

2002, Q18

2002, Q20

2003, Q21


2008, Q24

2010, Q25

2009, Q25

G8 Gauss Algebra

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