Math Nite will be running every Wednesday from 6pm-8pm in MS-431 at the University of Calgary, from the following dates:
September 20th, 2017 to December 6th,
2017 January 17th, 2018 to April 11th, 2018.
More detailed information about Math Nite can be found here: https://www.math.ucalgary.ca/community_outreach/math_nite.

Competitions

Cayley Contest Mathematics Contests, for Grade 10

American Mathematics Contest 10/12 (AMC 10/12)

AMC Problems and Solutions:

AMC 10 Problems and Solutions by AoP (Text version).

Many of these problems also have solutions presented in video tutorials on the AoP YouTube channel. Search the channel to check in a solution is available, for example:

Video Solution: Art of Problem Solving: 2017 AMC 10 A #22

Text version: select the year here, test A or B, next pick the problem or answer key: for ex. problem 22 solution in text version is here.

Shortcuts

3D Geometry

Algebraic Expressions

Polynomials and Factoring

Topics

3D Geometry (back to Shortcuts...)
	Activity	Use Tinkercad to identify the cross section of 3D objects.
	Build a hypercube This page is sponsored by:

	Cavalieri's Principle (Volume)

	The Volume of a Cone


Exponent Laws (back to Shortcuts...)	The rules:
	What is an "Integral exponent"?	An "Integral exponent" is an exponent that is a whole number (in contrast to the powers of radicals for example which are 1/n, i.e. fractional)
	see also	Exponent and radicals index cards



Irrational Numbers (back to Shortcuts...)	To understand irrational numbers, first we must understand rational ones.	Definition: Rational Numbers Do not think "rational" as in logical. Think as in "ratio", a.k.a. fraction. Rational numbers as such that can be accurately reverse engineered from their decimal form back into their fraction, or rather ratio - and thus are rational. Any decimal number with a finite number of digits is such, and any decimal with a group of digits that infinitely repeat after the decimal point is also such.
	Definition: Irrational Numbers	Irrational is the opposite of Rational. That is you cannot accurately reverse engineer from the decimal form back to a parent ratio (or fraction) - and thus such number is not rational, or we say it is rather irrational. You can create a fraction that is an approximation of that decimal, but it will not be an exact value and when reverting the fraction back into decimal you may get a somewhat different rounding than the one you started with. How do Irrationals look like typically? Irrational numbers appear as decimals with an infinite number of digits that do not repeat, and cannot be predicted. Such decimal number was most likely accomplished via a division that never stopped, and you were forced to round up so you can stop dividing. An example is Pi = π = 3.14159.... π is calculated via the division of any circle's circumference by its diameter. Another example is e, Euler's number, the same e as seen in natural logarithms. Read more about irrational numbers here. The problem is how do we know that a number is truly irrational and it's not that we just gave up to soon on the steps of a division? The number e bears Euler's name because he was the first to prove the number has an infinite number of decimals and there is no pattern of repetitions, and thus is irrational.
	Converting Decimals to Fractions	https://www.mathsisfun.com/converting-decimals-fractions.html

Linear Functions (back to Shortcuts...)
	Explaining functions: y = f(x)
	What does "Linear" mean?	"Linear" is anything that represents the formula of a line. This can be linear equations, linear graphs, linear progressions, etc. The typical formula for a line is given as: y = mx + b, where m is the slope of the line and b is its y-intercept.
	Lesson (slide show)
		This page is sponsored by:
	Problem solving Find the intercepts and draw the graph y = 4x-8
	Lessons and other resources	https://mathsradical.weebly.com/functions.html https://www.shelovesmath.com/algebra/beginning-algebra/coordinate-system-and-graphing-lines/ https://carlisleschools.ss13.sharpschool.com/cms/One.aspx?portalId=95563&pageId=768700
	Graphing Linear Equations	https://njctl.org/courses/math/algebra-i/graphing-linear-equations/
	Solving and Graphing Linear Inequalities	https://njctl.org/courses/math/algebra-i/solving-and-graphing-linear-inequalities/ Videos: An Introduction To Solving Linear Inequalities - Example 1 An Introduction To Solving Linear Inequalities - Example 2 An Introduction To Solving Linear Inequalities - Example 3 Solving Linear Compound Inequalities - Example 1 Solving Linear Compound Inequalities - Example 2 Solving Linear Compound Inequalities - Example 3
	Parallel and Perpendicular Lines	https://map.mathshell.org/lessons.php?unit=9220&collection=8

	Practice: Parallel Lines

	Practice Exercises (PDF download)	https://www.mchs.gsacrd.ab.ca/eteacher_download/1353/79308

	Practice: Shortest Distance between a Point and Line - Equations of Lines
	Practice: Given a line y = mx + b, find the formula of a parallel line at a distance d.
	Practice: Shortest distance between two parallel lines (based on the solution above):	Problems that require finding the shortest distance between two parallel lines: Using the above formula, we can isolate the distance d. This is assuming that the two line formulas are given. In other words: - m & b1 are known, - and b2 the parallel line's y-intercept is also given (or can be calculated). Since the distance is a length, taking the positive value is what we want.
	see also: https://njctl.org/courses/math/geometry/analytic- geometry	Distance Formula Midpoint Formula Partitions of a Line Segment Slopes of Parallel and Perpendicular Lines Eq of Parallel and Perpendicular Lines Triangle Coordinate Proofs Equation of a Circle and Completing the Square
	Graphing a linear equation
	Practice EXAM	https://courses.lumenlearning.com/epcc-atdcoursereview-collegealgebra-1-2/chapter/linear-functions-practice-test/ (press Next at the bottom for solutions to this exam)

Equations (back to Shortcuts...)
	Lessons and Tools	https://www.ck12.org/search/?q=equations&subject=algebra&subject=calculus&source=ck12&grade=10&grade=11&grade=12
	Linear Equations with Two Variables	https://map.mathshell.org/lessons.php?unit=9235&collection=8

Systems of Equations (back to Shortcuts...)
	Systems of Linear Equations	https://njctl.org/courses/math/algebra-i/systems-of-linear-equations/
	Solve linear systems visually/graphically
	Solving linear systems by substitution
	Solving systems of equations by elimination