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Math 10 concepts - Coggle Diagram
Math 10 concepts
Exponents
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-n^m = always negative
(-n)^m = if m is odd, answer is negative. If m is even, answer is positive.
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Negative exponent in the numerator: bring to denominator to make it positive
Negative exponent in the denominator: bring to numerator to make it positive
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Linear systems
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Lines have same slope, same y-intercept, then infinite solutions - consistent system
Lines have different slope, then ONLY ONE solution - consistent system
Solving by elimination
If the x or y variables differ in signs, eliminate through ADDITION
If x or y variables are exactly the same, eliminate through SUBTRACTION
If you multiply linear equation by constant, does not change the solution
Solving by substitution
- Using equation with variable that has coefficient of 1, solve that variable
- Substitute that solution in the other equation
Linear relations
Slope
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Rise: Up is positive, down is negative
Run: Right is positive, left is negative
Line that goes up to right is positive slope
Line that goes down to left is positive slope
Line that goes up to left is negative slope
Line that goes down to right is negative slope
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Slope-intercept form
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How to graph
Start with y-intercept
Using slope, find rise and run
If slope is not fraction, run = 1
ex. y = 4x + 5, then 4 = 4/1
Parallel & perpendicular
Parallel: Slope = same, y-intercept = different (Symbol ∥)
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Arithmetic sequence
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2, 4, 8, 16, 32.... (not an arithmetic pattern)
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Relations and functions
Relation
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Domain: first set of elements (Surrey, BC), x value(s)
Range: second set of elements (Surrey, BC), y value(s)
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Linear relation
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- Degree of equation = 1 (NO x^2 + y^2)
- Variables cannot multiply (NO xy)
- Variables cannot be in denominator (NO y = 7/x+3)
- Variables cannot be exponent (NO y = 7^x)
Function
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Tip: in a table, if any X (domain) value repeats, it is NOT a function
Tip: in a graph, any two points on same x axis, is NOT a function
Any points joined by vertical line, is NOT a function
- Arrows = line extends
- Solid dot = end point
- Outlined dot = approaching, but NOT REACHING end point
Inequality symbols
greater than: >
less than: <
greater than or equal to: ≥
less than or equal to: ≤
Tip: Smaller number then variable then larger number
Tip: always read from variable to the number
Set Notation
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Ex. y is an element of real numbers such that y is greater than -2 = {y | y > -2, y ∈ R}
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Interval Notation
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Ex. A range of numbers greater than -2 = (-2,∞)
To find y intercept, put x = 0
To find x intercept, put y = 0
Graph the equation using x and y intercepts
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Discrete data = points NOT connected in graph (integers)
Continuous data = points connected in graph (real numbers)
Rate of change = change in dependent variable ⁄ change in independent variable
Also known as... Slope = rise ⁄ run
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Simplifying Polynomials
If given x and y values for polynomial, input where is it appropriate and remember to put brackets around them
Then evaluate exponents first, if any
