Transcript AlgII

Algebra II
Math Methods II
Visual Mathematics
QuickTime™ and a
decompressor
are needed to see this picture.
Functions: CCSS
❖
◦
◦
◦
•
◦
◦
•
◦
◦
•
◦
◦
◦
Interpreting Functions
Understand the concept of a function and use function notation
Interpret functions that arise in applications in terms of the context
Analyze functions using different representations
Building Functions
Build a function that models a relationship between two quantities
Build new functions from existing functions
Linear, Quadratic, and Exponential Models
Construct and compare linear and exponential models and solve problems
Interpret expressions for functions in terms of the situation they model
Trigonometric Functions
Extend the domain of trigonometric functions using the unit circle
Model periodic phenomena with trigonometric functions
Prove and apply trigonometric identities
Esrevni Functions
❖ F-BF.4
Build new functions from existing
functions. Find inverse functions.
❖ Visually
show the concept with multiple
representations
❖ Inverse
❖ The
of the point (2,-3) is (-3,2)
DOMAIN and RANGE of the function
become the RANGE and DOMAIN of the Inverse
Inverse Functions
❖
8.G.1 Verify experimentally the properties of rotations,
reflections, and translations
❖
The Inverse of y = x2 becomes x = y2
Inverse Functions
Painted Cube Problem
❖
F-LE Construct and compare linear, quadratic, and
exponential models and solve problems.
❖
Different size cubes are constructed from unit cubes, the
surface areas of the resulting larger cubes are painted,
and then each of the larger cubes is disassembled into its
original unit cube?
❖
How many of the unit cubes are painted on 3 faces? 2
faces? 1 face? 0 faces?
❖
Use tables, graphs, and equations to explore.
Cubes & Spatial Thinking
Functions
❖ Problem 1
❖ The 10th grade class of Taft High is planning a
day to a local amusement park. It will cost $350
to rent a bus for one day. How will the size of
each person’s contribution depend upon the size
of the group going on the trip?
Functions
❖
Problem 2
❖
The following chart appeared in a mail order catalog. Use
this chart to determine your shipping charges.
❖
Merchandise Total
❖
Up to $15.00
❖
From $15.01 to $25.00
add $5.00
❖
From $25.01 to $50.00
add $7.00
❖
Over $50.00
add $3.00
add $9.00
Functions
❖
Problem 3
❖
The purchasing agent for the school store wants to buy
1200 pencils imprinted with the school logo. The pencils
can be purchased in packages of 12, 24, 48, 100, and 200
pencils but package sizes cannot be combined. Show the
function, in any form, that assigns to each possible
package size the number of packages that must be
purchased.
Functions
❖
Problem 4
❖
A, B, C are points in the coordinate plane. How many
functions can be drawn that include all three points A, B,
C? Explain.
❖
❖
Problem 5
Functions
A function is defined by the following recursion formula:
❖ f1=1; fn=√(2*fn-1)
❖
The first six values of the function are
❖
1
❖
≈1.4142
❖
≈1.6818
❖
≈1.8340
❖
≈1.9152
❖
≈1.9571
Functions
❖
Problem 6
❖
Show a different representation of the following function:
Space Math: NASA
Conversions (1.1.1)
❖
http://spacemath.gsfc.nasa.gov/algebra2/Algebra2V3.pdf
❖
6.RP.3d Use ratio reasoning to convert measurement
units.
❖
The Space Shuttle used 800,000 gallons of rocket fuel to
travel 400 km into space. If one gallon of rocket fuel has
the same energy as 5 gallons of gasoline, what is the
equivalent gas mileage of the Space Shuttle in gallons of
gasoline per mile?
❖
16,000 gallons/mile
Space Math: NASA
Pythagorean Theorem 3D (1.2.1)
8.G.6-8 Explain and apply Pythagorean Theorem
*Distance in light years
Space Math: NASA
The Hunt for Higgs Boson (1.6.3)
❖
A-CED Create
equationsconcluded
& inequalities
Fermilab's Tevatron accelerator
experiments
that it
must either be more massive than 170 GeV or less massive than
160 GeV.
❖
CERN's LEP accelerator concluded after years of searching that
the Higgs Boson must be more massive than 115 GeV
❖
The Standard Model, which describes all that is currently known
about the interactions between nuclear elementary particles,
provided two constraints depending on the particular assumptions
used: The Higgs Boson cannot be more massive than 190 GeV,
and it has to be more massive than 80 GeV but not more than 200
GeV.
❖
From all these constraints, what is the intersection of possible
masses for the Higgs Boson that is consistent with all of the
constraints?
Space Math : NASA
Solving Systems of Linear Equations (3.1.1)
A-CED.3 Represent & solve systems of linear equations
❖
Studies of the number of craters on Venus and Mars
have determined that for Venus, the number of craters
with a diameter of D kilometers is approximated by N =
108 – 0.78D while for Mars the crater counts can be
represented by N = 50 – 0.05 D.
❖
Graphically solve these two equations to determine for
what crater diameter the number of craters counted on
the two planets is the same over the domain D:[0,100
km].
Space Math: NASA
Logs (8.6.1)
F-BF.5 Understand logarithms
❖
❖
❖
For stars, the apparent brightness or ‘magnitude’ of a star
depends on its distance and its luminosity, also called its
absolute magnitude. What you see in the sky is the apparent
brightness of a star. The actual amount of light produced by the
surface of the star is its absolute magnitude. A simple equation,
basic to all astronomy, relates the star’s distance in parsecs, D,
apparent magnitude, m, and absolute magnitude, M as follows:
M = m + 5 - 5log(D)
Problem 1 – The star Sirius has an apparent magnitude of m = 1.5, while Polaris has an apparent magnitude of m = +2.3, if the
absolute magnitude of Sirius is M = +1.4 and Polaris is M = -4.6,
what are the distances to these two stars?
Space Math: NASA
Logs (8.4.1)
F-BF.5 Understand logarithms
❖
Log N = -0.0003 m^3 + 0.0019 m^2 + 0.484 m - 3.82
❖
A small telescope can detect stars as faint as magnitude
+10. If the human eye-limit is +6 magnitudes, how many
more stars can the telescope see than the human eye?
Trig Apps
Trig Apps
Trig Apps
Trig Apps