## Common Topics Covered in Standard Algebra II Textbooks

Algebra II is a course in mathematics offered in the United States public and private school systems taken by approximately 85% of all graduating high school seniors by the age of 17. Two major studies by the U.S Department of Education have shown that Algebra II is considered by many as a gateway course that predicts student graduation from college, and their eventual qualification for high-paying careers. The course is typically taught in Grade 10 as a two-semester series following prerequisite courses in Algebra I and/or Geometry. The course stresses student mastery of the analysis and graphing of polynomials, logarithmic, exponential and trigonometric functions, with some applications to real-world problems in which these modeling techniques can often be seen to apply.

In keeping with the intent to show how Algebra II topics connect with real-world applications,
textbooks commonly include several hundred word problems that are generally culled from situations that
students may encounter, often involving economics. What appears to be absent from the selection are an adequate
number of problems in earth or space science. For example, out of 700 application problems in the textbook **Algebra II** (McDougal-Littell, 2004)
one finds fewer than 30 that connect with physical science or space science. Many of these are fairly generic and do not
leverage recent discoveries in earth or space science as a way to stimulate the students interest in these topics and prospective careers.

Since 2004, Space Math@ NASA has developed math problems for grades 3-12 designed to showcase how NASA discoveries in earth and space science are connected to a variety of math topics and skills. By 2010, over 400 of these problems are available online, or can be found in a series of special-topic books (Black Hole Math, Earth Math, etc). Frequently, NASA press releases serve as the hook to provide a suitable topic from which an appropriate mathematical problem is developed. This also allows students to read about a new discovery on the Evening News or CNN.com, and then within a few days they can work through some mathematical issue presented by the news release. For example, the Gulf Oil Spill of 2010 was viewed by the NASA, Terra satellite and students used the satellite image to calculate its total area, mass and density. In other examples, students can read a press release announcing the discovery of a new planet, and calculate from two points on its elliptical orbit, the equation of the orbit, its semi-major axis and the orbit period of the planet.

This book contains over 200 problems spanning over 70 specific topic areas covered in a typical
Algebra II course. The content areas have been extracted from the McDougal-Littell **Algebra II** textbook
according to the sequence used therein. A selection of application problems featuring astronomy, earth science
and space exploration were then designed to support each specific topic, often with more than one example in a
specific category. Each problem is introduced with a brief paragraph about the underlying science, written in a
simplified, non-technical jargon where possible. Problems are often presented as a multi-step or multi-part activities.
The intent of these problems is not to follow an explicitly inquiry-based approach, but to systematically show
students how problems and questions of a specific type are often solved. Once students have mastered a particular
approach, there are many opportunities available for students to go beyond each problem and inquire about other
connections that may suggest themselves as the student completes each problem, or a collection of problems.

## Real Numbers and Operations

1.1.1 -- **Unit Conversions I **

1.1.2 -- **Unit Conversions II**

## Algebraic Expressions and Operations

1.2.1 -- **Calculating Star Distances**

1.2.2 -- **Black Hole Tidal Forces**

1.2.3 -- **Moon Crater Explosions**

1.2.4 -- **Secondary Physical Constants**

1.2.5 -- **Magnetic Fields**

1.2.6 -- **Ares IX Rocket Launch**

1.2.7 -- **Temperature of a Planet I**

1.2.8 -- **Density of the Solar Interior**

1.2.9 -- **Temperature of a Planet II**

## Solving Linear Equations

1.3.1 -- **Solving for X in Astronomy
**

**Rewriting Equations and Formulas**

1.4.1 -- **Lunar Escape Speed**

1.4.2 -- **Keplers Third Law
**

**Problem Solving using Algebraic Models**

1.5.1 -- **A Model for the Lunar Interior**

1.5.2 -- **Modeling Atmospheric CO2**

1.5.3 -- **Spitzer: New Saturn Ring**

1.5.4 -- **Spitzer: Weather on a New Planet**

1.5.5 -- **LRO: Water on the Moon**

1.5.6 -- **Spitzer: A Model for Planet Osiris**

## Solving Linear Inequalities

1.6.1 -- **Brown Dwarf Stars**

1.6.2 -- **Asteroid Math**

1.6.3 -- **The Higgs Boson Mass Limits**

1.6.4 -- **Neutron Star Mass Limits**

## Solving Absolute Value Equations and Inequalities

1.7.1 -- **Variable Stars**

## Functions and their Graphs

2.1.1 -- **Telescope Resolving Power**

2.1.2 -- **Sunspot Numbers**

## Slope and Rate of Change

2.2.1 -- **Slope in Astronomy**

2.2.2 -- **Mixed Units**

## Quick Graphs of Linear Equations

2.3.1 -- **The Moon�s Orbit**

2.3.2 -- **Temperature in Deep Mines**

2.3.3 -- **Solar Power**

## Writing Equations of Lines

2.4.1 -- **Recent Sea Level Rise**

2.4.2 -- **Loss of Arctic Ice**

## Correlation and Best-fitting Lines

2.5.1 -- **Gamma Ray Bursts**

## Linear Equalities In Two Variables

2.6.1 -- **Star Cluster Study**

2.6.2 -- **WIMPS and Dark Matter**

2.6.3 -- **Exoplanet Habitable Zones**

## Piecewise Functions

2.7.1 -- **The Expanding Universe**

## Absolute Value Functions

2.8.1 -- **Reflecting Light Rays **

## Solving Linear Systems By Graphing

3.1.1 -- ** Cratering on the Moon**

## Solving Linear Systems Algebraically

3.2.1 -- **Calculating Molecular Structure**

## Graphing and Solving Systems of Linear Equalities

3.3.1 -- **Graphing the Cosmos I**

3.3.2 -- **Graphing the Cosmos II**

3.3.3 -- **Graphing the Cosmos III**

3.3.4 -- **Graphing the Cosmos IV**

## Linear Programming

3.4 No Current Examples

## Graphing Linear Equations in Three Variables

3.5 No Current Examples

## Solving Systems of Equations in Three Variables

3.6.1 -- **Solving Molecular Structure**

3.6.2 -- **Solving Molecular Structure**

## Matrix Operations

4.1.1 -- **The Sunspot Cycle**

4.1.2 -- **Star Brightness and Distance**

4.1.3 -- **Analyzing Astronomical Photos**

4.1.4 -- **Star Brightnesses**

## Multiplying Matrices

4.2.1 -- **Rotation Matrices**

4.2.2 -- **Mass and Weight**

## Determinants and Cramers Rule

4.3 No Current Examples

## Identity and Inverse Matrices

4.4.1 -- **Coordinate Transformations**

4.4.2 -- **Astronomical Image Processing**

## Solving Systems Using Inverse Matrices

4.5.1 -- **Studying Solar Storms with Matrices**

4.5.2 -- **Communication Satellies and Matrices**

4.5.3 -- **Rotation Matrix Math**

4.5.3 -- **Solving Molecular Structure**

## Solving Systems Using Augmented Matrices

4.6 No Current Examples

## Graphing Quadratic Functions

5.1.1 -- **Vertical Motion under Gravity**

## Solving Quadratic Equations by Factoring

5.2.1 -- **LRO Creates a Water Fountain**

## Solving Quadratic Equations by Finding Square Roots

5.3.1 -- **The Speed of Sound**

5.3.2 -- **Gravitational Collapse**

5.3.3 -- **Comet Impact**

## Complex Numbers

5.4.1 -- **Interstellar Extinction**

## Completing the Square

5.5 No Current Examples

## The Quadratic Formula and the Discriminant

5.6.1 -- **Supernova Explosion**

5.6.2 -- **Detecting Exoplanets**

## Graphing and Solving Quadratic Functions

5.7 No Current Examples

## Modeling with Quadratic Functions

5.8.1 -- **Atmospheric Carbon Dioxide **

5.8.2 -- **The Power of a Supernova**

5.8.3 -- **Water Emission by Comets**

5.8.4 -- **The Pace of Exoplanet Discovery**

## Using Properties of Exponents

6.1.1 -- **Scientific Notation I**

6.1.2 -- **Scientific Notation II**

6.1.3 -- **Scientific Notation III**

## Evaluating and Graphing Polynomial Functions

6.2.1 -- **White Dwarf Fadeout**

6.2.2 -- **The Higgs Boson Mass**

6.2.3 -- **The Energy of Empty Space**

6.2.4 -- **The Interior of the Sun**

## Adding, Subtracting and Multiplying Polynomial Functions

6.3.1 -- **The Ares-1X Acceleration Curve**

## Factoring and Solving Polynomial Equations

6.4 No Current Examples

## The Remainder and Factor Theorems

6.5 No Current Examples

## Finding Rational Zeros

6.6 No Current Examples

## Using the Fundamental Theorem of Algebra

6.7 No Current Examples

## Analyzing Graphs of Polynomial Functions

6.8.1 -- **The Energy of the Vacuum**

## Modeling with Polynomials

6.9.1 -- **The Rotation of the Sun**

6.9.2 -- **Ejection of Water from Comets**

6.9.3 -- **An Erupting Solar Prominence**

## Nth Root and Rational Exponents

7.1.1 -- **Passing Time near a Black Hole**

7.1.2 -- **The Size of a Nebula**

7.1.3 -- **The Earth�s Bow Shock**

## Properties of Rational Exponents

7.2.1 -- **Accreting Gas near a Black Hole**

7.2.2 -- **Temperature of a Planet**

7.2.3 -- **The Temperature of the Big Bang**

7.2.4 -- **The Planet Gliese-581c**

## Power Functions and Operations

7.3.1 -- **No current example**

## Inverse Functions

7.4.1 -- **Expanding Interstellar Nebula**

7.4.2 -- **Time Distortion Near a Black Hole**

7.4.3 -- **The Longest Sound Wave**

7.4.4 -- **Collapsing Star Clouds**

## Graphing Square and Cube-root Functions

7.5.1 -- **Gravity and Time Distortion**

## Solving Radical Equations

7.6.1 -- **The Shape of a Galaxy**

7.6.2 -- **The Growth of Cosmic Structure**

## Statistics and Statistical Graphs

7.7.1 -- **The Average Speeds of Galaxies**

7.7.2 -- **Sunspot Cycles**

7.7.3 -- **Analyzing Astronomical Images **

## Exponential Growth

8.1.1 -- **Compound Interest**

## Exponential Decay

8.3.1 --**Carbon--**

8.3.2 --

**14 Dating**8.3.2 --

**Supernova Fadeout**## Logarithmic Functions

8.4.1 -- **Star Counting**

8.4.2 -- **The LogLog Universe I**

9.4.3 -- **The LogLog Universe II**

## Properties of Logarithms

8.5.1 -- **The Star Magnitude Scale**

## Solving Exponential and Logarithmic Equations

8.6.1 -- **The Distances to Stars**

8.6.2 -- **The Brightness of Stars and Magnitudes**

## Modeling with Exponential and Power Functions

8.7.1 -- **Keplers Third Law**

8.7.2 -- **Satellite Orbit Decay**

8.7.3 -- **Atmospheric Attenuation**

8.7.4 -- **The Thickness of the Atmosphere**

8.7.5 -- **Gamma Ray Bursts**

## Logistic Growth Functions

8.8.1 -- **Planet Formation and Growth**

## Inverse and Joint Variation

9.1.1 -- **Some Astronomical Examples**

9.1.2 -- **Sea Level Rise**

## Graphing Simple Rational Functions

9.2.1 -- **The Distance to Galaxies**

9.2.2 -- **The Doppler Shift**

## Graphing General Rational Functions

9.3.1 -- **Inside a Neutron Star**

9.3.2 -- **The Sun�s Corona**

## Multiplying and Dividing Rational Expressions

9.4 No Current Examples

## Adding and Subtracting Complex Fractions

9.5.1 -- **Simple Atomic Energy Diagrams**

9.5.2 -- **Chemistry Made Simple**

9.5.3 -- **The Periodic Table of the Elements**

9.5.4 -- **Relative Distances Between Galaxies**

## Solving Rational Equations

9.6 No Current Examples

## The Distance and Midpoint Formulas

10.1.1 -- **Astronomical Distances**

10.1.2 -- **Distances to Globular Star Clusters**

10.1.3 -- **Calculating Horizon Distances**

## Parabolas

10.2.1 -- **Comet Orbits**

10.2.2 -- **Solving for a Comet Orbit**

## Circles

10.3.1 -- **The Transit of Venus 2012**

## Ellipses

10.4.1 -- **The Orbit of an Exoplanet**

10.4.2 -- **The Orbit of a Comet**

10.4.3 -- **The Comet Wild-2**

## Hyperbolas

10.5.1 -- **The Butterfly Nebula**

10.5.2 -- **The Unusual Comet Lulin**

## Graphing and Classifying Conics

10.6 No Current Examples

## Solving Quadratic Systems

10.7.1 -- **The Large Hadron Collider**

10.7.2 -- **Determining a Comets Orbit**

10.7.3 -- **Halley�s Comet Orbit **

## An Introduction to Sequences and Series

11.1.1 -- **The Lyman Series of Hydrogen**

11.1.2 -- **The Titius-Bode Law of Planets**

## Arithmetic Sequences and Series

11.2.1 -- **Areas Under Curves as Series**

11.2.2 -- **The Speed of an Ion Spacecraft**

## Geometric Sequences and Series

11.3.1 -- **Fading Starlight Through a Cloud**

## Infinite Geometric Series

11.4.1 -- **The Brightness of a Star Field**

11.4.2 -- **The Maximum Speed of a Rocket**

## Recursive Rules for Sequences

11.5.1 -- **The Volume of a Hypersphere**

## The Fundamental Counting Principle and Permutations

12.1.1 -- **Solar Storms I**

12.1.2 -- **Solar Storms II**

12.1.3 -- **Craters on the Moon**

## Combinations and the Binomial Theorem

12.2.1 -- **Solar X-Ray Flares**

12.2.2 -- **Severe Space Weather **

## Introduction to Probability

12.3 No Current Examples

## Probability of Compound Events

12.4.1 -- **Solar Flares and Storms**

12.4.2 -- **Meteor Impacts on Earth**

12.4.3 -- **Craters on the Moon**

12.4.4 -- **Solar Storms and Compound Events**

## Probability of Dependent and Independent Events

12.5.1 -- **Reliable Decisions**

## Binomial Distribuitons

12.6.1 -- **Space Weather and Stormy Days**

12.6.2 -- **Stormy Space Weather**

12.6.3 -- **The Apollo Moon Landings**

## Normal DIstributions

12.7.1 -- **Astronomical Applications in Imaging**

12.7.2 -- **The Speed of Gas Particles**

12.7.3 -- **Measurement Error: Up Close **

## Right Triangle Trigonometry

13.1.1 -- **STEREO views of the Sun**

13.1.2 -- **Basic Similar Triangle Geometry**

## General Angle and Radian Measure

13.2.1 -- **Radians and Degrees in Astronomy**

13.2.2 -- **Angular and Linear Size**

13.2.3 -- **Degrees, Minutes, Seconds of Arc**

13.2.4 -- **Angular Resolution and Moon Details**

13.2.5 -- **Transits and Eclipses**

## Trigonometric Functions of Any Angle

13.3.1 -- **Rotation of Images**

## Inverse Trig Functions

13.4 No Current Examples

## Law of Sines

13.5.1 -- **Location of the Planets During the Transit of Venus in 2012
**

**Law of Cosines**

13.6.1 -- **Angular Distance Between Planets**

13.6.2 -- **The STEREO View of the Sun**

## Parametric Equations and Projectile Motion

13.7.1 -- **The Ares 1X Trajectory
**

**Graphing Sin, Cosine and Tangent Functions**

14.1.1 -- **Solar Power**

14.1.2 -- **Delta Cephi **

## Translations and Reflections of Trig Graphs

14.2 No Current Examples

## Verifying Trig Identities

14.3 No Current Examples

## Solving Trigonometric Equations

14.4.1 -- **Temperature on Mars**

14.4.2 -- **Spinning Satellites**

14.4.3 -- **The Distances to Stars and Nebula**

14.4.4 -- **The Surveyor�s Challenge**

## Modeling with Trigonometric Functions

14.5.1 -- **Electric Power Usage**

14.5.2 -- **Carbon Dioxide in the Atmosphere**

14.5.3 -- **The Liquid Mirror Telescope**

## Using Sum and Difference Formulas

14.6.1 -- **The Rising and Setting Formula**

## Using Half and Double-angle Formulas

14.7.1 -- **The Acceleration of Gravity on Earth**