# National Aeronautics and Space Administration

## Math problems involving Algebra 2 skills

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.

## 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
3.5.1 -- 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

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

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

6.2.2 -- 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

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-- 14 Dating

## 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
9.5.3 -- 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

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
13.5.1 -- 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