Experiment #1. Math Review

Size: px
Start display at page:

Download "Experiment #1. Math Review"

Transcription

1 A. Scientific notation and Significant Figures Experiment #1. Math Review While entering a number in scientific notation in your calculator, look for the EE or the exp key on your calculator. For example using the TI3-XA, one would enter x as EE 23. Using a TI-84 plus, the same number would be entered as nd EE 23. Using a TI-89, the same number would be entered as EE 23 Practice entering the following numbers in your calculator a) x b) 9.11 x c) 2.3 x 10 3 Rules for Counting Significant Figures: Example # S. F. 1. All nonzero integers are significant Leading zeros are never significant Captive zeros are always significant Trailing zeros in a decimal number are significant Trailing zeros in a number with no decimal are not significant Exponential /Scientific Notation: The number of significant figures in a number written in exponential notation is easily determined as the leading and trailing zeros are removed. Examples: Decimal Exponential/Scientific notation # S. F x x x x x Rules for sig figs in mathematical operations Multiplication and division The final answer must have the same number of sig figs as the number having the least sig figs Addition and subtraction The final answer must have the same number of decimal places as the number with the least decimal places Rules for Rounding: 1. In a calculation carry all of the significant figures through to the final result, then round to the correct number of significant figure based upon the data with the smallest number of significant figures. 2. If the digit to be removed is <5, the preceding digit remains unchanged. (25.44 rounds to 25.4) 3. If the digit to be removed is 5, then the preceding digit is incremented by 1. (25.46 rounds to 25.5)

2 Volume of gas (cm 3 ) B. Logarithms to the base 10 (log) and Natural Logarithms (ln, to the base e) Logarithms are the opposite of exponentials. For example: Since 10 2 = 100, we can write log 10 2 = 2 or log 100 = 2 Since 10 0 = 1, then log 1=0. Similarly, e 0 = 1, therefore ln 1 = 0 e lnx = x or lne x = x Similarly, log10 x = x or 10 log x = x Look for the log and the 10 x key on your calculator to get the log and the antilog of a number. Similarly, become familiar with the ln and e x key on your calculator. Example: If log x = 2, then x = 10 2 Ex: If ln x = 5, then x = e 5 Some basic rules for logarithms are: log(a*b) = log a + Log b log a log a log b b log a m = m log a ln (a*b) = ln a + ln b ln a ln a ln b b ln a m = m ln a C. Graphs A graph is a visual representation of the relationship between two quantities. Usually, the x axis is the independent variable and the y axis is the dependent variable. This means that the quantity plotted on the y axis depends on the value plotted on the x axis. A graph of concentration against time implies that the concentration is on the y axis (dependent variable) and time is on the X axis (independent variable). If you are told to plot a graph of ph versus volume, then ph is plotted on the Y axis and the volume is plotted on the X axis. Chemists mostly like to deal with linear relationships and will choose y and x units such that the plot is a straight line. Consider the following graph of volume of a gas versus number of moles: From the graph, we can see that when the y = 20x + 2E-14 R² = 1 moles of the gas changes from 0.5 to 1.0, the volume of the gas changed from 10 cm 3 to 20 cm 3. The Slope of this line can be calculated y change in y Slope x change in x as: cm Slope mol Moles of gas (n) The equation of a straight line is of the form y = m x + b, where m is the slope of the line and b is called the y intercept. Consider the linear form of the Clausius-Clapeyron equation Hvap 1 ln PVapor ln R T y = m x + b A graph of ln (P vapor) against 1 Hvap, will give a straight line with a slope = T R and an intercept = ln

3 CHM112 Lab Math Review Grading Rubric Name Criteria Points possible Points earned A. Simple Algebra (0.5 points each question) 4 B. Scientific Notation and Significant Figures (0.5 points each question) C1. Evaluating log and ln and their reciprocals (0.25 points each question) 2 2 C2. Rules of Logarithms (0.25 points each question) 1.5 C3. Solve for the unknown y in each case (0.5 points each question) 4 D1 (0.5 points each question) 1.5 D2 (0.5 points each question) 1 D3 (0.5 points each question) 1.5 D4 (0.5 points each question) 1.5 D5 (0.5 points each question) 1 Total 20 Subject to other additional penalties as per the instructor

4

5 CHM 112: Math Review A. Simple Algebra Name Solve for the unknown (y) in each of the following cases. Show your work. 2y 6 = 12 6y = = 30 5y 1 y y y y y y B. Scientific notation and Significant Figures Carry out the following calculations and report your answer in scientific notation with the correct sig figs a) 34 8 ( )( ) = ( ) c) 23 = b) 6.08 x x x 10-2 = d) ( ) / =

6 C. Logarithms C. 1. Evaluating log and ln and their reciprocals. Calculate the following quantities. 1. ln (e) = 2. log(1000) = 3. ln (e) 4 = 4. e (18200/(8.314*290)) = 5. ln (1) = 6. - log (0.050) = = 8. log (13) C. 2. Rules of Logarithms Complete the following calculations. (You can either use the rules of logarithms discussed earlier or evaluate these directly using your calculator. Try it both ways to see if you get the same answer) 1. log(20) log(2) = ln ln(80) + ln(20) = 5. 1 log log ln 40 C3. Solve for the unknown y in each case (You can either use the Rules of logarithms discussed earlier or evaluate these directly using your calculator. Try it both ways to see if you get the same answer) 1. y log(100) = ln(5 y) log(36) + ln(y) = log(12 y) log y = log 1.25 y y 4. ln ln(125 y) 4.248

7 D. Graphs D1. Complete the following table by comparing each equation to the equation of a straight line. Equation Slope Is the slope positive or negative? Intercept y = 310. x y = x y= x D2. Consider the equation y = x a. What will be the value of y when x = 4.5? b. What is the value of x when y = D3. Complete the following table by comparing each of the equations to y = m x + b Equation [A]t = [A]0 k t What is plotted on the y axis? What is plotted on the x axis? Slope Intercept ln k E a 1 ln A R T 1 1 kt [ A] [ A] t 0

8 H vap 1 D4. The linear form of the Claussius Clapeyron equation is ln P vapor ln R T a) What is plotted on the X axis? b) What is plotted on the Y axis? c) What will be the slope the graph? D5. A student plotted a graph of ln (VP in torr) versus 1/T in Kelvin for dichloromethane and obtained the best fitting line as y = -3805x a. What is the vapor pressure of dichloromethane at 85.0 C? b. What is the normal boiling point of dichloromethane? Remember that at the normal boiling point, the vapor pressure = 1 atmosphere.

CHM112 Lab Math Review Grading Rubric

CHM112 Lab Math Review Grading Rubric Name CHM112 Lab Math Review Grading Rubric Criteria Points possible Points earned A. Simple Algebra 4 B. Scientific Notation and Significant Figures (0.5 points each question) C1. Evaluating log and ln

More information

CHM111 Lab Math Review Grading Rubric

CHM111 Lab Math Review Grading Rubric Name CHM111 Lab Math Review Grading Rubric Part 1. Basic Algebra and Percentages Criteria Points possible Points earned Question 1 (0.25 points each question) 2 Question 2 (0.25 points each question) 1

More information

CHM101 Lab Math Review and Significant Figures Grading Rubric

CHM101 Lab Math Review and Significant Figures Grading Rubric Name CHM101 Lab Math Review and Significant Figures Grading Rubric Criteria Points possible Points earned Part A (0.25 each) 3.5 Part B (0.25 each) 2.5 Part C (0.25 each) 1.5 Part D (Q5 0.25 each, Q6 &

More information

Appendix A. Common Mathematical Operations in Chemistry

Appendix A. Common Mathematical Operations in Chemistry Appendix A Common Mathematical Operations in Chemistry In addition to basic arithmetic and algebra, four mathematical operations are used frequently in general chemistry: manipulating logarithms, using

More information

Appendix F. Treatment of Numerical Data. I. Recording Data F-1

Appendix F. Treatment of Numerical Data. I. Recording Data F-1 Treatment of umerical Data I. Recording Data When numerical data are recorded, three kinds of information must be conveyed: the magnitude of the number, how well the number is known, and the units used

More information

USE OF THE SCIENTIFIC CALCULATOR

USE OF THE SCIENTIFIC CALCULATOR USE OF THE SCIENTIFIC CALCULATOR Below are some exercises to introduce the basic functions of the scientific calculator that you need to be familiar with in General Chemistry. These instructions will work

More information

Experiment #1. Math Review

Experiment #1. Math Review Experiment #1. Math Review A. Scientific notation and Significant Figures While entering a number in scientific notation in your calculator, look for the EE or the exp key on your calculator. For example

More information

Notes: Unit 1: Math and Measurement

Notes: Unit 1: Math and Measurement Name: Regents Chemistry: Notes: Unit 1: Math and Measurement www.chempride.weebly.com Key Ideas Major Understandings: o Chemistry is the study of matter: Matter takes up space and has mass. (K- 4, 3.1a)

More information

Notes: Unit 1: Math and Measurement

Notes: Unit 1: Math and Measurement Name: Regents Chemistry: Notes: Unit 1: Math and Measurement www.chempride.weebly.com Key Ideas Major Understandings: o Chemistry is the study of matter: Matter takes up space and has mass. (K- 4, 3.1a)

More information

Section 1.1: Patterns in Division

Section 1.1: Patterns in Division Section 1.1: Patterns in Division Dividing by 2 All even numbers are divisible by 2. E.g., all numbers ending in 0,2,4,6 or 8. Dividing by 4 1. Are the last two digits in your number divisible by 4? 2.

More information

36-309/749 Math Review 2014

36-309/749 Math Review 2014 36-309/749 Math Review 2014 The math content of 36-309 is not high. We will use algebra, including logs. We will not use calculus or matrix algebra. This optional handout is intended to help those students

More information

Measurements and Calculations. Chapter 2

Measurements and Calculations. Chapter 2 Measurements and Calculations Chapter 2 Scientific Method Observing/Collecting Data Hypothesis Testing Theorizing Publishing Units of Measurement All measurements require two parts 1. Quantity 2. Unit

More information

YOU CAN BACK SUBSTITUTE TO ANY OF THE PREVIOUS EQUATIONS

YOU CAN BACK SUBSTITUTE TO ANY OF THE PREVIOUS EQUATIONS The two methods we will use to solve systems are substitution and elimination. Substitution was covered in the last lesson and elimination is covered in this lesson. Method of Elimination: 1. multiply

More information

ADVANCED PLACEMENT PHYSICS 1

ADVANCED PLACEMENT PHYSICS 1 ADVANCED PLACEMENT PHYSICS 1 MS. LAWLESS ALAWLESS@SOMERVILLESCHOOLS.ORG Purpose of Assignments: This assignment is broken into 8 Skills. Skills 1-6, and 8 are review of science and math literacy. Skill

More information

Section 3 Using Scientific Measurements. Look at the specifications for electronic balances. How do the instruments vary in precision?

Section 3 Using Scientific Measurements. Look at the specifications for electronic balances. How do the instruments vary in precision? Lesson Starter Look at the specifications for electronic balances. How do the instruments vary in precision? Discuss using a beaker to measure volume versus using a graduated cylinder. Which is more precise?

More information

Notes: Measurement and Calculation

Notes: Measurement and Calculation Name Chemistry-PAP Per. I. The Basics of Measurement Notes: Measurement and Calculation A. Measurement Most provide quantitative information, but because they are obtained experimentally, they are inexact.

More information

Base unit-a defined unit of measurement based on an object or event in the physical world. Length

Base unit-a defined unit of measurement based on an object or event in the physical world. Length Base unit-a defined unit of measurement based on an object or event in the physical world Five base units: Temperature Mass Length Time Energy Derived unit-a unit of measurement defined by a combination

More information

Sail into Summer with Math!

Sail into Summer with Math! Sail into Summer with Math! For Students Entering Algebra 1 This summer math booklet was developed to provide students in kindergarten through the eighth grade an opportunity to review grade level math

More information

AP Chemistry A Review of Analytical Chemistry

AP Chemistry A Review of Analytical Chemistry AP Chemistry A Review of Analytical Chemistry AP Chemistry Ch 1 (Prentice Hall) What Temperature Do You Read? A measurement always has some amount of uncertainty To indicate the uncertainty of a single

More information

Intermediate Algebra Chapter 12 Review

Intermediate Algebra Chapter 12 Review Intermediate Algebra Chapter 1 Review Set up a Table of Coordinates and graph the given functions. Find the y-intercept. Label at least three points on the graph. Your graph must have the correct shape.

More information

A. Incorrect! Check your algebra when you solved for volume. B. Incorrect! Check your algebra when you solved for volume.

A. Incorrect! Check your algebra when you solved for volume. B. Incorrect! Check your algebra when you solved for volume. AP Chemistry - Problem Drill 03: Basic Math for Chemistry No. 1 of 10 1. Unlike math problems, chemistry calculations have two key elements to consider in any number units and significant figures. Solve

More information

Chapter 2. Measurements and Calculations

Chapter 2. Measurements and Calculations Chapter 2 Measurements and Calculations Section 2.1 Scientific Notation Measurement Quantitative observation. Has 2 parts number and unit. Number tells comparison. Unit tells scale. If something HAS a

More information

Student Self-Assessment of Mathematics (SSAM) for Intermediate Algebra

Student Self-Assessment of Mathematics (SSAM) for Intermediate Algebra Student Self-Assessment of Mathematics (SSAM) for Intermediate Algebra Answer key 1. Find the value of 3x 4y if x = -2 and y = 5 To find the value, substitute the given values in for x and y 3x -4y Substitute

More information

Tools of Chemistry. Measurement Scientific Method Lab Safety & Apparatus

Tools of Chemistry. Measurement Scientific Method Lab Safety & Apparatus Tools of Chemistry Measurement Scientific Method Lab Safety & Apparatus Scientific Notation Scientific Notation a number described as a power of 10 (used for very large or small numbers) 1000 = 1 X 10

More information

Error Analysis. Table 1. Tolerances of Class A Pipets and Volumetric Flasks

Error Analysis. Table 1. Tolerances of Class A Pipets and Volumetric Flasks Error Analysis Significant Figures in Calculations Most lab report must have an error analysis. For many experiments, significant figure rules are sufficient. Remember to carry at least one extra significant

More information

The AP Chemistry Summer assignment is meant to help prepare you for the first few weeks of class

The AP Chemistry Summer assignment is meant to help prepare you for the first few weeks of class The AP Chemistry Summer assignment is meant to help prepare you for the first few weeks of class Part 1. Review the mole concept and how it s used. This includes mass (grams) to moles, moles-to-mass calculations,

More information

Algebra Summer Review Packet

Algebra Summer Review Packet Name: Algebra Summer Review Packet About Algebra 1: Algebra 1 teaches students to think, reason, and communicate mathematically. Students use variables to determine solutions to real world problems. Skills

More information

Every time a measurement is taken, we must be aware of significant figures! Define significant figures.

Every time a measurement is taken, we must be aware of significant figures! Define significant figures. SCHM 103: FUNDAMENTALS OF CHEMISTRY Ch. 2: Numerical Side of Chemistry Types of data collected in experiments include: Qualitative: Quantitative: Making Measurements Whenever a piece of data is collected,

More information

Lesson 4b More on LOGARITHMS

Lesson 4b More on LOGARITHMS Lesson 4b More on LOGARITHMS Learning Packet Student Name Due Date Class Time/Day Submission Date THIS BOX FOR INSTRUCTOR GRADING USE ONLY Mini-Lesson is complete and information presented is as found

More information

2017 SUMMER REVIEW FOR STUDENTS ENTERING GEOMETRY

2017 SUMMER REVIEW FOR STUDENTS ENTERING GEOMETRY 2017 SUMMER REVIEW FOR STUDENTS ENTERING GEOMETRY The following are topics that you will use in Geometry and should be retained throughout the summer. Please use this practice to review the topics you

More information

Remember that C is a constant and ë and n are variables. This equation now fits the template of a straight line:

Remember that C is a constant and ë and n are variables. This equation now fits the template of a straight line: CONVERTING NON-LINEAR GRAPHS INTO LINEAR GRAPHS Linear graphs have several important attributes. First, it is easy to recognize a graph that is linear. It is much more difficult to identify if a curved

More information

Name: Chapter 2: Analyzing Data Note Taking Guide This worksheet is meant to help us learn some of the basic terms and concepts of chemistry.

Name: Chapter 2: Analyzing Data Note Taking Guide This worksheet is meant to help us learn some of the basic terms and concepts of chemistry. Chemistry Name: Section ANALYZE DATA KEY Date: Chapter 2: Analyzing Data Note Taking Guide This worksheet is meant to help us learn some of the basic terms and concepts of chemistry. Most, but not all,

More information

Unit 2. Scientific Measurement

Unit 2. Scientific Measurement Unit 2 Scientific Measurement Qualitative vs quantitative Qualitative measurementsgive results in a descriptive, non-numerical form Ex. Observations taken in the demo lab Quantitative measurementsgive

More information

Accuracy: An accurate measurement is a measurement.. It. Is the closeness between the result of a measurement and a value of the measured.

Accuracy: An accurate measurement is a measurement.. It. Is the closeness between the result of a measurement and a value of the measured. Chemical Analysis can be of two types: Chapter 11- Measurement and Data Processing: - : Substances are classified on the basis of their or properties, such as - : The amount of the sample determined in

More information

Metric Prefixes UNITS & MEASUREMENT 10/6/2015 WHY DO UNITS AND MEASUREMENT MATTER?

Metric Prefixes UNITS & MEASUREMENT 10/6/2015 WHY DO UNITS AND MEASUREMENT MATTER? UNITS & MEASUREMENT WHY DO UNITS AND MEASUREMENT MATTER? Chemistry In Action On 9/3/99, $15,000,000 Mars Climate Orbiter entered Mar s atmosphere 100 km (6 miles) lower than planned and was destroyed by

More information

Chapter 1 and 3 Guided Notes

Chapter 1 and 3 Guided Notes What is Chemistry? Chemistry: 5 areas of Chemistry: o Organic- o Inorganic- o Biochemistry- o Analytical- o Physical- Chapter 1 and 3 Guided Notes Scientific Method: 1. 2. 3. 4. 5. Variables: -The variable

More information

Helping Students Understand Algebra

Helping Students Understand Algebra Helping Students Understand Algebra By Barbara Sandall, Ed.D., and Mary Swarthout, Ph.D. COPYRIGHT 2005 Mark Twain Media, Inc. ISBN 10-digit: 1-58037-293-7 13-digit: 978-1-58037-293-0 Printing No. CD-404020

More information

Measurement. New Topics accuracy vs. precision rounding in chemistry significant figures determining uncertainty of a measurement % error moles - 1 -

Measurement. New Topics accuracy vs. precision rounding in chemistry significant figures determining uncertainty of a measurement % error moles - 1 - Measurement Unit Description In this unit we will focus on the mathematical tools we use in science, especially chemistry the metric system and moles. We will also talk about how to gauge the accuracy

More information

N= {1,2,3,4,5,6,7,8,9,10,11,...}

N= {1,2,3,4,5,6,7,8,9,10,11,...} 1.1: Integers and Order of Operations 1. Define the integers 2. Graph integers on a number line. 3. Using inequality symbols < and > 4. Find the absolute value of an integer 5. Perform operations with

More information

Solutions to MAT 117 Test #3

Solutions to MAT 117 Test #3 Solutions to MAT 7 Test #3 Because there are two versions of the test, solutions will only be given for Form C. Differences from the Form D version will be given. (The values for Form C appear above those

More information

CH1810 Lecture #2 Vapor Pressure of Liquids and Solutions

CH1810 Lecture #2 Vapor Pressure of Liquids and Solutions CH1810 Lecture #2 Vapor Pressure of Liquids and Solutions Vaporization and Condensation Kinetic Energy and Temperature Molecules in a liquid are constantly in motion Types of motion: vibrational, and limited

More information

Chapter 2 Math Skills

Chapter 2 Math Skills Chapter 2 Math Skills 2.1 Measurements Measurement number with a unit Units are very important o A student wouldn t ask a teacher Could you please hand me 6? The student would instead ask, Could you please

More information

Chapter 7: Exponents

Chapter 7: Exponents Chapter : Exponents Algebra Chapter Notes Name: Notes #: Sections.. Section.: Review Simplify; leave all answers in positive exponents:.) m -.) y -.) m 0.) -.) -.) - -.) (m ) 0.) 0 x y Evaluate if a =

More information

Warm-up: Are accuracy and precision the same thing? (If so do you want to bet the house on it?)

Warm-up: Are accuracy and precision the same thing? (If so do you want to bet the house on it?) Obj: Students will: 1. Distinguish between accuracy and precision. 2. Examine various pieces of lab equipment for their accuracy. 3. Define and identify significant figures. Warm-up: Are accuracy and precision

More information

Chapter 2 - Analyzing Data

Chapter 2 - Analyzing Data Chapter 2 - Analyzing Data Section 1: Units and Measurements Section 2: Scientific Notation and Dimensional Analysis Section 3: Uncertainty in Data Section 4: Representing Data Chemists collect and analyze

More information

Math 1 Variable Manipulation Part 1 Algebraic Equations

Math 1 Variable Manipulation Part 1 Algebraic Equations Math 1 Variable Manipulation Part 1 Algebraic Equations 1 PRE ALGEBRA REVIEW OF INTEGERS (NEGATIVE NUMBERS) Numbers can be positive (+) or negative (-). If a number has no sign it usually means that it

More information

Vapor Pressure of Liquids Equilibria and Thermodynamics

Vapor Pressure of Liquids Equilibria and Thermodynamics Chemistry 1B-Foothill College Vapor Pressure of Liquids Equilibria and Thermodynamics In this exercise, you will investigate the relationship between the vapor pressure of a liquid and the thermodynamic

More information

Chapter 2 Measurements & Calculations. Quantity: A thing that can be measured. ex. Length (6.3 ft), mass (35 kg), and time (7.2 s)

Chapter 2 Measurements & Calculations. Quantity: A thing that can be measured. ex. Length (6.3 ft), mass (35 kg), and time (7.2 s) Chapter 2 Measurements & Calculations Quantity: A thing that can be measured. ex. Length (6.3 ft), mass (35 kg), and time (7.2 s) Measurements can be expressed in a variety of units: Example: length(cm,

More information

Numbers in Science Exploring Measurements, Significant Digits, and Dimensional Analysis

Numbers in Science Exploring Measurements, Significant Digits, and Dimensional Analysis Numbers in Science Exploring Measurements, Significant Digits, and Dimensional Analysis TAKING MEASUREMENTS The accuracy of a measurement depends on two factors: the skill of the individual taking the

More information

Lecture 3. - all digits that are certain plus one which contains some uncertainty are said to be significant figures

Lecture 3. - all digits that are certain plus one which contains some uncertainty are said to be significant figures Lecture 3 SIGNIFICANT FIGURES e.g. - all digits that are certain plus one which contains some uncertainty are said to be significant figures 10.07 ml 0.1007 L 4 significant figures 0.10070 L 5 significant

More information

Chapter 2 - Measurements and Calculations

Chapter 2 - Measurements and Calculations Chapter 2 - Measurements and Calculations 2-1 The Scientific Method "A logical approach to solving problems by observing and collecting data, formulating hypotheses, testing hypotheses, and formulating

More information

Third Grade Report Card Rubric 1 Exceeding 2 Meeting 3 Developing 4 Area of Concern

Third Grade Report Card Rubric 1 Exceeding 2 Meeting 3 Developing 4 Area of Concern Concepts Assessed by Unit and Trimester Units 5, 6, 7, 8 Units 5, 6, 7 Units 5, 6, 7, 8 1 Exceeding 2 Meeting 3 Developing 4 Area of Concern Student exceeds expectations of this unit Student is meeting

More information

How do physicists study problems?

How do physicists study problems? What is Physics? The branch of science that studies the physical world (from atoms to the universe); The study of the nature of matter and energy and how they are related; The ability to understand or

More information

Experimental Uncertainty (Error) and Data Analysis

Experimental Uncertainty (Error) and Data Analysis Experimental Uncertainty (Error) and Data Analysis Advance Study Assignment Please contact Dr. Reuven at yreuven@mhrd.org if you have any questions Read the Theory part of the experiment (pages 2-14) and

More information

Introduction to 1118 Labs

Introduction to 1118 Labs Name: Partner(s): 1118 section: Desk # Date: Introduction to 1118 Labs Introductory materials are at: www.langaraphysics.com/lab.html. You may find following 3 links useful for this lab: Measurements:

More information

Scientific Measurement

Scientific Measurement Scientific Measurement A quantity is anything having a measurable size or amount For Example: 5 But 5 what? A unit assigns value to a measured quantity For Example: 5 ft, 5 gal, 5 sec, 5 m, 5 g. Base Units

More information

Introduction to Determining Power Law Relationships

Introduction to Determining Power Law Relationships 1 Goal Introduction to Determining Power Law Relationships Content Discussion and Activities PHYS 104L The goal of this week s activities is to expand on a foundational understanding and comfort in modeling

More information

How long is the arrow?

How long is the arrow? 1.2 Measurements Measuring We have all measured things before, but how would you define it? Measurement: comparing an unknown quantity to a standard unit (known quantity) How long is the arrow? Any measurement

More information

Scientific Method: a logical approach to understanding or solving problems that needs solved.

Scientific Method: a logical approach to understanding or solving problems that needs solved. Chapter 2 Section 1 Section 2-1 Objectives Describe the purpose of the scientific method. Distinguish between qualitative and quantitative observations. Describe the differences between hypotheses, theories,

More information

PART 1: USING SCIENTIFIC CALCULATORS (41 PTS.) 1) The Vertex Form for the equation of a parabola in the usual xy-plane is given by y = 3 x + 4

PART 1: USING SCIENTIFIC CALCULATORS (41 PTS.) 1) The Vertex Form for the equation of a parabola in the usual xy-plane is given by y = 3 x + 4 MIDTERM SOLUTIONS (CHAPTERS AND 3: POLYNOMIAL, RATIONAL, EXP L, LOG FUNCTIONS) MATH 141 FALL 018 KUNIYUKI 150 POINTS TOTAL: 41 FOR PART 1, AND 109 FOR PART PART 1: USING SCIENTIFIC CALCULATORS (41 PTS.)

More information

Logarithms Tutorial for Chemistry Students

Logarithms Tutorial for Chemistry Students 1 Logarithms 1.1 What is a logarithm? Logarithms Tutorial for Chemistry Students Logarithms are the mathematical function that is used to represent the number (y) to which a base integer (a) is raised

More information

Scientific Notation. Chemistry Honors

Scientific Notation. Chemistry Honors Scientific Notation Chemistry Honors Used to easily write very large or very small numbers: 1 mole of a substance consists of 602,000,000,000,000,000,000,000 particles (we ll come back to this in Chapter

More information

Significant Figures. Significant Figures 18/02/2015. A significant figure is a measured or meaningful digit.

Significant Figures. Significant Figures 18/02/2015. A significant figure is a measured or meaningful digit. Significant Figures When counting objects, it is easy to determine the EXACT number of objects. Significant Figures Unit B1 But when a property such as mass, time, volume, or length is MEASURED, you can

More information

Prerequisite: Qualification by assessment process or completion of Mathematics 1050 or one year of high school algebra with a grade of "C" or higher.

Prerequisite: Qualification by assessment process or completion of Mathematics 1050 or one year of high school algebra with a grade of C or higher. Reviewed by: D. Jones Reviewed by: B. Jean Reviewed by: M. Martinez Text update: Spring 2017 Date reviewed: February 2014 C&GE Approved: March 10, 2014 Board Approved: April 9, 2014 Mathematics (MATH)

More information

Lecture Notes 1: Physical Equilibria Vapor Pressure

Lecture Notes 1: Physical Equilibria Vapor Pressure Lecture Notes 1: Physical Equilibria Vapor Pressure Our first exploration of equilibria will examine physical equilibria (no chemical changes) in which the only changes occurring are matter changes phases.

More information

Chemistry Chapter 2 Data Analysis

Chemistry Chapter 2 Data Analysis Chemistry Chapter 2 Data Analysis I. Units of Measurement 2.1 (pages 25-30) A. The metric system (SI units) Why the metric system? B. Base Units of the SI System Based on an object or event of the of other

More information

Chapter 3 - Measurements

Chapter 3 - Measurements Chapter 3 - Measurements You ll learn it in the summer, If not, it ll be a bummer. You ll need to know conversions, For units, Euro version. Metrics are powers of ten, And you might cry when, You re forced

More information

Algebra II Summer Packet. Summer Name:

Algebra II Summer Packet. Summer Name: Algebra II Summer Packet Summer 2017 Name: NAME ALGEBRA II & TRIGONOMETRY SUMMER REVIEW PACKET To maintain a high quality program, students entering Algebra II are expected to remember the basics of the

More information

Module 1: Whole Numbers Module 2: Fractions Module 3: Decimals and Percent Module 4: Real Numbers and Introduction to Algebra

Module 1: Whole Numbers Module 2: Fractions Module 3: Decimals and Percent Module 4: Real Numbers and Introduction to Algebra Course Title: College Preparatory Mathematics I Prerequisite: Placement with a score below 20 on ACT, below 450 on SAT, or assessing into Basic Applied Mathematics or Basic Algebra using Accuplacer, ASSET

More information

Appendix. Using Your Calculator. Squares, Square Roots, Reciprocals, and Logs. Addition, Subtraction, Multiplication, and Division

Appendix. Using Your Calculator. Squares, Square Roots, Reciprocals, and Logs. Addition, Subtraction, Multiplication, and Division 370770_app.qxd 1/9/03 7:2 PM Page A1 mac114 Mac 114:2nd shift:4_rst: Using Your Calculator In this section we will review how to use your calculator to perform common mathematical operations. This discussion

More information

Chapter 7 - Exponents and Exponential Functions

Chapter 7 - Exponents and Exponential Functions Chapter 7 - Exponents and Exponential Functions 7-1: Multiplication Properties of Exponents 7-2: Division Properties of Exponents 7-3: Rational Exponents 7-4: Scientific Notation 7-5: Exponential Functions

More information

CHAPTER FIVE. Solutions for Section 5.1. Skill Refresher. Exercises

CHAPTER FIVE. Solutions for Section 5.1. Skill Refresher. Exercises CHAPTER FIVE 5.1 SOLUTIONS 265 Solutions for Section 5.1 Skill Refresher S1. Since 1,000,000 = 10 6, we have x = 6. S2. Since 0.01 = 10 2, we have t = 2. S3. Since e 3 = ( e 3) 1/2 = e 3/2, we have z =

More information

3.5. Equation Solving and Modeling. Copyright 2011 Pearson, Inc.

3.5. Equation Solving and Modeling. Copyright 2011 Pearson, Inc. 3.5 Equation Solving and Modeling Copyright 2011 Pearson, Inc. What you ll learn about Solving Exponential Equations Solving Logarithmic Equations Orders of Magnitude and Logarithmic Models Newton s Law

More information

Section 5.1 Polynomial Functions and Models

Section 5.1 Polynomial Functions and Models Term: A term is an expression that involves only multiplication and/or division with constants and/or variables. A term is separated by + or Polynomial: A polynomial is a single term or the sum of two

More information

Algebra 1 S1 Lesson Summaries. Lesson Goal: Mastery 70% or higher

Algebra 1 S1 Lesson Summaries. Lesson Goal: Mastery 70% or higher Algebra 1 S1 Lesson Summaries For every lesson, you need to: Read through the LESSON REVIEW which is located below or on the last page of the lesson and 3-hole punch into your MATH BINDER. Read and work

More information

see page 8 of these notes )

see page 8 of these notes ) UNIT 1 Note Packet INTRODUCTION TO CHEMISTRY Name: METRICS AND MEASUREMENT In the chemistry classroom and lab, the metric system of measurement is used, so it is important to know what you are measuring,

More information

Page 24 Monday August 03, 2015

Page 24 Monday August 03, 2015 Page Monday August 0, 05 Convert with-in the metric system Practice: How many. Practice: How many.. Centimeters in a meter?. Grams in Kilogram?. Liters in Kiloliter?. Meters in Kilometer? 5. Millimeters

More information

Northwest High School s Algebra 1

Northwest High School s Algebra 1 Northwest High School s Algebra 1 Summer Review Packet 2015 DUE THE FIRST DAY OF SCHOOL Student Name This packet has been designed to help you review various mathematical topics that will be necessary

More information

Chemistry Basic Science Concepts. Observations: are recorded using the senses. Examples: the paper is white; the air is cold; the drink is sweet.

Chemistry Basic Science Concepts. Observations: are recorded using the senses. Examples: the paper is white; the air is cold; the drink is sweet. Note Packet # 1 1 Chemistry: the study of matter. Chemistry Basic Science Concepts Matter: anything that has mass and occupies space. Observations: are recorded using the senses. Examples: the paper is

More information

Core Mathematics 3 Exponentials and Natural Logarithms

Core Mathematics 3 Exponentials and Natural Logarithms Edexcel past paper questions Core Mathematics 3 Exponentials and Natural Logarithms Edited by: K V kumaran Email: kvkumaran@gmail.com Core Maths 3 Exponentials and natural Logarithms Page Ln and Exponentials

More information

SCIENTIFIC MEASUREMENT C H A P T E R 3

SCIENTIFIC MEASUREMENT C H A P T E R 3 SCIENTIFIC MEASUREMENT C H A P T E R 3 WHAT IS MEASUREMENT? Comparing one object to a standard In science, we use SI Units meters, o C, grams NOT o F, pounds, ounces etc. TWO TYPES OF MEASUREMENTS 1.

More information

EXPONENTIAL AND LOGARITHMIC FUNCTIONS

EXPONENTIAL AND LOGARITHMIC FUNCTIONS Mathematics Revision Guides Exponential and Logarithmic Functions Page 1 of 14 M.K. HOME TUITION Mathematics Revision Guides Level: A-Level Year 1 / AS EXPONENTIAL AND LOGARITHMIC FUNCTIONS Version : 4.2

More information

Accessible Topic - Topics accessible to visually impaired students using a screen reader.

Accessible Topic - Topics accessible to visually impaired students using a screen reader. Course Name: Winter 2018 Math 95 - Course Code: ALEKS Course: Developmental Math Instructor: Course Dates: Begin: 01/07/2018 End: 03/23/2018 Course Content: 390 Topics (172 goal + 218 prerequisite) / 334

More information

Calculations In Chemistry

Calculations In Chemistry Calculations In Chemistry Module 27 Kinetics: Rate Laws Module 27 Kinetics: Rate Laws...773 Lesson 27A: Kinetics Fundamentals...771 Lesson 27B: Rate Laws...778 Lesson 27C: Integrated Rate Law --Zero Order...787

More information

Skill 6 Exponential and Logarithmic Functions

Skill 6 Exponential and Logarithmic Functions Skill 6 Exponential and Logarithmic Functions Skill 6a: Graphs of Exponential Functions Skill 6b: Solving Exponential Equations (not requiring logarithms) Skill 6c: Definition of Logarithms Skill 6d: Graphs

More information

ABE Math Review Package

ABE Math Review Package P a g e ABE Math Review Package This material is intended as a review of skills you once learned and wish to review before your assessment. Before studying Algebra, you should be familiar with all of the

More information

Significant Figures And The Density Of Water - Version 1.5

Significant Figures And The Density Of Water - Version 1.5 Significant Figures And The Density Of Water - Version 1.5 Michael J. Vitarelli Jr. Department of Chemistry and Chemical Biology Rutgers University, 610 Taylor Road, Piscataway, NJ 08854 I. INTRODUCTION

More information

Accuracy of Measurement: how close your measured value is to the actual measurement

Accuracy of Measurement: how close your measured value is to the actual measurement Standard: an exact quantity that people use to make measurements Good Example: a meter stick (everyone one knows the length of a meter) Bad Example: Ms. Pluchino s foot (everyone does not know how big

More information

Exponential Functions

Exponential Functions CONDENSED LESSON 5.1 Exponential Functions In this lesson, you Write a recursive formula to model radioactive decay Find an exponential function that passes through the points of a geometric sequence Learn

More information

Syllabus Tutors Review from previous class. Resources. Lecture: MW 5:30PM-6:50PM Room 425

Syllabus Tutors Review from previous class. Resources. Lecture: MW 5:30PM-6:50PM Room 425 Chapter 2 Syllabus Tutors Review from previous class 1 Chapter 2 Resources Lecture: MW 5:30PM-6:50PM Room 425 Text book: Steven S. Zumdahl, Donald DeCosta, Introductory Chemistry: A Foundation, 8th Website:

More information

Measurements, Sig Figs and Graphing

Measurements, Sig Figs and Graphing Measurements, Sig Figs and Graphing Chem 1A Laboratory #1 Chemists as Control Freaks Precision: How close together Accuracy: How close to the true value Accurate Measurements g Knowledge Knowledge g Power

More information

1) [3pts] 2. Simplify the expression. Give your answer as a reduced fraction. No credit for decimal answers. ( ) 2) [4pts] ( 3 2 ) 1

1) [3pts] 2. Simplify the expression. Give your answer as a reduced fraction. No credit for decimal answers. ( ) 2) [4pts] ( 3 2 ) 1 Math 097 Winter 2018 Final Exam (Form A) Name: Instructor s Name: Score: /100 (+ 3 bonus) 1. Evaluate 2(x h) 3 when x = 2 and h = 5. 1) 2. Simplify the expression. Give your answer as a reduced fraction.

More information

APPENDIX D. Appendix D. Scientific conventions BIOLOGY 3201 CURRICULUM GUIDE 183

APPENDIX D. Appendix D. Scientific conventions BIOLOGY 3201 CURRICULUM GUIDE 183 Appendix D Scientific conventions BIOLOGY 3201 CURRICULUM GUIDE 183 184 BIOLOGY 3201 CURRICULUM GUIDE Scientific Conventions Scientific information should be communicated according to accepted scientific

More information

Corner Brook Regional High School

Corner Brook Regional High School Corner Brook Regional High School Measurement and Calculations Significant Digits Scientific Notation Converting between Units Accuracy vs. Precision Scalar Quantities Distance Calculations Speed Calculations

More information

Definition of a Logarithm

Definition of a Logarithm Chapter 17 Logarithms Sec. 1 Definition of a Logarithm In the last chapter we solved and graphed exponential equations. The strategy we used to solve those was to make the bases the same, set the exponents

More information

Chemistry 1104 Introduction:

Chemistry 1104 Introduction: Chemistry 1104 Introduction: Time requirements. Start early. Need help. See instructor early and often. Only requirement: be prepared. Understanding vs. memorization. Chemistry requires practice. Use problem

More information

Math Practice Exam 3 - solutions

Math Practice Exam 3 - solutions Math 181 - Practice Exam 3 - solutions Problem 1 Consider the function h(x) = (9x 2 33x 25)e 3x+1. a) Find h (x). b) Find all values of x where h (x) is zero ( critical values ). c) Using the sign pattern

More information

Chapter 12 Intermolecular Forces of Attraction

Chapter 12 Intermolecular Forces of Attraction Chapter 12 Intermolecular Forces of Attraction Intermolecular Forces Attractive or Repulsive Forces between molecules. Molecule - - - - - - Molecule Intramolecular Forces bonding forces within the molecule.

More information

Topic 11: Measurement and data processing

Topic 11: Measurement and data processing Topic 11: Measurement and data processing 11.1 Uncertainty and error in measurement 11.2 Uncertainties in calculated results 11.3 Graphical techniques -later! From the syllabus Precision v. Accuracy The

More information

Essential Mathematics

Essential Mathematics Appendix B 1211 Appendix B Essential Mathematics Exponential Arithmetic Exponential notation is used to express very large and very small numbers as a product of two numbers. The first number of the product,

More information