Preparation for College Mathematics Second Edition

Preparation for College Mathematics coverThe new edition of Preparation for College Mathematics now covers even more intermediate-level algebraic topics and increases focus on application, conceptual understanding, and the development of the academic mindset. Request an examination copy.

The goal of this newly enhanced title is to develop holistic learners who are adequately prepared for subsequent, higher-level math courses on their path to college success.

View a free sample of the new edition of Preparation for College Mathematics.

 


NEW features include:

  • Strategies for Academic Success – study skills and learning strategies build stronger learners with tips on note taking, time management, test taking, and more
  • Chapter Projects – discovery-based projects promote collaboration and practical applications of mathematics
  • Concept Checks – exercise sets assess students’ conceptual understanding of topics before each practice set
  • Applications – exercise sets for each section challenge students to apply topics learned to real-world contexts
  • Extra Material – more advanced topics cover all learning outcomes to prepare students for future college math courses
  • Writing & Thinking – opportunities for students to independently explore and expand on chapter concepts

 


Table of Contents:

1. Whole Numbers

Introduction to Whole Numbers
Addition and Subtraction with Whole Numbers
Multiplication with Whole Numbers
Division with Whole Numbers
Rounding and Estimating with Whole Numbers
Problem Solving with Whole Numbers
Solving Equations with Whole Numbers (x + b = c and ax = c)
Exponents and Order of Operations
Tests for Divisibility
Prime Numbers and Prime Factorizations

2. Integers

Introduction to Integers
Addition with Integers
Subtraction with Integers
Multiplication, Division, and Order of Operations with Integers
Simplifying and Evaluating Expressions
Translating English Phrases and Algebraic Expressions
Solving Equations with Integers (ax + b = c)

3. Fractions, Mixed Numbers, and Proportions

Introduction to Fractions and Mixed Numbers
Multiplication with Fractions
Division with Fractions
Multiplication and Division with Mixed Numbers
Least Common Multiple (LCM)
Addition and Subtraction with Fractions
Addition and Subtraction with Mixed Numbers
Comparisons and Order of Operations with Fractions
Solving Equations with Fractions
Ratios and Rates
Proportions
Probability

4. Decimal Numbers

Introduction to Decimal Numbers
Addition and Subtraction with Decimal Numbers
Multiplication and Division with Decimal Numbers
Estimating and Order of Operations with Decimal Numbers
Statistics: Mean, Median, Mode, and Range
Decimal Numbers and Fractions
Solving Equations with Decimal Numbers

5. Percents

Basics of Percent
Solving Percent Problems Using Proportions
Solving Percent Problems Using Equations
Applications of Percent
Simple and Compound Interest
Reading Graphs

6. Measurement and Geometry

US Measurements
The Metric System: Length and Area
The Metric System: Weight and Volume
US and Metric Equivalents
Angles and Triangles
Perimeter
Area
Volume and Surface Area
Similar and Congruent Triangles
Square Roots and the Pythagorean Theorem

7. Solving Linear Equations and Inequalities

Properties of Real Numbers
Solving Linear Equations: x + b = c and ax = c
Solving Linear Equations: ax + b = c
Solving Linear Equations: ax + b = cx + d
Working with Formulas
Applications: Number Problems and Consecutive Integers
Applications: Distance-Rate-Time, Interest, Average, and Cost
Solving Linear Inequalities
Compound Inequalities
Absolute Value Equations
Absolute Value Inequalities

8. Graphing Linear Equations and Inequalities

The Cartesian Coordinate System
Graphing Linear Equations in Two Variables
Slope-Intercept Form
Point-Slope Form
Introduction to Functions and Function Notation
Graphing Linear Inequalities in Two Variables

9. Systems of Linear Equations

Systems of Linear Equations: Solutions by Graphing
Systems of Linear Equations: Solutions by Substitution
Systems of Linear Equations: Solutions by Addition
Applications: Distance-Rate-Time, Number Problems, Amounts, and Costs
Applications: Interest and Mixture
Systems of Linear Equations: Three Variables
Matrices and Gaussian Elimination
Systems of Linear Inequalities

10. Exponents and Polynomials

Rules for Exponents
Power Rules for Exponents
Applications: Scientific Notation
Introduction to Polynomials
Addition and Subtraction with Polynomials
Multiplication with Polynomials
Special Products of Binomials
Division with Polynomials
Synthetic Division and the Remainder Theorem

11. Factoring Polynomials

Greatest Common Factor (GCF) and Factoring by Grouping
Factoring Trinomials: x^2+bx+c
Factoring Trinomials: ax^2+bx+c
Special Factoring Techniques
Review of Factoring Techniques
Solving Quadratic Equations by Factoring
Applications: Quadratic Equations

12. Rational Expressions

Introduction to Rational Expressions
Multiplication and Division with Rational Expressions
Least Common Multiple of Polynomials
Addition and Subtraction with Rational Expressions
Simplifying Complex Fractions
Solving Rational Equations
Applications: Rational Expressions
Applications: Variation

13. Roots, Radicals, and Complex Numbers

Evaluating Radicals
Rational Exponents
Simplifying Radicals
Addition, Subtraction, and Multiplication with Radicals
Rationalizing Denominators
Solving Radical Equations
Functions with Radicals
Introduction to Complex Numbers
Multiplication and Division with Complex Numbers

14. Quadratic Equations

Quadratic Equations: The Square Root Method
Quadratic Equations: Completing the Square
Quadratic Equations: The Quadratic Formula
More Applications of Quadratic Equations
Equations in Quadratic Form
Graphing Quadratic Functions
More on Graphing Functions and Applications
Solving Polynomial and Rational Inequalities

15. Exponential and Logarithmic Functions

Algebra of Functions
Composition of Functions and Inverse Functions
Exponential Functions
Logarithmic Functions
Properties of Logarithms
Common Logarithms and Natural Logarithms
Logarithmic and Exponential Equations and Change-of-Base
Applications: Exponential and Logarithmic Functions

16. Conic Sections

Translations and Reflections
Parabolas as Conic Sections
Distance Formula, Midpoint Formula, and Circles
Ellipses and Hyperbolas
Nonlinear Systems of Equations

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Developmental Mathematics Second Edition

Developmental Mathematics Second Edition coverThis new edition offers more robust exercise sets that include conceptual assessment, an increased focus on real-world application, new lessons on study skills to develop the academic mindset of mathematics learners, chapter projects and collaborative opportunities for discovery-based learning with peers, and additional content to cover all topics through intermediate algebra.

View a free sample of the new edition of Developmental Mathematics.

Request an examination copy.


NEW features include:

  • Strategies for Academic Success – study skills and learning strategies build stronger learners with tips on note taking, time management, test taking, and more
  • Chapter Projects – discovery-based projects promote collaboration and practical applications of mathematics
  • Concept Checks – exercise sets assess students’ conceptual understanding of topics before each practice set
  • Applications – exercise sets for each section challenge students to apply topics learned to real-world contexts
  • Extra Material – more advanced topics cover all learning outcomes to prepare students for future college math courses
  • Writing & Thinking – opportunities for students to independently explore and expand on chapter concepts

Table of Contents:

1. Whole Numbers

Introduction to Whole Numbers
Addition and Subtraction with Whole Numbers
Multiplication with Whole Numbers
Division with Whole Numbers
Rounding and Estimating with Whole Numbers
Problem Solving with Whole Numbers
Exponents and Order of Operations
Tests for Divisibility
Prime Numbers and Prime Factorizations

2. Fractions and Mixed Numbers

Introduction to Fractions and Mixed Numbers
Multiplication with Fractions
Division with Fractions
Multiplication and Division with Mixed Numbers
Least Common Multiple (LCM)
Addition and Subtraction with Fractions
Addition and Subtraction with Mixed Numbers
Comparisons and Order of Operations with Fractions

3. Decimal Numbers

Introduction to Decimal Numbers
Addition and Subtraction with Decimal Numbers
Multiplication with Decimal Numbers
Division with Decimal Numbers
Estimating and Order of Operations with Decimal Numbers
Decimal Numbers and Fractions

4. Ratios, Proportions, and Percents

Ratios and Unit Rates
Proportions
Decimals and Percents
Fractions and Percents
Solving Percent Problems Using Proportions
Solving Percent Problems Using Equations
Applications of Percent
Simple and Compound Interest

5. Measurements

US Measurements
The Metric System: Length and Area
The Metric System: Capacity and Weight
US and Metric Equivalents

6. Geometry

Angles and Triangles
Perimeter
Area
Circles
Volume and Surface Area
Similar and Congruent Triangles
Square Roots and the Pythagorean Theorem

7. Statistics, Graphs, and Probability

Statistics: Mean, Median, Mode, and Range
Reading Graphs
Constructing Graphs from a Database
Probability

8. Introduction to Algebra

The Real Number Line and Absolute Value
Addition with Real Numbers
Subtraction with Real Numbers
Multiplication and Division with Real Numbers
Order of Operations with Real Numbers
Properties of Real Numbers
Simplifying and Evaluating Algebraic Expressions
Translating English Phrases and Algebraic Expressions

9. Solving Linear Equations and Inequalities

Solving Linear Equations: x + b = c
Solving Linear Equations: ax = c
Solving Linear Equations: ax + b = c
Solving Linear Equations: ax + b = cx + d
Working with Formulas
Applications: Number Problems and Consecutive Integers
Applications: Distance-Rate-Time, Interest, Average
Solving Linear Inequalities in One Variable
Compound Inequalities
Absolute Value Equations
Absolute Value Inequalities

10. Graphing Linear Equations and Inequalities

The Cartesian Coordinate System
Graphing Linear Equations in Two Variables
Slope-Intercept Form
Point-Slope Form
Introduction to Functions and Function Notation
Graphing Linear Inequalities in Two Variables

11. Systems of Linear Equations

Systems of Linear Equations: Solutions by Graphing
Systems of Linear Equations: Solutions by Substitution
Systems of Linear Equations: Solutions by Addition
Applications: Distance-Rate-Time, Number Problems, Amounts, and Costs
Applications: Interest and Mixture
Systems of Linear Equations: Three Variables
Matrices and Gaussian Elimination
Systems of Linear Inequalities

12. Exponents and Polynomials

Rules for Exponents
Power Rules for Exponents
Applications: Scientific Notation
Introduction to Polynomials
Addition and Subtraction with Polynomials
Multiplication with Polynomials
Special Products of Binomials
Division with Polynomials
Synthetic Division and the Remainder Theorem

13. Factoring Polynomials

Greatest Common Factor (GCF) and Factoring by Grouping
Factoring Trinomials: x^2+bx+c
Factoring Trinomials ax^2+bx+c
Special Factoring Techniques
Review of Factoring Techniques
Solving Quadratic Equations by Factoring
Applications: Quadratic Equations

14. Rational Expressions

Introduction to Rational Expressions
Multiplication and Division with Rational Expressions
Least Common Multiple of Polynomials
Addition and Subtraction with Rational Expressions
Simplifying Complex Fractions
Solving Rational Equations
Applications: Rational Expressions
Applications: Variation

15. Roots, Radicals, and Complex Numbers

Evaluating Radicals
Rational Exponents
Simplifying Radicals
Addition, Subtraction, and Multiplication with Radicals
Rationalizing Denominators
Solving Radical Equations
Functions with Radicals
Introduction to Complex Numbers
Multiplication and Division with Complex Numbers

16. Quadratic Equations

Quadratic Equations: The Square Root Method
Quadratic Equations: Completing the Square
Quadratic Equations: The Quadratic Formula
More Applications of Quadratic Equations
Equations in Quadratic Form
Graphing Quadratic Functions
More on Graphing Functions and Applications
Solving Polynomial and Rational Inequalities

17. Exponential and Logarithmic Functions

Algebra of Functions
Composition of Functions and Inverse Functions
Exponential Functions
Logarithmic Functions
Properties of Logarithms
Common Logarithms and Natural Logarithms
Logarithmic and Exponential Equations and Change-of-Base
Applications: Exponential and Logarithmic Functions

18. Conic Sections

Translations and Reflections
Parabolas as Conics
Distance Formula, Midpoint Formula, and Circles
Ellipses and Hyperbolas
Nonlinear Systems of Equations

Request an examination copy.

Want to learn more? Contact us at sales@hawkeslearning.com!

Introducing the Third Edition of Discovering Statistics and Data

Discovering Statistics and Data coverWe’re proud to announce the new edition of Discovering Statistics and Data!

This new edition pays homage to modern day’s technology-driven data explosion, helping students understand the context behind future statistical concepts to be learned and explaining why the study of statistics is critical.
View a free sample of the new edition of Discovering Statistics and Data.

The text opens by describing the necessity of understanding the data around us, introducing students to what data is, how we measure it, where it comes from, how to visualize it, and what kinds of career opportunities surround its analysis and processing. This focus makes upcoming content more meaningful for students and then challenges them to think with statistics. Request an examination copy.


NEW features include:

  • Greater focus on data – Introductory chapters place a strong emphasis on helping students understand where data comes from, data visualization techniques, “Big Data,” and the problems arising from having large data sets.
  • Downloadable data sets – More real data sets are available for download, including over 15 large data sets and one giant data set. 
  • More technology integration – Detailed instruction using graphing calculators, Excel, Minitab, and R Statistical language are included.
  • Real-world applications – Larger scale chapter projects challenge students and brief, relatable articles engage readers.
  • Expanded exercises and examples – Over 60 examples and 200 exercises, including new conceptual questions, have been added.
  • Pedagogy modernization – GAISE guidelines were carefully considered and incorporated, and the most current P-value significance testing recommendations published by the ASA for guidance on hypothesis testing are included.
  • Virtual simulations and games – Students develop conceptual understanding and statistical literacy through hands-on interactives and simulations.

Table of Contents:

1. Statistics and Problem Solving

The Meaning of Data
Statistics as a Career
The Data Explosion
Modern Computing, Networks, and Statistics
Big Data
Introduction to Statistical Thinking
Descriptive vs. Inferential Statistics
The Consequences of Statistical Illiteracy

2. Data, Reality, and Problem Solving

Collecting Data
Data Classification
Time Series Data vs. Cross-Sectional Data
Data Resources

3. Visualizing Data

Frequency Distributions
Displaying Qualitative Data Graphically
Constructing Frequency Distributions for Quantitative Data
Histograms and Other Graphical Displays of
Quantitative Data
Analyzing Graphs

4. Describing and Summarizing Data from One Variable

Measures of Location
Measures of Dispersion
Measures of Relative Position, Box Plots, and Outliers
Data Subsetting
Analyzing Grouped Data
Proportions and Percentages

5. Discovering Relationships

Scatterplots and Correlation
Fitting a Linear Model
Evaluating the Fit of a Linear Model
Fitting a Linear Time Trend
Scatterplots for More Than Two Variables

6. Probability, Randomness, and Uncertainty

Introduction to Probability
Addition Rules for Probability
Multiplication Rules for Probability
Combinations and Permutations
Combining Probability and Counting Techniques
Bayes’ Theorem

7. Discrete Probability Distributions

Types of Random Variables
Discrete Random Variables
The Discrete Uniform Distribution
The Binomial Distribution
The Poisson Distribution
The Hypergeometric Distribution

8. Continuous Probability Distributions

The Uniform Distribution
The Normal Distribution
The Standard Normal Distribution
Applications of the Normal Distribution
Assessing Normality
Approximations to Other Distributions

9. Samples and Sampling Distributions

Random Samples and Sampling Distributions
The Distribution of the Sample Mean and the Central Limit Theorem
The Distribution of the Sample Proportion
Other Forms of Sampling

10. Estimation: Single Samples

Point Estimation of the Population Mean
Interval Estimation of the Population Mean
Estimating the Population Proportion
Estimating the Population Standard Deviation or Variance
Confidence Intervals Based on Resampling (Bootstrapping) (Courseware only)

11. Hypothesis Testing: Single Samples

Introduction to Hypothesis Testing
Testing a Hypothesis about a Population Mean
The Relationship between Confidence Interval
Estimation and Hypothesis Testing
Testing a Hypothesis about a Population Proportion
Testing a Hypothesis about a Population Standard Deviation or Variance
Practical Significance vs. Statistical Significance

12. Inferences about Two Samples

Inference about Two Means: Independent Samples
Inference about Two Means: Dependent Samples (Paired Difference)
Inference about Two Population Proportions
Inference about Two Population Standard Deviations or Variances

13. Regression, Inference, and Model Building

Assumptions of the Simple Linear Model
Inference Concerning β1
Inference Concerning the Model’s Prediction

14. Multiple Regression

The Multiple Regression Model
The Coefficient of Determination and Adjusted R2
Interpreting the Coefficients of the Multiple Regression Model
Inference Concerning the Multiple Regression Model and its Coefficients
Inference Concerning the Model’s Prediction
Multiple Regression Models with Qualitative Independent Variables

15. Analysis of Variance (ANOVA)

One-Way ANOVA
Two-Way ANOVA: The Randomized Block Design
Two-Way ANOVA: The Factorial Design

16. Looking for Relationships in Qualitative Data

The Chi-Square Distribution
The Chi-Square Test for Goodness of Fit
The Chi-Square Test for Association

17. Nonparametric Tests

The Sign Test
The Wilcoxon Signed-Rank Test
The Wilcoxon Rank-Sum Test
The Rank Correlation Test
The Runs Test for Randomness
The Kruskal-Wallis Test

18. Statistical Process Control (Courseware only)


Request an examination copy.

Want to know more? Contact us at sales@hawkeslearning.com!

Use this grammar diagnostic test to target which lessons students must master.

Customize the way students learn.

Save class time and identify individual areas of weakness for remediation with Hawkes Learning’s free grammar diagnostic test! Click through a demonstration of the test at your own pace.

This 50-question assessment identifies areas of proficiency and specific knowledge gaps for individual students. A customized curriculum is developed for each student to strengthen their grammar skills and eliminate those errors from their writing.

A report shows student progress in both a pie chart and bar graph. The part of the graphs in green represents the number of correct answers, while pink represents the number of incorrect answers. The bar graph breaks down each lesson number.

The tailored learning path through the grammar curriculum provides students the opportunity to learn, practice, and then master each topic. Let Hawkes assist you in ensuring these skills become second nature for your students, helping them become more effective communicators of their ideas.

While diagnostic tests are pre-created to save you time for both Hawkes Learning’s Foundations of English and English Composition courses, you can also customize either by removing or adding questions based on your own lesson objectives.

As you click through the demonstration here, you’ll see how students access their assessment, answer questions, and receive a performance breakdown of each topic covered in the test.


Want to see more? Contact your Hawkes courseware specialist at 1-800-426-9538 or sales@hawkeslearning.com today!

Interactive and Relevant Applications of Statistics

Hawkes statistics courses include games and simulations that help students apply key concepts to the world outside of the classroom. Check these out below! If you’re an instructor who would like to explore these games and simulations yourself, sign up for free student access today.

GAMES

1. Games of Chance

gamesofchance2

Relevant Application:
This lesson helps students apply the concept of the expected value of a random variable to winning or losing games. Students develop a rational approach to analyzing decisions that involve risk. After all, many business decisions—such as purchasing new equipment, hiring additional employees, and expanding into new markets—involve some kind of risk, and students need to assess these situations as best as they can.

Learn Key Concepts:

  • Basic probability distribution
  • Binomial distribution function
  • Hypergeometric distribution function

2. Direct Mail

directmail2

Relevant Application:
Even in today’s digital world, direct mail marketing remains one of the most viable and proven strategies to connect with customers.

Active Learning Approach:
By assuming the role of a direct mail marketing manager, students start off with $20,000. They are then tasked with developing a strategy by finding mailing lists that will produce sufficient sales, using confidence intervals to determine which lists to use to reach their $40,000 goal.

They win when they correctly formulate which questions they need to solve, collect the data, and analyze the data to evaluate potential risk and profitability for each mailing list.

Learn Key Concepts:
The game provides an environment in which students apply statistical concepts while making business decisions. They also learn the following:

  • Confidence intervals
  • Experimentation
  • Statistical analysis
  • Inference

3. Estimating Population Proportions

estimatingpopulationproportions

Relevant Application:
Students might not realize at first how many decisions involve measurements of a population attribute. For example, television stations base advertising charges on
ratings that reflect the percentage of viewers who watch a particular show. Political analysts are concerned with the fraction of voters who prefer a certain candidate. No
matter the field, estimating population proportions gives us greater insight into the data given to us.

Active Learning Approach:
In the game, students see a box filled with red and blue balls, and are asked to estimate the proportion of red balls in the population. They can draw sample sizes of 20, 50, or
100 to help them estimate the population proportion.

Learn Key Concepts:

  • Determine the minimum sample size for a particular confidence level.
  • Construct a confidence interval for a population proportion.

4. Central Limit Theorem with Proportions

Relevant Application:
In many decisions, the variable of interest is a proportion. A university may want to know the fraction of first-year students with low grades in order to provide more support and resources for them. Manufacturers may be concerned with the fraction of parts that are defective.

Active Learning Approach:
Students see a box of red and blue balls, then draw three samples to calculate the sample proportions for each sample taken. Students draw samples again after being informed that samples of first 20 balls and then 40 balls were drawn 200 times to determine the proportion of the number of red balls to the total number of balls chosen. Students then view the data, including tables and histograms, to understand that the sampling distribution of the sampling proportion is approximately normal.

Learn Key Concepts:
Determine p-hat using the Central Limit Theorem for population proportions.

 

 

SIMULATIONS

1. Name That Distribution

namethatdistribution

Relevant Application:
This concept builder strengthens analytical skills in distribution recognition and data analysis. By detecting symmetric or skewed data, students will begin to understand how to apply this knowledge in the real world.

Active Learning Approach:
Students are asked to identify the type of distribution from a given histogram, frequency/relative frequency distribution, statistics table, or set of sample data. They
can increase the number of intervals on the histogram or frequency distribution, view different sample displays, or choose to view a hint before submitting their answer.

Learn Key Concepts:

  • Analyze the histogram, frequency, statistics, and sample data of a distribution.
  • Identify different distribution types: uniform, normal, exponential, chi-square, Poisson, and mystery.

2. Central Limit Theorem

The simulation can run automatically and in bursts. This image shows histograms for n=5, n=15, and n=30. It includes the histogram of the parent function.

Relevant Application:
This simulation shows students how to use samples to make useful predictions about a population. Since many population sizes are too large to have their data collected and analyzed, we turn to the Central Limit Theorem for help.

The visual nature of this simulation lets students truly comprehend how the sample means from any population are normally distributed, regardless of the original
population’s distribution.

Active Learning Approach:
Students select a parent distribution and set the sample sizes and the burst rate. They choose the desired distribution type: exponential, chi-square, normal, Poisson, or bi-modal. Students can decide to run the simulation a set number of times or automatically, which will keep the simulation running.

Learn Key Concepts:

  • Sample population
  • Mean
  • Variance
  • Standard deviation
  • Distribution type

3. Type II Error

You can select the plus or minus buttons for alpha, true mean, and sample size to change the graph. The shaded part increases or decreases depending on the number, and the bell curve moves forward or backward when you change the true mean.

Relevant Application:
Understanding hypothesis testing and type II error is essential to fields like evidence-based medicine, quality engineering, and reliability engineering, among others.

Active Learning Approach:
The variance, hypotheses, and critical values are given. Students can increase or decrease the level of significance (α), true mean (μ), and sample size to see how these
changes affect the other factors involved.

Learn Key Concepts:

  • Examine the interrelationship between α, sample size, and β (the probability of making a type II error).
  • Develop an understanding of the concept of type II errors and the calculation of beta.
  • Explore the relationship between α and β.

Are you an instructor who would like to explore these lessons further?

Sign up for FREE student access today!

Additional Questions in Foundations of English Composition

New questions are available in the curriculum for Foundations of English. We’ve expanded the question bank so that you can assign more material related to reading skills and grammar & mechanics. Check out which questions are new below, then assign them using the Assignment Builder in your Hawkes Grade Book!

Lesson Question Serial No.
2.1 11
12
13
14
15
2.2 11
12
13
14
15
2.3 11
12
13
14
15
4.3 21
22
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24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
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48
49
50
4.6 15
16
17
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19
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21
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25
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27
28
4.7 18
19
20
4.8 12
13
14
15
16
4.12 19
20
5.6 30