Elliot Mendelson was a professor of mathematics at Queens College, the City University of New York. He taught mathematics at the college level for more than 30 years.
Frances R. Curcio is a test prep author.
Number Systems | |
The Earliest Mathematics | |
Additive Systems | |
The Egyptian Number System | |
Alphabetic Systems | |
Positional Systems on a Fixed Base | |
Historical Examples of Positional Systems with a Base Different from Ten | |
The Babylonian Number System | |
The Mayan Number System | |
Method for Translating Base Ten into Base Two | |
Sets | |
The Algebra of Sets | |
Set Theoretic Exponentiation | |
Cardinal Numbers | |
Theory of Numbers | |
Mathematical Induction | |
Complete Induction | |
Prime Numbers | |
The Division Theorem | |
Testing for Primality | |
The Greatest Common Divisor | |
Irrational Numbers | |
Factorization into Primes | |
The Least Common Multiple | |
The Euclidean Algorithm | |
Some Famous Unsolved Problems (Perfect numbers | |
Fermat primes, The Goldbach Conjecture) | |
Linear Diophantine Equations | |
Fractions | |
Introduction | |
Try These First | |
What is a "fraction"? | |
How is a fraction represented in diagrams? | |
How are fractions represented on a number line? | |
What is the "unit"? | |
What is the "shifting unit"? | |
What is the multiplicative identity element for fractions? | |
What is a proper fraction? | |
What is an improper fraction? | |
When is a fraction larger than one whole? | |
What is a Unit fraction? | |
How are fractions "simplified" (or "reduced")? | |
When is a fraction in "simplest form" (or "lowest terms")? | |
How are mixed numbers changed to improper fractions? | |
What are equivalent fractions? | |
How can we determine when fractions are equivalent? | |
How are fractions ordered from largest to smallest or from smallest to largest? How are fractions compared to find the largest or smallest value? | |
How is the least common denominator (LCD) determined? | |
How is the numerator determined once the LCD or common denominator is known? | |
How are fractions added and subtracted? | |
What are the properties of fraction addition? | |
How are fractions multiplied? | |
What are the properties of fraction multiplication? | |
Why is the product of two proper fractions smaller in value than either fraction factor? | |
What is the "multiplicative inverse," or "reciprocal" of a fraction? | |
How are fractions divided? | |
Why does the "invert-and-multiply" rule "work" when dividing fractions? | |
What are complex fractions? | |
How are complex fractions simplified? | |
End of Chapter Exercises | |
Sample Certification Test Items | |
Decimals, Ratios, Proportions, and Percents | |
Introduction | |
Try These First | |
What is a decimal fraction? | |
What is a mixed decimal? | |
What are the place values for decimals? | |
How are decimals written in expanded form? | |
What are terminating decimals? | |
What are equivalent decimals? | |
What are repeating (or recurring) nonterminating decimals? | |
What are nonepeating, nonterminating decimals? | |
How can common fractions be written as decimals? | |
How can decimals be written as common fractions? | |
How are mixed numbers written as decimals? | |
How are decimals ordered and compared? | |
How are decimals rounded? | |
How are decimals added and subtracted? | |
How are decimals multiplied? | |
Why is the placement of the decimal point in the product of two decimals determined by counting the number of decimal places in the factors? | |
How is decimal multiplication the same as whole number multiplication? How is decimal multiplication different from whole number multiplication? | |
How are decimals divided? | |
How is decimal division different from whole number division? How is decimal division the same as whole number division? | |
What does it mean to "add a zero" to the end of a decimal fraction? | |
What is scientific notation and how is it used? | |
What is a ratio? | |
What is a rate? | |
How are ratios and rates the same? How are they different? | |
How are ratios expressed as decimals? As percents? | |
When are two ratios equal? | |
What is a proportion? | |
What is a scaled drawing? | |
How are scales used to calculate actual quantities? | |
What does percent mean? | |
How are percents changed to decimals? | |
How are decimals changed to percents? | |
How are percents changed to common fractions? | |
How are common fractions changed to percents? | |
What does a percent greater than 100% mean? | |
What does a percent less than 1% mean? | |
How is a percent of a number calculated and what does it mean? | |
What are the aliquot parts of 100? | |
How is the percent of a number calculated? | |
When finding the percent of a number, when is it appropriate to use the fraction form of a rational number and when is it appropriate to use a decimal form of a rational number? | |
How can we find a number when a percent of it is known? | |
How is the percent of increase or decrease found? | |
End of Chapter Exercises | |
Sample Certification Test Items | |
Algebra, Patterns, and Functions | |
Introduction | |
Try These First | |
What is algebra? | |
What is a variable? | |
How are a "variable" and an "unknown" the same? How are they different? | |
What does the equal sign mean? | |
What is an algebraic expression? | |
What is an equation? | |
What is a linear equation? | |
How are linear equations solved? | |
What is an inequality? | |
How are linear inequalities solved? | |
What is the absolute value of a number? | |
What is a pattern? How are patterns used to solve problems? | |
What is a function? | |
What is the slope of a line? | |
What is the y-intercept of a line? | |
How is a linear equation graphed? | |
What is factoring? | |
How are algebraic expressions factored? | |
What is the Pythagorean Theorem? | |
What are Pythagorean triples? | |
What is a quadratic equation? | |
What is covariation? | |
What is direct variation? | |
What is inverse variation? | |
End of Chapter Exercises | |
Sample Certification Test Items | |
Geometry and Measurement | |
Combinatorics and Probability | |
Let Us Count the Ways | |
The Multiplication Principle | |
Terminology of Sets | |
Probability | |
The Meaning of Probability | |
Basic Ideas of Probability Theory: Probability Spaces | |
Events | |
Conditional Probability | |
Independent Events | |
Random Variables and Expected Values | |
Statistics | |
Introduction | |
Try These First | |
Distributions and Types of Data | |
What is a distribution? | |
What is a normal distribution? | |
What is a skewed distribution? | |
What are discrete data (also known as "categorical data") and how are they analyzed? | |
What are continuous data (sometimes also called, numerical data) and how are they analyzed? | |
Populations and Samples | |
What is the difference between a population and a sample? | |
What is convenience sampling? | |
What is systematic sampling? | |
What is voluntary-response sampling? | |
What is random sampling? | |
What is a biased sample? | |
What is a simulation? | |
What are frequency tables and how are they constructed? | |
What is relative frequency? | |
What is a picture graph (also known as a pictograph, pictogram, or pictorial graph) and how is it constructed? | |
What is a bar graph (also known as a bar chart) and how is it constructed? | |
What is a double or multiple bar graph and how is it constructed? | |
What is a stacked bar graph and how is it constructed? | |
What is a histogram and how is it constructed? | |
How are bar graphs and histograms the same? How are they different? | |
What is a line graph (also known as a broken line graph) and how is it constructed? | |
What is a double line graph and how is it constructed? | |
What is a circle graph (also known as a pie graph, pie chart, pie diagram, area graph) and how is it constructed? | |
What is a line plot? | |
What is a stemplot (also known as a stem-and-leaf plot) and how is it constructed? | |
What is a back-to-back stem-and-leaf plot and how is it constructed? | |
What is a scatterplot and how is it constructed? | |
What is correlation? | |
What is a line of best fit and how can it be found? | |
Measures of Center | |
What are measures of central tendency? | |
What is the mean of a set of data (also known as the arithmetic mean or arithmetic average) and how is it determined? | |
What is the median of a set of data and how is it found? | |
What is the mode of a set of data? | |
Measures of Spread | |
What are measures of dispersion? | |
What is the range of a set of data and how is it calculated? | |
What is the variance of a set of data and how is it calculated? | |
What is the standard deviation of a set of data and how is it calculated? | |
What are percentiles? | |
What are quartiles and how are they determined? | |
What is the interquartile range? | |
What is a boxplot (also known as a box-and-whisker plot) and how is it constructed? | |
What is an outlier and how is it determined? | |
What is a cluster? | |
What is a gap? | |
What is a z-score (also standard score) and how is it calculated? | |
End of Chapter Exercises | |
Sample Certification Test Items | |
Bibliography | |
Answer Key | |
Index | |
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