The CLAST Manual helps build students’ proficiency in 55 mathematical skills in the fields of Arithmetic, Geometry, Algebra, Statistics, and Logic. Written as an additional supplement for students who are required to take the CLAST (students in the State of Florida), the first part of the CLAST Manual focuses on the skill-by-skill description of each of the 55 skills required in the exam, including worked out examples.The second part of this manual is a collection of CLAST-style homework exercises linked to various sections of Thinking Mathematically 4e.
Chapter 1. Problem Solving and Critical Thinking
1.1 Inductive and Deductive Reasoning
1.2 Estimation, Graphs, and Mathematical Models
1.3 Problem Solving
Chapter 2. Set Theory
2.1 Basic Set Concepts
2.2 Subsets
2.3 Venn Diagrams and Set Operations
2.4 Set Operations and Venn Diagrams with Three Sets
2.5 Survey Problems
Chapter 3. Logic
3.1 Statements, Negations, and Quantified Statements
3.2 Compound Statements and Connectives
3.3 Truth Tables for Negation, Conjunction, and Disjunction
3.4 Truth Tables for the Conditional and the Biconditional
3.5 Equivalent Statements, Variations of Conditional Statements, and DeMorgan’s Laws
3.6 Arguments and Truth Tables
3.7 Arguments and Euler Diagrams
Chapter 4. Number Representation and Calculation
4.1 Our Hindu-Arabic System and Early Positional Systems
4.2 Number Bases in Positional Systems
4.3 Computation in Positional Systems
4.4 Looking Back at Early Numeration Systems
Chapter 5. Number Theory and the Real Number System
5.1 Number Theory: Prime and Composite Numbers
5.2 The Integers; Order of Operations
5.3 The Rational Numbers
5.4 The Irrational Numbers
5.5 Real Numbers and Their Properties
5.6 Exponents and Scientific Notation
5.7 Arithmetic and Geometric Sequences
Chapter 6. Algebra: Equations and Inequalities
6.1 Algebraic Expressions and Formulas
6.2 Linear Equations in One Variable
6.3 Applications of Linear Equations
6.4 Ratio, Proportion, and Variation
6.5 Linear Inequalities in One Variable
6.6 Quadratic Equations
Chapter 7. Algebra: Graphs, Functions, and Linear Systems
7.1 Graphing and Functions
7.2 Linear Functions and Their Graphs
7.3 Systems of Linear Equations in Two Variables
7.4 Linear Inequalities in Two Variables
7.5 Linear Programming
7.6 Approximating Reality with Nonlinear Models
Chapter 8. Consumer Mathematics and Financial Management
8.1 Percent, Sales Tax, and Income Tax
8.2 Simple Interest
8.3 Compound Interest
8.4 Annuities, Stocks, and Bonds
8.5 Installment Buying
8.6 Amortization and the Cost of Home Ownership
Chapter 9. Measurement
9.1 Measuring Length; The Metric System
9.2 Measuring Area and Volume
9.3 Measuring Weight and Temperature
Chapter 10. Geometry
10.1 Points, Lines, Planes, and Angles
10.2 Triangles
10.3 Polygons, Perimeter, and Tessellations
10.4 Area and Circumstances
10.5 Volume
10.6 Right Triangle Trigonometry
10.7 Beyond Euclidean Geometry
Chapter 11. Counting Methods and Probability Theory
11.1 The Fundamental Counting Principle
11.2 Permutations
11.3 Combinations
11.4 Fundamentals of Probability
11.5 Probability with the Fundamental Counting Principle, Permutations, and Combinations
11.6 Events Involving Not and Or; Odds
11.7 Events Involving And; Conditional Probability
11.8 Expected Value
Chapter 12. Statistics
12.1 Sampling, Frequency Distributions, and Graphs
12.2 Measures of Central Tendency
12.3 Measure of Dispersion
12.4 The Normal Distribution
12.5 Scatter Plots, Correlation, and Regression Lines
Chapter 13. Mathematical Systems
13.1 Mathematical Systems
13.2 Rotational Symmetry, Groups, and Clock Arithmetic
Chapter 14. Voting and Apportionment
14.1 Voting Methods
14.2 Flaws of Voting Methods
14.3 Apportionment Methods
14.4 Flaws of Apportionment Methods
Chapter 15. Graph Theory
15.1 Graphs, Paths, and Circuits
15.2 Euler Paths and Euler Circuits
15.3 Hamilton Paths and Hamilton Circuits
15.4 Trees