Course Description:

This course provides students with foundational mathematical skills essential for problem-solving in academic and real-life contexts. Topics include the properties of real numbers, sets, algebraic operations, statistics, probability, sequences, and basic graphing techniques. The course emphasizes critical thinking and the effective use of calculators for computation, data interpretation, and visualization of mathematical concepts.

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Course Objectives:

Upon completion of this course, students should be able to:

• Recognize and apply the properties of real numbers.

• Demonstrate appropriate and effective use of a scientific calculator.

• Construct and interpret a variety of graphs based on quantitative data.

• Solve problems involving sets, Venn diagrams, and basic statistics.

• Analyze and solve probability problems involving simple, compound, and conditional events.

• Apply permutations and combinations in counting and probability.

• Perform algebraic manipulations including simplifying, factoring, and solving equations and inequalities.

• Graph linear equations and represent inequalities visually.

• Solve basic linear programming problems.

• Recognize and apply arithmetic and geometric sequences.

 

Course Learning Outcomes:

By the end of the course, students will be able to:

• Identify, classify, and operate with different types of real numbers.

• Simplify and evaluate algebraic expressions and solve various types of equations.

• Accurately interpret and solve problems using set theory and Venn diagrams.

• Analyze statistical data using measures of central tendency and dispersion.

• Apply principles of probability using diagrams, formulas, and combinatorial techniques.

• Graph mathematical relationships and interpret their meaning in applied contexts.

• Solve word problems and real-world scenarios using mathematical reasoning and models.

• Utilize mathematical tools for effective decision-making and critical analysis.

 

Recommended Course Materials:

• Supplementary handouts and online exercises provided by the instructor

• Scientific calculator (Casio fx-82MS or similar)

• Graph paper, ruler, and geometry set

 

Course Content:

1. Real Numbers

• Definition and types of real numbers

• Properties and operations

• Number line representation

• Calculator functions and appropriate usage

 

2. Algebraic Manipulations

• Construction and simplification of expressions

• Factoring techniques and solving quadratic equations

• Formula manipulation and transposition

• Solving simultaneous equations

• Word problems and inequalities

• Graphing lines and parabolas

• Linear programming basics

 

3. Sequences

• Patterns and types of sequences

• Arithmetic and geometric progressions

• Applications of sequences in problem-solving

 

4. Sets and Venn Diagrams

• Set notation and types of sets

• Operations: union, intersection, complement

• De Morgan’s laws

• Venn diagram representation and survey applications

 

5. Statistics

• Types of data: qualitative vs. quantitative

• Measures of central tendency: mean, median, mode

• Dispersion: range, variance, standard deviation

• Frequency distributions and graphs (bar charts, pie charts, histograms, stem-and-leaf plots, box plots)

• Cumulative frequency and quartile estimation

 

6. Probability and Counting

• Probability concepts and rules

• Simple and compound events

• Tree diagrams and sample spaces

• Conditional probability

• Permutations and combinations

• Application to real-world problems

 

Course Assessment & Evaluation:

Class Participation & Homework - 10%

Midterm Examination - 30%

Final Examination - 60%