IBDP Mathematics Applications & Interpretations HL Chapter 1 Notes
basic geometry and mathematics
STUDY NOTES FOR MATHEMATICS – CHAPTER 1 – Basic GEOMETRY AND MATHEMATICS
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All DP mathematics courses serve to accommodate the diverse range of needs, interests and abilities of students, and to fulfill the requirements of various university and career aspirations. The aims of these courses are to enable students to: develop mathematical knowledge, concepts, principles, logical, critical and creative thinking, employ and refine their powers of abstraction and generalization. Students are also encouraged to appreciate the international dimensions of mathematics and the multiplicity of its cultural and historical perspectives.
This chapter covers the basic topics of mathematics such as rounding, percentage errors and more. Before understanding how to round numbers we need to know what approximations and estimations mean. Approximations are a value or quantity that is nearly but not exactly correct. Estimations are rough calculations of the value, number, quantity, or extent of something. In giving an estimation or approximation, measurements are often rounded to some level of accuracy. In this chapter of approximation and error, we deal with two major topics: errors in measurement and absolute and percentage error. When describing quantities, we often give an approximate answer rather than an exact answer. This chapter discusses the errors that arise when we approximate values. When we measure the length of an object, it is likely to fall between two divisions, and so a measurement is accurate to ±1/2 of the smallest division on the scale. The second subtopic in this chapter is absolutely and percentage error. Whenever we measure a quantity there is almost always a difference between our measurement and the actual value. This difference is called the error. The size or magnitude of the error, whether the measured or estimated value is too high or too low, is known as the absolute error. If the actual or exact value is Ve and the approximate value is Va then the absolute error is Va minus Ve. This error can often be expressed as a percentage of the exact value, known as the percentage error.
We also learn the rules in exponents and logarithms as well as a basic understanding of angles, triangles, circles and finding the area and volume of various figures.
- Chapter 1 Basic Geometry and Mathematics
- Chapter 2 Functions
- Chapter 3 Sequences and Series
- Chapter 4 Geometry and Trigonometry
- Chapter 5 Complex Number
- Chapter 6 Matrix Algebra
- Chapter 7 Vectors
- Chapter 8 Probability
- Chapter 9 Descriptive Statistics
- Chapter 10 Probability
- Chapter 11 Differential Calculus
- Chapter 12 Probability Distribution
- Chapter 13 Integral Calculus
- Chapter 14 Testing For Validity
- Chapter 15 Graph Theory