IBDP Mathematics Applications & Interpretations SL Chapter 1 Notes
Measuring space: accuracy and 2D geometry
STUDY NOTES FOR MATHEMATICS – CHAPTER 1 – Measuring space: accuracy and 2D geometry
These notes have specially been curated by expert teachers to simplify and enlighten concepts given in IB Mathematics SL. The notes are comprehensive in nature and are sufficient to study the chapter in depth and one need not look for other resources beyond the notes provided on our website which can be accessed for free. The notes for Mathematics IBDP SL are available on our official website and can be downloaded for free. You are one click away from obtaining all that you need to score well in IB Mathematics SL.
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. This chapter also gives us a brief introduction to trigonometry of right-angled triangles and angles of elevation and depression.
- Chapter 1 Measuring space: accuracy and 2D geometry
- Chapter 2 Representing space : non right angled trigonometry and volumes
- Chapter 3 Representing and describing data: descriptive statistics
- Chapter 4 Dividing up space : coordinate geometry , lines , Voronoi diagrams
- Chapter 5 Modelling constant rate of change: linear function
- Chapter 6 Modelling relationships: linear correlation of bivariate data
- Chapter 7 Quantifying uncertainty: probability, binomial and normal distributions
- Chapter 8 – Testing for validity: Spearman’s hypothesis testing and x^2 test for independence
- Chapter 9 Modelling relationships with functions: power f unctions
- Chapter 10 Modelling Rates of change: Exponential and logarithmic functions
- Chapter 11 Modelling Periodic Phenomena: Trigonometric Functions
- Chapter 12 Analyzing Rates of Change: Differential Calculus
- Chapter 13 Approximating Irregular Spaces: Integration