AFDELING A VRAAG 1 Oorweeg die volgende punte op ‘n Kartesiese vlak:    

QUESTION 6 6.1 Find two values for    in the interval [

QUESTION 2 In the figure below the equation of AB is      Right-click to open the figure in a new tab   2.1 Determine the co-ordinates of A if  

SECTION A QUESTION1 Consider the following points on a Cartesian plane:    

SECTION B QUESTION 4 The points A (-4;0), B (3;7) and C (4;-1) form a triangle on the Cartesian plane as shown in the figure below Right-click to open the figure in a new tab   4.1  Prove that triangle ABC is an isosceles triangle (5) 4.2 Find the co-ordinates of D (D lies on AB) (4) 4.3 Determine if  DC

QUESTION 5 A pilot is landing a plane. He must make sure that the plane is constantly kept equidistant (equal distances) from the two outer landing lights   and   . The line between the two landing lights is perpendicular to the runway. The co-ordinates of the landing lights are    and   . Find the equation of his flight path in the form     (Hint: find the gradient of the flight path) Right-click to open the figure in a new tab   [7]

INSTRUCTIONS 1. This question paper consists of 7 questions. Answer ALL questions. 2. Read questions carefully and number your answers correct according to question paper. 3, Diagrams are not necessarily drawn to scale. 4. A non-programmable and non-graphical calculator may be used. 5. Round answers off to two decimals where necessary unless otherwise stated. 6. Answers must be done on paper in your own handwriting. 7. Show all working details clearly. Working not shown may result in a loss of marks. 8. Write legibly and neatly. 9. The answers you provide must be your own original work. No copying from any source is allowed. 10. Scan all your answers to this topic test into one .pdf file. Name your file as indicated: MATH IEB GR11E InitialSurname T02 SBA004b Exam

Let us say the cost of a False Positive is 10 units and the cost of a False negative is 2 units. In this context answer the following. (a) (6) How would you adjust the decision tree algorithm so that its performance on unseen cases minimizes the total expected cost instead of maximizing the accuracy?   (b) (6) Recall the Support Vector Machine formulation discussed in class, specifically the case in which we minimize the cost of misclassifications using a constant parameter C. Suggest a solution for learning an SVM classifier in which the cost of the two types of errors are different. Do not write any formulas, describe your ideas in language.  

(10) Consider the context of selecting the best attribute for decision tree construction. Explain briefly the difference between “information gain” and “gain ratio” metrics for selecting the best attributes.  Is any one of these two better than the other – explain why? Do not write any formulas. Explain in language only.

Answer the following in the context of the Adaboost algorithm. (No formulas, only language description). (a) (4) Which points are given higher/lower weights after learning each weak-classifier?   (b) (4) How is the weight for each data point used by the algorithm?   (c) (4) How do we assign weights to weak classifiers for their contribution in the global decision?