Remember - show your work! Some of the answers are on the last page - what we want to see is all your work. Otherwise you may find things written in the "Needs Corrections" Box. @ 1. a) Define a fractal. b) Use the definition and defining nature of a fractal to create your own fractal pattern. Include its original iteration (shape) and the first and second iterations. 2. For the fractal below, the lengths of the sides of each new square formed is halved after each iteration. -8 cm -8 cm Iteration 0 Iteration I Iteration 2 (Original) a) The area of each new smaller square formed in iteration 3 and 4 is _ cm and _ CHI. b) The number of new smaller squares added in iteration 3 and 4 is and Page 13. The diagrams below show the first two iterations of a fractal pattern. In each consecutive iteration, B new circles are drawn around the circles created in the previous iteration. The radius of the original circle is 2 cm and in the next iteration, the circles will have a radius of % the previous iteration. Original Pattern Iteration I Beration 2 a) For this fractal pattern, draw Iteration 2 above. b) Fill in the table completely and then answer the following question. Iteration Radius of Number Area of Newest Circle Area Added Total Area of All Number Newest of Circles Circles in the Circle Newest In cm- Fractal (cm) Circles In cm Original 2 cm (2) =12.5664 12.5664 cm 1 1 cm 8 *(1) =3.1416 8 x 3.1416= 25.1328 37.6992 cm 3 c) What is the total number of new circles created in iteration 6? 4. Name the four conics formed by the intersection of a plane with the cone shown below. Conic Sections5. Use the locus definition of a circle and the distance formula to find the radius of the circle below. P( 2, 3.4641) 6. The sum of the focal radii of an ellipse is 10, and the foci are at (-4,0) and (4,0) as shown below. Only one of the points below is on the graph of this ellipse. Use the locus definition and the distance formula to determine which ONE is on P(0.8)1 7 this ellipse. Q(1,5) P(0,8) F (-4,0) F (4.0) R(5,0) or Q(1,5) or R(5,0) 7. In the hyperbola shown below, one focus is at F1(-2,12) and the other at F2(-2,-8). The points A(-2,8) and B(-2,-4) he on the graph of the hyperbola. F, (-2.12) Use the locus definition of a hyperbola and A(-2.8) either point A or B to determine the difference in the distance from any point on this hyperbola to each foci. Difference = Page 3TRANSFORMATIONS - REVIEW ASSIGNMENT 8. Construct the perpendicular bisector to the line segment below. Leave all construction lines and curves in your final answer. 9. Construct the angle bisector to the angle below. Leave all construction lines and curves in your final answer. 10. Construct a pentagon inside a circle with a radius of 4cm. (Draw the circle lightly and erase it after the polygon has been constructed) Use the formula _ = 2r sin 180 to find the length of each side of your pentagon. Page 4TRANSFORMATIONS - REVIEW ASSIGNMENT 11. What is a correct naming of the tessellation below? 12. Construct a tangent to the circle below, going through point P. Leave all construction lines and curves in your final answer. 13. Construct a tangent to the parabola helow, going through print P. leave all construction lines and curves in your final answer. P Page 5TRANSFORMATIONS - REVIEW ASSIGNMENT 14. In the diagram Ofand OC are both radius' of the circle, while AB and CBare tangents to the circle. 18 B 0 24 Find the values of x and y