Good Luck To Period Date DIRECTIONS: Answer each question and show all work in the space provided. 1. Find the next two terms of the sequence. 6, 36, 216, 1296, _?_, _?_ The next two terms of the sequence are, 2. Find the next two terms of the sequence. 4, 16, 256, _?_, _?_ The next two terms of the sequence are, 3. Draw the next two terms of the sequence. 4 th Term 5 th Term Page 1 of 8
4. Draw the next term terms in the sequence. 4 th Term 5 th Term 5. Complete the table. n 1 2 3 4 5 f (n) = 5n-7 6. Complete the table. n 1 2 3 4 5 f (n) = -3n+8 Page 2 of 8
7. Complete the table by finding the rule for the nth term and the 100 th term. Term 1 2 3 4 n 100 Value 29 25 21 17 8. Complete the table by finding the rule for the nth term and the 100 th term. Term 1 2 3 4 n 100 Value 7 12 17 22 9. In the sequence below, the first term has four triangles. How many triangles are in the 6 th term? Write the nth rule for determining the number of triangles in the figure. Then use the rule to find the number of triangles in the 100 th term. Number of triangles in the 6 th term Nth rule for the number of triangles Number of triangles in the 100 th term. Page 3 of 8
10. If each team in a twelve team league plays each of the other team twice in a season, how many league games are played during the one season? Number of games played during the one season 11. The table below is used to record the number of two person conversations between n people. How many two people conversations are possible at a party of 4 people? n people? Of 200 people? People 1 2 3 4 n 200 Conversations 0 1 3... 12. Describe in words the pattern found in the following sequence. The pattern of the sequence is Page 4 of 8
13. reasoning is the process of showing that certain statements follow logically from agreed-upon assumptions and proven facts. a. Inductive b. Deductive 14. reasoning is the process of observing data, recognizing patterns, and making generalizations about those patterns. a. Inductive b. Deductive 15. When you are finding the next term in a sequence. What type of reasoning are you using? a. Inductive b. Deductive 16. A and B are supplementary. m A= 36. What is m B? What type of reasoning did you use, inductive or deductive, to solve this problem? m B Type of reasoning 17. The definition of a trapezoid says, If a quadrilateral has exactly one pair of parallel sides, then it is a trapezoid. Quadtrilateral ABCD has AB parallel to CD. What conclusion can you make about the quadrilateral. What type of reasoning did you use? Quadrilateral ABCD is a Reasoning used Page 5 of 8
18. Solve the equation for x. Give a reason for each step in the process. What type of reasoning, inductive or deductive, do you use when solving this problem? 3x+ 2( x 2) = 7+ 4x a. a. b. b. c. c. d. d. Type of reasoning used 19. The table below shows the number of diagonals of several regular polygons. Number of sides of a polygon Number of diagonals 3 4 5 6 7 8 9 0 2 5 9 14? If the pattern in the table continues, how many diagonals does a regular polygon with 9 sides have? a. 24 b. 25 c. 26 d. 27 Page 6 of 8
20. The sum of the measures of the angles of each polygon are shown below. If the patterns continues what would the sum of the measures of the angles of a hexagon be? What type of reasoning did you use? 180 360 540 Sum of the measures of a hexagon Type of reasoning used Page 7 of 8
TOPIC II ANSWER KEY Problem Number Answer Standard 1. 7776, 46656 MA.912.D.1.1 2. 65536, 4294967296 MA.912.D.1.1 3. MA.912.D.1.1 4., MA.912.D.1.1, 5. -2, 3, 8, 13, 18 MA.912.D.1.1 6. 5, 2, -1, -4, -7 MA.912.D.1.1 7. -4n+33, -367 MA.912.D.1.2 8. 5n+2, 502 MA.912.D.1.2 9. 24, 4n, 400 MA.912.D.1.2 10. 132 MA.912.D.1.1 11. 6,, 19900 MA.912.D.1.2 12. The pattern of the sequence is the number of MA.912.G.8.4 vertices of the polygon increases by one. 13. a. MA.912.D.6.5 14. b. MA.912.D.6.5 15. a. MA.912.D.6.5 16. 144, deductive MA.912.D.6.5 17. Trapezoid, Deductive MA.912.D.6.5 18. a. 3x+ 2x 4= 7+ 4x, Distributive Property b. 5x 4= 7+ 4x, Closure for Addition(Simplify by combining like terms) c. x 4= 7, Additive Property of Equality Closure MA.912.G.8.4 for Addition (Subtract from both sides) d. x = 11, Additive Property of Equality Closure for Addition (Add 2 to both sides) Deductive Reasoning 19. d. MA.912.G.8.4 20. 720, Inductive MA.912.G.8.4 Page 8 of 8