Honors Discrete Chapter 9 Test Review Guide



Honors Discrete Chapter 9.1 and 9.3 Test Review Guide

9.1 - Recursive Sequences:

▪ Identify the pattern of a sequence

o Write the recursive rule and seed

▪ Find a future terms in the sequence

o Using recursive rule with …

▪ first previous term (an-1),

▪ second previous term (an-2), or

▪ term location (n).

9.3 - Gnomons:

▪ Solve problems with Similar Shapes

▪ Solve for the measurements of a gnomon

▪ Create proportions for corresponding sides

9.1 - Fibonacci Sequence:

Recursive Rule: FN = FN-1+ FN-2

Seed: F1 = 1 and F2 = 1

▪ Binet’s Formula:

[pic]

▪ Find any term in the Fibonacci Sequence

▪ Operations with Fibonacci Numbers

Test Practice Problems

1) Find the RECURSIVE RULE and the SEED for each sequence. (Use Correct Notation)

▪ Provide the NEXT TERM of the sequence as well.

a) 4, -12, 36, -108, 324, …

b) 17, 33, 65, 129, 257, …

c) 29, 12, -5, -22, -39, …

2) For the given recursive rule and seed, write the FIRST 5 TERMS of the sequence.

a) an = 2(an-1) - 1

a1 = 5

b) an = - 1/3 (an-1)

a1 = -2916

c) an = (n-1) (an-1)

a1 = 5

d) an = 3(an-1) - 2(an-2)

a1 = 4 and a2 = 3

e) an = (an-1)(an-2)

a1 = -2 and a2 = 7

f) an = an-2 – an-1

a1 = 9 and a2 = 2

3) Use the FIBONACCI SEQUENCE to compute each of the following:

a) F9

b) 3 F108 - 99

c) F8 + F10

d) [pic]

e) [pic]

f) F15 /5

g) 4F7 - 9

h) F24

4) C is a circle with circumference 12π and area 36π. If C’ is 2.5 times larger than circle C, then what is the circumference and area of C’?

5) R is a 6 by 9 rectangle. Suppose R’ is a 8.4 by 12.6 rectangle. Is R’ similar to R? Provide support with calculations for your response.

6) For the original picture LEFT:

a) Find the value of x so that the shaded rectangle is a gnomon to the white rectangle (15 by 25).

b) What is the area of the shaded region?

7) For the original picture RIGHT:

a) Find the value of x so that the shaded region is a gnomon to the white square that is 8 by 8.

b) What is the area of the shaded region?

8) Pictured LEFT: Find the value of x and y so that the shaded triangle is a gnomon to the white triangle.

9) Pictured RIGHT: Given the white triangle T and the shaded region gnomon G, find the value of x, y, and z such that G&T is 3.5 times larger than T.

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15

25

x

2

5

x

4

8

6

4

x

y

3

4

5

z

x

y

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