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.
-----------------------
15
25
x
2
5
x
4
8
6
4
x
y
3
4
5
z
x
y
................
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