Download Chapter 6 Practice Test

Chapter 6 Practice Test
For questions 1 to 5, select the best answer.
1. Which is a recursion
f (n)
formula for the
sequence shown?
12
A f (n) 5 f (n  1)  4
B f (n) 5 4n  2
C f (n) 5 2  (n  1)(4)
D f (1) 5 2,
6. Determine the first five terms of each
sequence. Graph the sequence and state
whether it is arithmetic, geometric, or
neither.
8
a) tn 5 9  5n
4
b) f (n) 5 2n2  3n  4
_1 (4)
c) f (n) 5
0
2
4
n
f (n) 5 f (n  1)  4
2. Which expressions represent the missing
terms in the binomial expansion shown?
(x  y)7 5 x7  7x 6y  ■  35x 4y 3  35x 3y 4
 21x2y 5  ■  y7
n1
8
d) tn 5 0.2n  0.8
n4
e) tn 5 __
2
f) f (n) 5 3(2)n
7. Write an explicit formula and a recursion
formula for each sequence.
a) 64, 32, 16, 8, …
A 21y 5x2, 7yx 6
b) 20, 17, 14, 11, …
B 21x 5y 2, 7xy 6
c) 80, 76, 72, 68, …
C 21x 5y 2, 7xy 6
d) 4000, 1000, 250, 62.5, …
D x 5y 2, xy 6
e) 3, 6, 12, 24, …
3. What is the formula for the general term of
an arithmetic sequence with a 5 8 and
d 5 2?
A tn 5 2  (n  1)(8)
B tn 5 8  (n  1)(2)
C tn 5 8  (n  1)(2)
D tn 5 2  (n  1)(8)
4. What are the first three terms of a
geometric sequence with a 5 3 and r 5 2?
A 3, 5, 7
__
__
a) 6, 10, 14, 18, …
b) 3, 6, 12, 24, …
c) 5, 10, 20, 40, …
d) 5, 10, 15, 20, …
9. Given the explicit formula, write t15 for
each sequence.
a) f (n) 5 2(3)n  1
b) tn 5 25n  50
C 3, 6, 12
c) tn 5 10(0.1)2n
D 2, 5, 8
d) f (n) 5
geometric?
A 9  15  21  27  ...
B 1  8  27  64  ...
C 64  32  16  8  ...
__
8. Write t11 for each sequence.
B 2, 6, 18
5. Which series is neither arithmetic nor
__
f) 12 2 , 10 2 , 8 2 , 6 2 , ...
3n
_
4
10. Determine the number of terms in each
sequence.
a) 5, 8, 11, …, 62
b) 4, 12, 36, …, 19 131 876
D 3  2.7  2.4  2.1  ...
412 MHR • Functions 11 • Chapter 6
Functions 11 CH06.indd 412
6/10/09 4:21:10 PM
11. A new lake is being excavated. One day,
19. In the arrangement of letters shown,
1.6 t of material is removed from the lake
bed. On each of 10 days after that, 5%
more is removed.
starting from the top, proceed to the
row below by moving diagonally to the
immediate right or left. Determine the
number of different paths that will spell
the name PASCAL.
a) Write the first three excavation amounts
as a sequence.
P
b) Write a recursion formula to represent
A
the amount removed each day. Use this
to determine the amount removed on
the fifth day.
S
C
A
12. Determine the specified sum for each
L
series.
a) S10 for 200  100  50  ...
b) S18 for 12  5  2  ...
15. Use Pascal’s triangle to help you expand
each expression.
a) (b  3)5
23. A magic square is an arrangement of
numbers in which all rows, columns,
and diagonals have the same sum. Using
the magic square shown, substitute each
number with the corresponding term from
the Fibonacci sequence.
b) 25
17. Determine the sum of the first 15 terms
of an arithmetic series if the middle term
is 92.
L
in the first year and 10% every year after
that. How much will it be worth 8 years
after it is bought?
is 32. Determine the fourth term if the sum
of the first four terms is
reasoning.
A 5 502  492  482  472  ...  22  12
B 5 50  49  48  47  ...  2  1
L
22. A sailboat worth $140 000 depreciates 18%
b) (2x  5y)6
18. Which is greater, A or B? Explain your
L
A
and the 14th term is 122. Determine the
sum of the first 30 terms.
16. The sum of the first three terms of a series
a) 40
L
C
A
21. In an arithmetic series, the 4th term is 62
14. Determine the sum of each geometric
series.
8
4
2
a) _  _  _  ...  6912
81
27
9
b) 5  10  20  ...  2560
L
C
A
every year in a city that experiences a lot
of hot, sunny days. What percent of colour
will a fence in this city have 6 years after
being stained?
series.
b) 8  24  40  ...  280
C
A
S
20. A new wood stain loses 6.5% of its colour
13. Determine the sum of each arithmetic
a) 120  110  100  ...  250
A
S
2
7
6
9
5
1
4
3
8
Show that the sum of the products of the
rows is equal to the sum of the products of
the columns.
Chapter 6 Practice Test • MHR 413
Functions 11 CH06.indd 413
6/10/09 4:21:11 PM