Exam rehearsals for the units on Circular Functions and Combinatorics.

2. Circular Functions Exam Rehearsal

3. Through how many radians does the minute hand of a clock turn in 24 minutes?
(a) 0.2π (b) 0.4π (c) 0.6π (d) 0.8π

4. If and < 0, the value of is:
(a) (b) (c) (d)

5. If , what is the minimum value of y?

6. If , find the value(s) of ?

7. The tide at a boat dock can be modeled by the equation ,
where d is the depth of the water in feet.
(a) How deep is the water at high tide? low tide?
(b) How long is it between one high tide and the next?
(c) For how many hours, between t = 0 and t = 12 is the tide at least 7 feet deep?

8. Combinatorics Exam Rehearsal

9. The number of different arrangements of 3 boys and 4 girls
in a row, if the girls must stand together, is represented by:
(a) (b) (c) (d)

10. The students in a music department have practised 6 contemporary and 5
traditional choruses. For their concert, they will choose a program in which
they present 4 of the contemporary and 3 of the traditional choruses. How
many different programs can be presented, if the order of the choruses does
not matter?
(a) 25 (b) 35 (c) 150 (d) 330

11. All telephone numbers are preceded by a 3-digit area code. In the original Bell
Telephone System of assigning area codes, the first digit could be any number
from 2 to 9, the second digit was either 0 or 1, and the third digit could be any
number except 0. In this system, the number of different area codes possible was:

12. A paperboy who delivers papers on his bike
can travel only on the trails represented in the
diagram. The number of different trails
that the paperboy can take to get
from house A to house B
without backtracking is:

14. (a) How many groups of 3 chairs can be chosen from 7 chairs if the
chairs are all different colours?
(b) How many different ways can 7 chairs be arranged in a row if 2 of
the chairs are blue, 3 are yellow, 1 is red and 1 is green? (Assume that
all of the chairs are identical except for colour.)
(c) How many different ways can the chairs in (b) above be arranged in
a circle?