Circular Functions Exam Rehearsal

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

If and < 0, the value of is:

(a) (b) (c) (d)

If , what is the minimum value of y?

If , find the value(s) of ?

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?

(c) For how many hours, between t = 0 and t = 12 is the tide at least 7 feet deep?

(b) How long is it between one high tide and the next?

Combinatorics Exam Rehearsal

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)

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

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:

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:

(a) How many groups of 3 chairs can be chosen from 7 chairs if the chairs are all different colours?

(c) How many different ways can the chairs in (b) above be arranged in a circle?

(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.)