Pure Math 30
Module 5Test
Multiple choice – select the best answer for each of the following.
1.In which quadrant does the terminal ray of a standard position angle of radians lie?
A. 1
B. 2
C. 3
D. 4
2.If , and , what is the value of ?
A.
B.
C.
D.
3.The exact value of is
A.
B.
C.
D.
4.Given the graph , where a>0, determine the value of b.
A.
B. 2
C.
D. 4
Numerical Response – record your answer in the numerical response section.
An angle in standard position has a measure of 9.6 radians. Expressed in degrees the measure of a coterminal angle between and (to the nearest whole number) would be ______.
5.Which of the following is an equation having an amplitude of 2 and a period of 3?
A.
B.
C.
D.
6.Given the graph , determine the value of d.
A.
B.
C. 7
D. 5
7.Which of the following is an equation for the sine wave graphed to the right?
A.
B.
C.
D.
8.The equation of a trigonometric function is:
, where a > 0
An expression that defines the range of this function is:
A.
B.
C.
D.
Numerical Response – record your answer in the numerical response section on the answer sheet.
On a circle of radius 4cm an arc of 18cm subtends a sector angle . The measure of to the nearest degree is ______.
9.The partial graph of a periodic function is shown to the right. For this function the range and period are respectively:
A. and
B. and
C. or and
D. or and
10.Which equation is a vertical asymptote of the graph of ?
A. x = 0
B.
C.
D.
11.The general equation of a sine function is . Which parameters in this equation could affect the - intercepts of the sine function?
A. a, b, and c
B. a, b, and d
C. b, c ,and d
D. a, c, and d
12. For state the (1) amplitude, (2) period, (3) vertical translation, and (4) phase shift.
A. (1) 8, (2) , (3) 17, (4) right
B. (1) 8, (2) , (3) 17, (4) right
C. (1) 8, (2) , (3) 17, (4) left
D. (1) 17, (2) , (3) 8, (4) right
Numerical Response – record your answer in the numerical response section.
The pedals of a bicycle are mounted on a bracket whose centre is 29.0 cm above the ground. Each pedal is 17 cm from the centre of the bracket. Assuming that the bike can be pedaled at 10 cycles per minute and that the pedal starts at time t = 0s at the topmost point, the height of the top pedal after 2.5 seconds to the nearest centimetre is ______.
Written Response
1. Write an equation of a sine function whose range is and whose period is . (2 marks)
2. Write the equation of a cosecant function with a domain of (1 mark)
3. The graph below represents a sine function that has been shifted to the right. Answer the questions below and then write the equation of the function in the form . (4 marks)
a. amplitude:
b. horizontal phase shift:
c. domain:
d. period:
e. vertical displacement:
f. range:Equation:
4. A Ferris wheel with a radius of 30m rotates once every 60 s. Passengers get on at a point 2m above the ground at the bottom of the wheel.
a. Draw a graph showing the height above the ground from t = 0s to t = 120s. (1 mark)
b. Write an expression for the function in part “a”. Use h(t) for the height and t for time and express your answer in the form . (2 mark)
c.If a person was at the bottom of the Ferris wheel when it began to move, how high off the ground will he be when the wheel has been in motion for 38 seconds to the nearest tenth. (1 mark)
Pure Math 30 Formula Sheet