1. a Physical Fitness Centre Charges $100 for an Annual Membership and $5 Per Visit. Find The

1.  A physical fitness centre charges $100 for an annual membership and $5 per visit. Find the

rule of:

a) The function which gives the total cost c spent during the year as a function of the

number v of visits.

b) The function which gives the number v of visits as a function of the total cost c spent

during the year.

2.  One cycle of the periodic function f is drawn.

Determine the period P and the frequency F of this function

a)  Complete the graph of f when .

b)  Determine: a) ran f. b) min.f c) max. f

c)  What are the zeros of f over the interval ?

d)  For what values of x, over the interval , does the function f reach its maximum?

e)  When x varies between 0 and 14, find the intervals over which the function f is:

a)  strictly increasing b) strictly decreasing c) constant

3.  For each of the following tables of values, find the rule of the function associated with it:

x / 0 / 1 / 2 / 3
y / 16 / 8 / 4 / 2
x / 1 / 2 / 3 / 4
y / 12 / 6 / 4 / 3

4.  A herd presently contains 7 elephants. This herd doubles every 6 years. After how many

years will the herd contain 112 elephants?

5.  A $1000 capital is invested for 5 years at an interest rate of 10% compounded twice a year. Determine the accumulated capital.

6.  A ball bounces to a height equal to 3/5 of the height reached with the previous rebound. The

ball is dropped from a 25m tall building. What height does the ball reach after the sixth

rebound?

7.  The monthly salary y of an employee depends on the amount of sales made during the month.

The function f which gives the employee’s salary has the rule:

1. Graph this function on a Cartesian plane.
2. What is the salary of an employee who makes $30 000 in sales in a month?
3. What is the amount of sales made by an employee who receives a salary of $4700?

8.  For each of the following functions, indicate if the function is increasing or decreasing:

1. b. c.

d. e. f.

9. Given two points A(-2, 1) and B(4, -3), determine:

a. the distance between A and B

b. the coordinates of point P that divides segment AB in a ratio of 2:1 from A

10. Represent the solution set of the following inequalities on a graph:

a. b.

11. The student council of a school decides to organize a car wash to raise money for their activities. It decides to charge $8 per car and $12 per van. The goal is to raise more than $600.

a. Identify the variables in this situation.

b. Write a two-variable first degree inequality which describes this situation.

c. Represent this situation on a graph.

12. Solve the following systems using an appropriate method:

a. b.

13. A group of 5 adults and 8 children must pay a total of $170 to enter an amusement park. Another group of 4 adults and 6 children must pay a total of $132 to enter the same park. How much will it cost for a group of 7 adults and 12 children to enter the park?

14. In the figure on the right, we have: ,

, . Justify the following steps

in finding th measure of . Consider triangles ABC and AED.

Statement / Justification
1. 
2. 
3. 
4. 
5. 

15. The shadow cast by a building measures 30m when the sun’s rays hit the ground at an angle of 50o. What to the nearest metre is the height of the building?

16. Solve for triangle ABC if angle A is 80o, angle B is 70o and side BC is 6cm.

17. A card is drawn from a 52-card deck. What are the chances:

a. of drawing a red card? b. of drawing a spade?

c. of drawing an ace? d. of drawing the ace of spades?

18. A quality control test is performed on a sample of ten metallic rods to verify if the diameter conforms to prescribed specifications. Here are the data (in mm):

a.  Calculate and interpret the range of the distribution.

b.  Calculate and interpret the interquartile range.

c.  Calculate and interpret the mean deviation.

19. The heights (in cm) of the 50 players from the 4 teams participating in a tournament are recorded. The data are placed in increasing order:

Calculate and interpret: a. the mean b. the median

d.  the first quartile e. the third quartile f. the interquartile interval

20. The table below gives the number of years of schooling (x) of eight people chosen at random as well as their weekly salary (y) in hundred of dollars.

a.  Draw the scatter plot on a graph.

b.  Calculate the correlation coefficient r.

c.  Is the correlation significant?

d.  Find the equation of the regression line and draw it.

e.  Estimate the weekly salary of a person with 16 yers of schooling using the regression line.