The Chess Club at Asiniboyne High School consists of 6 seniors and 11 juniors. Presently, the club president and the club secretary are both seniors. (They must be different people.) If the students were selected randomly for these offices, what is the probability both would be seniors?

a. Show how to find the answer to this question using the General Multiplication Rule for probability.

b. Show how to find the answer using the Multiplication Principle of Counting and the definition of probability.

Below are responses from two students related to the club election problems. Carefully read each student's response.

a. Analyze Amy's reasoning about the number of French Club officer selections.

There are 15 choices for President. Once the President is chosen, then there are 14 members left who could be chosen for Vice-President. Once the President and Vice-President have been chosen, then there are 13 members left who could be Treasurer. So, there are $15 \times 14 \times 13=2,730$ different possibilities for the three officers. This counts different orders as different possibilities. For example, ABC is different than BAC.

This reasoning is essentially correct. Compare Amy's reasoning and answer with yours in the earlier exercise. If necessary, revise your work.

b. Analyze Latricia's reasoning about the number of Ski Club committees.

There are 15 choices for the first committee member. This leaves 14 club members who could be chosen as the second committee member, and 13 choices for the third committee member. So far, this is $15 \times 14 \times 13$ possibilities. However, in this situation, the order doesn't matter. For example, a committee of ABC is the same as a committee of BAC. In fact, for a committee consisting of A, B, and C, there are 6 different orderings that make the same committee. So, you must divide the first calculation by 6. This gives a final answer of $\frac{15 \times 14 \times 13}{16}=455$ possible committees.

This reasoning is essentially correct. Compare Latricia's reasoning and answer to yours in the earlier exercise. If necessary, revise your work.

Suppose that you roll a regular tetrahedral die that has the letters F, N, T, and S on its faces and then spins a spinner that is divided into two equal parts with the letter O on one side and the letter Y on the other side. You make note of the letter on the bottom face of the tetrahedral die and the letter of the region in which the pointer lands.

a. Construct a sample space of all possible two-letter outcomes where the first letter is from a roll of the die and the second letter is from a spin of the spinner. What is the probability of each outcome?

b. What is the probability that your outcome spells a word?

c. What is the probability that both of the letters come before S in the alphabet?

d. What is the probability that your outcome spells a word if you spin an O?

e. Are the two events of rolling the die and spinning the spinner independent events? Explain your reasoning.

Without using technology, write a function rule that matches each description.

a. A linear function whose graph contains the points (1, 7) and (3, -5)

b. A linear function whose graph is parallel to the graph of g(x) = $\frac{1}{2} x-\frac{2}{5}$ and containing the point (7, 2)

c. A quadratic function with vertex (2, -3) and x-intercept (5, 0)

Write each product in standard polynomial form.

a. (2 x+3)(5 x-1)

b. (x$^3$ - 4)(x$^3$ + 4)

c. (x - 7)$^2$

d. (3x + 5)$^2$

e. (x + 3)(x + 8)(x + 2)

Write each product or sum as a fraction in simplest form.

a. 3/4 $\cdot$ 2/3 $\cdot$ 1/2

b. 130/405 $\cdot$ 129/404

c. 3/5 + 1/8

d. -3/4 + 3/8 + 1/2

Consider a right cylinder that has a diameter of 6 cm and a height of 12 cm.

a. Will this cylinder hold more or less than a 355-ml can of soda? (Recall that 1 ml =1 cm cubed Explain your reasoning or show your work.

b. Could you place a pencil that is 12.5 cm long completely inside this cylinder? Explain your reasoning.

In the diagram shown, l $\|$ m $\|$ n. Determine the following measures.

a. HD

b. EB

c. m$\angle$HAF

d. m$\angle$H

e. m$\angle$FEB

f. m$\angle$BED

For each function listed below, determine:

I f(x) = 2$^x$ + 3

II g(x) = 1/x + 7

III h(x) = -5x/4 + 18

IV k(x) = (x - 3)$^2$

a. the function family to which it belongs.

b. its domain and range.

In March 2011, the journal Pediatrics reported on a study of obesity in preschool-age children. Susanna Huh and her colleagues considered the relationship between obesity and the age at which formula-fed babies were introduced to solid food. There were 279 formula-fed babies in their study. Of the 91 babies who were introduced to solid food before they were four months old, 23 of them were obese at age 3. Out of the 188 babies who were introduced to solid foods after they were four months old, 12 were obese at age 3.

a. What are the two groups under study here? What is the response variable?

b. Summarize the information in a two-way table, with the numbers for each group in separate rows.

c. Compute and interpret the difference in absolute risk of obesity at age 3.

d. Compute and interpret the relative risk of obesity at age 3.

e. Write a conclusion based on this evidence.

Each of the following graphs is a transformation of the graph of f(x) = x$^2$ - 4. For each graph, describe the transformation and then write a function rule that matches the graph.

Consider the following two functions:

$$\begin{align*} & f(x)=x+a, a \neq 0 \\ & g(x)=a^x, a>0 \end{align*}$$

Determine whether each statement is true or false. Provide reasoning to support your answer.

a. 2f(x) = f(2x)

b. f(x) + 2 = f(x + 2)

c. 2g(x) = g(2x)

d. g(x + 2) = g(x) + 2

Solve each equation.

a. x/(x + 5) = 3/8

b. -5(7 - 2x) = 4 + (6x - 5)

c. (2x + 3)/4 = (x - 9)/8

d. 3/4 + 1/2 (x - 6) = 9

For each quadratic expression, find an integer value of $k$ so that the expression can be factored into a product of two binomials. Then write the factored form of your trinomial.

a. x$^2$ + 7x + k

b. x$^2$ + kx + 9

c. 2x$^2$ - 5x + k