y=x² - a
In the equation above, a is a positive constant and the graph of the equation in the xy‑plane is a parabola. Which of the following is an equivalent form of the equation?

The expression above is equivalent to , where a is a positive constant and
x ≠ −2.  What is the value of a ?

x² + 20x + y² + 16y = -20
The equation above defines a circle in the xy-plane. What are the coordinates of the center of the circle?

The graph of the linear function f is shown in the xy-plane above. The slope of the graph of the linear function g is 4 times the slope of the graph of f. If the graph of g passes through the point ( 0, −4), what is the value of g(9 ) ?

The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score?

If a² + b² = z and ab = y, which of the following is equivalent to 4z + 8y ?

Intersecting lines r, s and t are shown below .

The surface area of a cube is 6(a/4)²,where a is a positive constant. Which of the following gives the perimeter of one face of the cube?

If (x, y) is a solution of the system of equations above and x > 0, what is the value of xy ?

In triangle ABC above, side AC is extended to
point D. What is the value of y-x?

Note:
It is important to know the basic properties of a triangle to solve such problems. The most important property to remember is; the sum the interior angles of a triangle is 180°. This is often used in solving problems in geometry.

A psychologist set up an experiment to study the tendency of a person to select the first item when presented with a series of items. In the experiment, 300 people were presented with a set of five pictures arranged in random order. Each person was asked to choose the most appealing picture. Of the first 150 participants, 36 chose the first picture in the set. Among the remaining 150 participants, p people chose the first picture in the set. If more than 20% of all participants chose the first picture in the set, which of the following inequalities best describes the possible values of p ?

In air, the speed of sound S, in meters per second, is a linear function of the air temperature T, in degrees Celsius, and is given by S(T)  = 0.6T + 331.4. Which of the following statements is the best interpretation of the number 331.4 in this context?

Jackie has two summer jobs. She works as a tutor, which pays $12 per hour, and she works as a lifeguard, which pays $9.50 per hour. She can work no more than 20 hours per week, but she wants to earn at least $220 per week. Which of the following systems of inequalities represents this situation in terms of x and y, where x is the number of hours she tutors and y is the number of hours she works as a lifeguard?

The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.
Townsend Realty purchased the Glenview Street property and received a 40% discount off the original price along with an additional 20% off the discounted price for purchasing the property in cash. Which of the following best approximates the original price, in dollars, of the Glenview Street property?

The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.
The relationship between the monthly rental price r, in dollars, and the property’s purchase price p, in thousands of dollars, can be represented by a linear function. Which of the following functions represents the relationship?

In a survey, 607 general surgeons and orthopedic surgeons indicated their major professional activity. The results are summarized in the table above. If one
of the surgeons is selected at random, which of the following is closest to the probability that the selected surgeon is an orthopedic surgeon whose indicated
professional activity is research?