The function f has the property that, for all x , 3f(x) = f(3x). If f(6) = 12, what is the  value of f(2)?

Radioactive substances decay over time. The mass M, in grams, of a particular  radioactive substance d days after the beginning of an experiment is shown in the table below.

Number of days, d	Mass, M (grams)
0	120.00
30	103.21
60	88.78
90	76.36

If this relationship is modeled by the function M ( d) = a • 10^bd, which of the  following could be the values of a and b ?

The table below shows the number of lakes in the United Kingdom classified by  alkalinity and depth.

Depth class	Alkalinity Class
	Low	Medium	High	Total
Shallow	87	61	209	357
Moderate	227	86	110	423
Deep	130	35	21	186
Total	444	182	340	966

If a lake has high alkalinity, which of the following is closest to the probability that  the lake also has a shallow depth?

a(-3x-1) + x = 7x - 2
The equation above has no solutions, and a is a constant. What is the value of a ?

A signal from a spacecraft orbiting Mercury travels to Earth at a speed of 3 x 10⁸  meters per second. If the distance between Earth and the spacecraft is 2.0221 x 10⁸ kilometers, which of the following ·is closest to the number of minutes it will take  for a signal from the spacecraft to reach Earth?
(1 kilometer= 1,000 meters)

y = (x-h)² (x+h)(x+k)
The equation above is graphed in the xy-plane. If h and k are positive constants and  h k, how many distinct x-intercepts does the graph have?

The scatterplot above represents the salary y, in thousands of dollars, and the  number of years of experience, x, for each of six employees at a company. A line of best fit for the data is also shown. Which of the following could be an equation of the line of best fit?

x(x + 1) + 2(x + 1) = ax² +bx+ c
In the equation above, a, b, and c are constants. If the equation is true for all values  of x, what is the value of a + b + c ?

kx+ y = 1
y = -x² + k
In the system of equations above, k is a constant. When the equations are graphed  in the xy-plane, the graphs intersect at exactly two points. Which of the following  CANNOT be the value of k ?

y=x² -6x - 16
The graph of the equation above in the xy-plane is a parabola. Which of the  following equivalent forms of the equation includes the x- and y-coordinates of the  
vertex as constants?

s = 9.8t
The equation above can be used to approximate the speed s, in meters per second  (m/s), of an object t seconds after being dropped into a free fall. Which of the  following is the best interpretation of the number 9.8 in this context?

Note: Figure not drawn to scale.
In the figure above, sin(90° - x⁰) = . What is the value of sin x⁰ ?

The graph above models the speed, s, of an automobile during the first 5 minutes of travel time, t. What was the total distance traveled from t=1 to t=4?

The energy pyramid below shows four trophic levels in an ecosystem and the direction of energy transfer between those levels.

On average, 10% of the net energy of one trophic level is transferred to the next trophic level in an ecosystem. Based on the energy pyramid, if primary producers have 5,000 joules (J) of energy, approximately how much of this energy, in calories, is transferred to the secondary consumers in this ecosystem? (1 calorie= 4.18 J)

Energy flow direction within an ecosystem
1. An ecosystem's energy flow is always unidirectional.
2. It is said to be unidirectional because energy is lost in heat when moving from one trophic level to the next to maintain an organism's homeostasis.
3. As a result, each successive trophic level receives less energy than the previous trophic level.
4. Some energy is lost as heat when an organism moves from one trophic level to the next to maintain homeostasis.
5. As a result, each successive trophic level receives less energy than the previous trophic level.
6. Because the sun is the only energy source for all ecosystems on Earth, the energy flow in the food chain is unidirectional.
7. The energy captured by autotrophs does not return to the sun.
8. As a result, energy flows through various trophic levels in a food chain.
9. Energy comes from the sun and is consumed by producers in most natural ecosystems.
10. It is then passed down through the trophic levels as food.
11. As a result, energy flows from the prey to the predator rather than the other way around.

x = 3
y = x + 3
What is the solution (x, y) to the given system of equations?

A sample of 600 ninth graders was selected at random and asked how much time  they spend on homework each day. Of the ninth graders selected, 220 spend less  than 2 hours on homework each day. If the conclusion was drawn that  "approximately 1.35 million ninth graders spend less than 2 hours on homework  each day," which of the following is closest to the population, in millions, of ninth graders?