1.
If (1/3)y + 9 = 0, then y =
Correct Answer
A. -27
Explanation
To find the value of y, we can start by isolating the variable. We can begin by subtracting 9 from both sides of the equation: (1/3)y = -9. Next, we can multiply both sides by 3 to eliminate the fraction: y = -27. Therefore, the correct answer is -27.
2.
In the figure above, P, Q, and R lie on the same line. P is the center of the larger circle, and Q is the center of the smaller circle. If the radius of the larger circle is 4, what is the radius of the smaller circle?
Correct Answer
B. 2
Explanation
Since P is the center of the larger circle and Q is the center of the smaller circle, the line connecting P and Q is the line passing through the centers of both circles. Since P, Q, and R lie on the same line, R must also lie on this line. Therefore, the line connecting P and R is also the line passing through the centers of both circles. Since the radius of the larger circle is 4, the distance between P and R is 8. Since the radius of a circle is half of its diameter, the radius of the smaller circle is half of 8, which is 4. Therefore, the radius of the smaller circle is 2.
3.
Roy planted corn on 1/5 of his land. If he planted 45 acres of corn, how many acres of land does he have?
Correct Answer
D. 225
Explanation
If Roy planted 45 acres of corn, which represents 1/5 of his land, we can determine the total number of acres he has by multiplying 45 by 5. This calculation gives us 225 acres, which is the correct answer.
4.
6, 10, 18, 34, 66
The first number in the list above is 6. Which of the following gives a rule for finding each successive number in the list?
Correct Answer
C. Double the preceding number and then subtract 2 from that result.
Explanation
Each number in the list is obtained by doubling the preceding number and then subtracting 2 from that result. Starting with 6, doubling it gives 12, and then subtracting 2 gives 10. Continuing this pattern, we get 18, 34, and 66.
5.
The two semicircles in the figure above have centers R and S, respectively. If RS = 12, what is the total length of the darkened curve?
Correct Answer
C. 12Ï€
Explanation
The total length of the darkened curve can be found by adding the circumference of both semicircles. Since the radius of each semicircle is not given, we cannot determine the exact length. However, we do know that RS = 12, which means the distance between the centers of the semicircles is 12. Therefore, the total length of the darkened curve is equal to the circumference of one semicircle plus the circumference of the other semicircle, which is equal to 2Ï€r + 2Ï€r = 4Ï€r. Since the radius is not given, we cannot determine the exact length, but it will be equal to 12Ï€.
6.
If h and k are positive numbers and h + k = 7, then (7 - k)/h =
Correct Answer
A. 1
Explanation
Given that h and k are positive numbers and h + k = 7, we can substitute the value of h + k into the expression (7 - k)/h. This gives us (7 - k)/h = (7 - k)/(7 - h). Simplifying this expression further, we get (7 - k)/(7 - h) = 1. Therefore, the correct answer is 1.
7.
The table above shows the populations of two
countries and their population densities. The
number of square miles in the area of Country B
is approximately how much greater than the
number of square miles in the area of Country A ?
Correct Answer
D. 8,000
Explanation
Country B has a population density of 200 people per square mile. The number of square miles in the area of Country B is approximately 8,000 greater than the number of square miles in the area of Country A.
8.
If x^{2} = x + 6, which of the following must be true?
Correct Answer
E. X^2 > x
Explanation
If x^2 = x + 6, then rearranging the equation we get x^2 - x - 6 = 0. Factoring this quadratic equation, we have (x - 3)(x + 2) = 0. Therefore, the solutions for x are x = 3 and x = -2. By substituting these values into the inequality x^2 > x, we find that x = 3 satisfies the inequality, but x = -2 does not. Hence, x^2 > x must be true.
9.
Let the functions f be defined by f(x) = 5x - 2a, where a is a constant. If f(10) + f(5) = 55, what is the value of a?
Correct Answer
C. 5
Explanation
The given question states that the sum of f(10) and f(5) is equal to 55. Substituting the values of x into the function, we get 5(10) - 2a + 5(5) - 2a = 55. Simplifying this equation, we have 50 - 2a + 25 - 2a = 55. Combining like terms, we get 75 - 4a = 55. Solving for a, we subtract 75 from both sides and divide by -4, giving us a = 5.
10.
A number is called “even-odd” if it is halfway between
an even integer and an odd integer. If x is an even-odd
number, which of the following must be true?
I. 2x is an integer.
II. 2x is even-odd.
III. x is halfway between two even integers.
Correct Answer
A. I only
Explanation
If x is an even-odd number, it means that x is halfway between an even integer and an odd integer. Since an even integer multiplied by 2 is always an integer, statement I must be true. However, statement II cannot be determined because it is not specified whether multiplying x by 2 will still result in a number that is halfway between an even and odd integer. Statement III cannot be determined either because it is not specified whether x is exactly halfway between two even integers or if it is closer to one of them.
11.
If m is a positive integer, which of the following is NOT equal to (2^{4})^{m} ?
Correct Answer
D. 4^m(2^m)
Explanation
The expression (24)m can be simplified to 2^(4m), which means that it is equal to 2 raised to the power of 4m. Looking at the answer choices, all of them involve raising 2 to some power except for 4^m(2^m). This expression involves multiplying 4^m and 2^m together, which is not equivalent to 2^(4m). Therefore, 4^m(2^m) is NOT equal to (24)m.
12.
In the figure above, l || m. Which of the following must equal 180?
Correct Answer
B. K + p + s
Explanation
Since l || m, we can conclude that the angles formed by the transversal line are congruent. Therefore, the sum of the angles k, p, and s must equal 180 degrees.
13.
How many different ordered pairs (x, y) are there such that x is an even integer, where 4 ≤ x ≤ 10, and y is an integer, where 4 < y < 10 ?
Correct Answer
C. 20
Explanation
There are 4 even integers between 4 and 10, which are 4, 6, 8, and 10. There are 5 integers between 4 and 10, which are 5, 6, 7, 8, and 9. Therefore, there are 4 even integers for each integer between 4 and 10, resulting in a total of 4 * 5 = 20 different ordered pairs (x, y).
14.
N(t) = 500(0.81)^{t}
The function above can be used to model the population of a certain endangered species of animal. If n(t) gives the number of the species living t decades after the year 1900, which of the following is true about the population of the species from 1900 to 1920 ?
Correct Answer
C. It decreased by about 180.
Explanation
The function n(t) = 500(0.81)t represents the population of the species t decades after the year 1900. Since we are interested in the population from 1900 to 1920, we can substitute t = 2 into the equation.
n(2) = 500(0.81)2
n(2) = 500(0.6561)
n(2) â‰ˆ 328.05
Therefore, the population decreased by about 180 individuals from 1900 to 1920.
15.
A sphere of radius r inside a cube touches each one
of the six sides of the cube. What is the volume of the
cube, in terms of r ?
Correct Answer
E. 8r^3
Explanation
The cube has a side length equal to twice the radius of the sphere. Since the sphere touches each side of the cube, the diagonal of the cube is equal to the diameter of the sphere. Using the Pythagorean theorem, we can find that the diagonal of the cube is equal to 2âˆš3 times the side length of the cube. Therefore, the side length of the cube is equal to râˆš3. The volume of the cube is then (râˆš3)^3 = 27r^3. Simplifying, we get the answer of 8r^3.
16.
According to the graph above, in which year was the
ratio of the number of students enrolled at School B
to the number of students enrolled at School A the
greatest?
Correct Answer
E. 1994
Explanation
Based on the graph, the ratio of the number of students enrolled at School B to the number of students enrolled at School A is highest in the year 1994.