1.
What is the cardinality of the empty set?
Correct Answer
A. 0
Explanation
The cardinality of a set refers to the number of elements it contains. The empty set, also known as the null set, is a set that does not contain any elements. Therefore, the cardinality of the empty set is 0, as there are no elements to count.
2.
If lnl = 8, which integer/s can replace it n?
Correct Answer
D. Both a and c
Explanation
The given equation lnl = 8 implies that the natural logarithm of n is equal to 8. The natural logarithm of a negative number does not exist, so the integer -8 cannot replace n. However, the natural logarithm of 1 is 0, so the integer 0 can replace n. Additionally, the natural logarithm of 8 is not equal to 8, but it is a valid solution. Therefore, both -8 and 8 can replace n in the equation.
3.
Which of the following is not a subset of set A = {1, 4, 9, 16, 25}?
Correct Answer
C. {1, 2, 3, 4, 5}
Explanation
The set {1, 2, 3, 4, 5} is not a subset of set A = {1, 4, 9, 16, 25} because it contains elements that are not present in set A. Set A only contains the squares of the numbers 1, 2, 3, 4, and 5, while the set {1, 2, 3, 4, 5} includes additional numbers that are not squares of the given numbers.
4.
Which of the following is an infinite set?
Correct Answer
C. The set of natural numbers
Explanation
The set of natural numbers is an infinite set because it includes all positive whole numbers starting from 1 and continuing indefinitely. There is no largest natural number, so the set does not have an endpoint and can be considered infinite. The empty set and universal set are both finite sets, as they have a specific number of elements or include all possible elements, respectively. Therefore, the correct answer is the set of natural numbers.
5.
Which of the following statements is false?
Correct Answer
B. All fractions are rational.
Explanation
The statement "All fractions are rational" is false because there are fractions that are not rational, such as irrational numbers like âˆš2 or Ï€. Rational numbers can be expressed as a ratio of two integers, while fractions can have a numerator and denominator that are not both integers. Therefore, not all fractions are rational.
6.
Think of x as a real number. Which of the following numbers when added to x gives x?
Correct Answer
A. 0
Explanation
When 0 is added to any real number x, the sum will always be x. This is because the additive identity property states that any number plus 0 is equal to that number. Therefore, 0 is the correct answer as it satisfies the condition of adding to x and giving x as the result.
7.
What system of measurement is internationally recognized and widely used by nearly all countries in the world?
Correct Answer
D. International System of Units or SI
Explanation
The International System of Units or SI is internationally recognized and widely used by nearly all countries in the world. It is a decimal-based system of measurement that provides a uniform and consistent way to measure physical quantities such as length, mass, time, and temperature. The SI system is based on seven base units, including the meter, kilogram, second, ampere, kelvin, mole, and candela. It is used in various fields such as science, engineering, and commerce, allowing for easy communication and standardization of measurements across different countries and industries.
8.
Which of the following is not a unit of volume?
Correct Answer
A. Ha
Explanation
The correct answer is "ha" because it is not a unit of volume. "ha" is actually a unit of area, specifically hectare, which is commonly used to measure land area. Volume, on the other hand, is a measure of the amount of space occupied by an object or substance. The other options - cubic inches, liters, and cubic meters - are all units of volume commonly used in different contexts.
9.
What property is illustrated by the equation (5)(3+4)=(5)(3)+(5)(4)?
Correct Answer
B. Distributive property
Explanation
The equation (5)(3+4)=(5)(3)+(5)(4) demonstrates the distributive property. This property states that when multiplying a number by a sum, you can distribute the multiplication to each term inside the parentheses. In this equation, the number 5 is being multiplied by the sum (3+4), and the distributive property allows us to multiply 5 by each term inside the parentheses separately, resulting in (5)(3)+(5)(4).
10.
An electric fan has a power rating of 65 W. If it is used for 3 hours, what is the electric consumption?
Correct Answer
A. 0.195 kWh
Explanation
The electric consumption can be calculated by multiplying the power rating of the fan (65 W) by the time it is used (3 hours). This gives us a total energy consumption of 195 Wh. To convert this to kilowatt-hours, we divide by 1000, resulting in 0.195 kWh.
11.
What is the degree of the polynomial x^{3} - 9x^{2}y + 7xy^{2} + y^{5}?
Correct Answer
C. 5
Explanation
The degree of a polynomial is determined by the highest power of the variable in the polynomial. In this case, the highest power of the variable "y" is 5, so the degree of the polynomial is 5.
12.
Which of the following is not a term in the expansion of (x + y + 3)^{2}?
Correct Answer
B. 6xy
Explanation
In the expansion of (x + y + 3)2, all the terms are obtained by multiplying the terms in the two brackets. The term 6xy cannot be obtained because there is no term in the other bracket that contains both x and y. Therefore, 6xy is not a term in the expansion.
13.
Which of the following represents the algebraic expression 5(x - y)?
Correct Answer
D. Five times the difference of x and y
Explanation
The correct answer is "five times the difference of x and y". This is because the given algebraic expression, 5(x - y), represents the product of 5 and the difference between x and y. In other words, it is five times the difference of x and y.
14.
Which of the following is a/are solution/s to the equation x^{3} - x = 0?
Correct Answer
D. All of the above
Explanation
The equation x^3 - x = 0 can be factored as x(x^2 - 1) = 0. This equation is satisfied when x = 0, x = 1, and x = -1. Therefore, all of the given options (-1, 0, and 1) are solutions to the equation.
15.
Which of the following equations is not equivalent to 3 + 2x = 1?
Correct Answer
C. 1 = 3 - 2x
Explanation
The equation 1 = 3 - 2x is not equivalent to 3 + 2x = 1 because the terms are rearranged in a different order. In the original equation, the constant term is on the right side, while in the given equation, the constant term is on the left side. Additionally, the sign of the coefficient of x is different in the two equations.
16.
If the sum of the measures of two angles is 90 degrees, what do you cal the two angles?
Correct Answer
D. Complementary angles
Explanation
If the sum of the measures of two angles is 90 degrees, they are called complementary angles. Complementary angles are a pair of angles that add up to form a right angle. In this case, since the sum of the measures of the two angles is 90 degrees, they are considered complementary angles.
17.
If angles form a linear pair, which of the following statements is true?
Correct Answer
B. They are adjacent and supplementary.
Explanation
When angles form a linear pair, it means that they are adjacent, which means they share a common vertex and side. Additionally, they are supplementary, which means that their measures add up to 180 degrees. Therefore, the correct statement is that they are adjacent and supplementary.
18.
How many diagonals can be drawn in a dodecagon?
Correct Answer
D. 54
Explanation
A dodecagon is a polygon with 12 sides. To find the number of diagonals that can be drawn in a dodecagon, we can use the formula n(n-3)/2, where n is the number of sides of the polygon. Plugging in 12 for n, we get 12(12-3)/2 = 12(9)/2 = 108/2 = 54. Therefore, the correct answer is 54.
19.
What do you call a data set presented in a tabular form?
Correct Answer
C. Frequency distribution
Explanation
A data set presented in a tabular form is commonly known as a frequency distribution. This type of representation organizes data into categories or intervals and displays the number of occurrences or frequency of each category. It provides a clear and organized way to analyze and understand the data, making it easier to identify patterns, trends, and outliers. A frequency distribution is widely used in statistics and data analysis to summarize and present data in a meaningful way.
20.
Which of the following measures divides a given data set such that half of the data is greater than it and the other half is less than it?
Correct Answer
A. Mean
Explanation
The mean is calculated by summing all the values in a data set and dividing by the total number of values. It represents the average value of the data set. However, it does not necessarily divide the data set into half. Therefore, the correct answer is not mean.