Ultimate High School Math Trivia

1) Which pair of terms are like terms?

2x & 2x^2

2 & 3x

2x & 6x

3z & 2x

The pair of terms "2x" and "6x" are like terms because they both have the same variable "x" raised to the first power. The coefficients (2 and 6) can be different, but as long as the variables and their exponents are the same, the terms are considered like terms.

Explanation

The pair of terms "2x" and "6x" are like terms because they both have the same variable "x" raised to the first power. The coefficients (2 and 6) can be different, but as long as the variables and their exponents are the same, the terms are considered like terms.

2) What is 6x - 2 + 3x simplified?

7x

11x

3x - 2

9x - 2

The expression 6x - 2 + 3x can be simplified by combining like terms. The like terms in this expression are the terms with x, which are 6x and 3x. Combining these terms gives us 9x. The constant term in the expression is -2. Therefore, the simplified form of the expression is 9x - 2.

Explanation

The expression 6x - 2 + 3x can be simplified by combining like terms. The like terms in this expression are the terms with x, which are 6x and 3x. Combining these terms gives us 9x. The constant term in the expression is -2. Therefore, the simplified form of the expression is 9x - 2.

3) Which number is both prime and odd?

9

21

15

7

The number 7 is both prime and odd. A prime number is a number that is only divisible by 1 and itself, and 7 satisfies this condition. Additionally, 7 is odd because it is not divisible by 2. Therefore, 7 is the correct answer to the question.

Explanation

The number 7 is both prime and odd. A prime number is a number that is only divisible by 1 and itself, and 7 satisfies this condition. Additionally, 7 is odd because it is not divisible by 2. Therefore, 7 is the correct answer to the question.

4) If we have two unknowns, how many equations do we need to solve for both of them?

2

4

3

1

To solve for two unknowns, we need two equations. Each equation provides a relationship between the unknowns, and by solving the system of equations, we can determine the values of the unknowns. Having fewer than two equations would not provide enough information to solve for both unknowns accurately. Having more than two equations may result in redundancy or inconsistency, making it unnecessary or impossible to find a unique solution. Therefore, two equations are necessary to solve for both unknowns.

Explanation

To solve for two unknowns, we need two equations. Each equation provides a relationship between the unknowns, and by solving the system of equations, we can determine the values of the unknowns. Having fewer than two equations would not provide enough information to solve for both unknowns accurately. Having more than two equations may result in redundancy or inconsistency, making it unnecessary or impossible to find a unique solution. Therefore, two equations are necessary to solve for both unknowns.

5) To evaluate (3^2)(3^7), what do you do to the exponents?

Add

Multiply

Divide

Subtract

To evaluate (3^2)(3^7), you need to multiply the base, which is 3, and add the exponents, which are 2 and 7. This can be done by adding the exponents together, resulting in 3^9.

Explanation

To evaluate (3^2)(3^7), you need to multiply the base, which is 3, and add the exponents, which are 2 and 7. This can be done by adding the exponents together, resulting in 3^9.

6) What is the base in the binary numeration system?

10

8

16

2

The base in the binary numeration system is 2. In binary, only two digits, 0 and 1, are used to represent numbers. Each digit's value is a power of 2, with the rightmost digit representing 2^0, the next digit representing 2^1, and so on. This system is commonly used in computer science and digital electronics, as it aligns with the binary nature of electronic circuits.

Explanation

The base in the binary numeration system is 2. In binary, only two digits, 0 and 1, are used to represent numbers. Each digit's value is a power of 2, with the rightmost digit representing 2^0, the next digit representing 2^1, and so on. This system is commonly used in computer science and digital electronics, as it aligns with the binary nature of electronic circuits.

7) What numbers are added when like variable terms are combined?

Variables

Integers Only

Numerical Coefficients

Exponents

When like variable terms are combined, the numbers that are added are the numerical coefficients. Numerical coefficients refer to the numbers that are multiplied by the variables in a term. For example, in the expression 3x + 2y, the numerical coefficients are 3 and 2. When like terms with the same variables are combined, the numerical coefficients are added together.

Explanation

When like variable terms are combined, the numbers that are added are the numerical coefficients. Numerical coefficients refer to the numbers that are multiplied by the variables in a term. For example, in the expression 3x + 2y, the numerical coefficients are 3 and 2. When like terms with the same variables are combined, the numerical coefficients are added together.

8) To evaluate (x^9)/(x^3), what do you do to the exponents?

Subtract

Multiply

Divide

Add

To evaluate (x^9)/(x^3), you divide the exponents. In this case, you subtract the exponent of x^3 from the exponent of x^9. This can be done because when you divide two numbers with the same base, you subtract the exponents. Therefore, the correct answer is to subtract the exponents.

Explanation

To evaluate (x^9)/(x^3), you divide the exponents. In this case, you subtract the exponent of x^3 from the exponent of x^9. This can be done because when you divide two numbers with the same base, you subtract the exponents. Therefore, the correct answer is to subtract the exponents.

9) What do we call the combination of the rational and irrational numbers?

Natural Numbers

Real Numbers

Integers

Whole Numbers

The combination of rational and irrational numbers is referred to as real numbers. Rational numbers are those that can be expressed as a fraction or a ratio of two integers, while irrational numbers cannot be expressed as a fraction and have non-repeating decimal representations. Real numbers encompass both rational and irrational numbers, making it the correct answer.

Explanation

The combination of rational and irrational numbers is referred to as real numbers. Rational numbers are those that can be expressed as a fraction or a ratio of two integers, while irrational numbers cannot be expressed as a fraction and have non-repeating decimal representations. Real numbers encompass both rational and irrational numbers, making it the correct answer.

10) What do we call a System of Equations that doesn't have a solution?

Coincident

Inconsistent

Independent

Consistent

A system of equations that doesn't have a solution is called inconsistent. This means that the equations in the system do not intersect and cannot be satisfied simultaneously. In other words, there are no values for the variables that can make all the equations true at the same time.

Explanation

A system of equations that doesn't have a solution is called inconsistent. This means that the equations in the system do not intersect and cannot be satisfied simultaneously. In other words, there are no values for the variables that can make all the equations true at the same time.

11) What is 90 degrees in terms of pi?

Pi

2(pi)

Pi/2

Pi/4

The angle measurement of 90 degrees is equivalent to pi/2 radians. Radians are a unit of measurement for angles that are based on the radius of a circle. In a complete circle, there are 2(pi) radians, so 90 degrees, which is a quarter of a circle, is equal to pi/2 radians.

Explanation

The angle measurement of 90 degrees is equivalent to pi/2 radians. Radians are a unit of measurement for angles that are based on the radius of a circle. In a complete circle, there are 2(pi) radians, so 90 degrees, which is a quarter of a circle, is equal to pi/2 radians.

12) If f(x) = 3^x, what is f(-2)?

9

3

9-Jan

3-Jan

The given function is f(x) = 3^x. To find f(-2), we substitute -2 for x in the function. Therefore, f(-2) = 3^(-2). When a number is raised to a negative exponent, it is equal to 1 divided by that number raised to the positive exponent. So, 3^(-2) = 1/(3^2) = 1/9. Therefore, the answer is 9-Jan.

Explanation

The given function is f(x) = 3^x. To find f(-2), we substitute -2 for x in the function. Therefore, f(-2) = 3^(-2). When a number is raised to a negative exponent, it is equal to 1 divided by that number raised to the positive exponent. So, 3^(-2) = 1/(3^2) = 1/9. Therefore, the answer is 9-Jan.

13) When working with a function such as f(x) = x, what are all the possible values of f(x) called?

Range

Extended Numbers

Domain

Real Numbers

The range of a function refers to all the possible values of the output or the dependent variable. In the given function f(x) = x, the output values are equal to the input values, which means the range includes all real numbers. Therefore, the correct answer is "Range."

Explanation

The range of a function refers to all the possible values of the output or the dependent variable. In the given function f(x) = x, the output values are equal to the input values, which means the range includes all real numbers. Therefore, the correct answer is "Range."

14) If two equations with two variables are to be solved together, what are they called?

Differential Equations

Simultaneous Equations

Parametric Equations

Linear Equations

When two equations with two variables are solved together, they are referred to as simultaneous equations. This term is used because the equations are solved simultaneously, meaning they are considered together as a system and the goal is to find the values of the variables that satisfy both equations at the same time. Simultaneous equations are commonly used in various fields of mathematics, physics, and engineering to model and solve real-world problems involving multiple variables.

Explanation

When two equations with two variables are solved together, they are referred to as simultaneous equations. This term is used because the equations are solved simultaneously, meaning they are considered together as a system and the goal is to find the values of the variables that satisfy both equations at the same time. Simultaneous equations are commonly used in various fields of mathematics, physics, and engineering to model and solve real-world problems involving multiple variables.

15) What is the additive identity?

0

1

-1

Reciprocal

The additive identity refers to the number that when added to any other number, it does not change the value of that number. In other words, it is the number that acts as a neutral element under addition. In this case, the correct answer is 0 because when 0 is added to any number, the result is always that number.

Explanation

The additive identity refers to the number that when added to any other number, it does not change the value of that number. In other words, it is the number that acts as a neutral element under addition. In this case, the correct answer is 0 because when 0 is added to any number, the result is always that number.