Algebra & Statistics: Key Concepts Quiz

1. What is a prime number?

A number divisible by 3 and itself, such as 6, 9, 12, 15, 18, etc.

A number divisible only by itself and 12, 3, 5, 7, 11, 13 . . .

A number divisible by 1, 2, and itself, such as 4, 6, 8, 9, 10, etc.

A number divisible by 2 and itself, such as 4, 6, 8, 10, 12, etc.

Prime numbers are integers greater than 1 that have no positive divisors other than 1 and themselves. They cannot be divided evenly by any other number except for 1 and the number itself.

Explanation

Prime numbers are integers greater than 1 that have no positive divisors other than 1 and themselves. They cannot be divided evenly by any other number except for 1 and the number itself.

2. In the number 12,408.57, what place is the number 7 in?

Thousands

Ones

Tenths

Hundredths

The correct answer is 'hundredths' because the number 7 is in the hundredths place in the decimal number 12,408.57. The hundredths place is two places to the right of the decimal point.

Explanation

The correct answer is 'hundredths' because the number 7 is in the hundredths place in the decimal number 12,408.57. The hundredths place is two places to the right of the decimal point.

3. Multiplying a negative number by a negative number always results in a ______ number.

Zero

Fraction

Positive

Negative

When two negative numbers are multiplied, they result in a positive number due to the rules of multiplication involving the signs of the numbers.

Explanation

When two negative numbers are multiplied, they result in a positive number due to the rules of multiplication involving the signs of the numbers.

4. What is a numerator?

The number on the top of a fraction

The result of subtracting two numbers.

The number on the bottom of a fraction.

A whole number.

In a fraction, the numerator is the number above the line, representing the part being considered.

Explanation

In a fraction, the numerator is the number above the line, representing the part being considered.

5. How is a decimal converted to a percent?

Add the decimal to 100. For example, 0.37 + 100 = 100.37%

Multiply the decimal by 1000.37 × 100 = 37%

Subtract the decimal from 100. For example, 100 - 0.37 = 99.63%

Divide the decimal by 100. For example, 0.37 / 100 = 0.0037%

To convert a decimal to a percent, you need to multiply the decimal by 100 to move the decimal point two places to the right, making it a percentage.

Explanation

To convert a decimal to a percent, you need to multiply the decimal by 100 to move the decimal point two places to the right, making it a percentage.

6. What is x0?

X0 = 1

X0 = 0

X0 = 2

X0 = -1

In mathematics, x0 is a variable representing the value of the variable x when it is equal to 0. Therefore, x0 = 1 means that when x is 0, the value of x0 is 1. The incorrect answers provide different values for x0 which do not align with the correct definition.

Explanation

In mathematics, x0 is a variable representing the value of the variable x when it is equal to 0. Therefore, x0 = 1 means that when x is 0, the value of x0 is 1. The incorrect answers provide different values for x0 which do not align with the correct definition.

7. What are irrational numbers?

Irrational numbers are numbers that are multiples of each other.

Irrational numbers are numbers that cannot be written as fractions.

Irrational numbers are numbers with decimal points.

Irrational numbers are numbers that can be written as ratios of integers.

Irrational numbers cannot be represented as a simple fraction. They are non-repeating and non-terminating decimals.

Explanation

Irrational numbers cannot be represented as a simple fraction. They are non-repeating and non-terminating decimals.

8. What is the distributive property?

The distributive property is used to add two or more terms inside a set of parentheses.

The distributive property is used to divide two or more terms inside a set of parentheses.

The distributive property is used to multiply a single term by two or more terms inside a set of parentheses.

The distributive property is used to subtract two or more terms inside a set of parentheses.

The distributive property involves multiplying a single term by each term in the parentheses, not dividing, adding, or subtracting.

Explanation

The distributive property involves multiplying a single term by each term in the parentheses, not dividing, adding, or subtracting.

9. How can miles per hour be converted to feet per second?

Divide the original value by 5280.

Multiply the original value by the appropriate conversion factors. The original units should cancel, leaving only the new units.

Convert miles to kilometers and then to feet per second.

Subtract the original value from 60.

Converting miles per hour to feet per second involves a straightforward multiplication process using the correct conversion factors.

Explanation

Converting miles per hour to feet per second involves a straightforward multiplication process using the correct conversion factors.

10. What does PEMDAS stand for?

A formula for calculating area of a triangle

A medical term related to heart health

An acronym for a programming language

The order of operations: parentheses, exponents, multiplication/division, and addition/subtraction.

PEMDAS is a mnemonic device used to remember the order of operations in arithmetic and algebraic equations.

Explanation

PEMDAS is a mnemonic device used to remember the order of operations in arithmetic and algebraic equations.

11. How is percent difference calculated?

Percent difference is calculated by multiplying one value by another and expressing the result as a percentage.

Percent difference is calculated by subtracting one value from another and expressing the result as a percentage of one of the values.

Percent difference is calculated by dividing one value by another and expressing the result as a percentage.

Percent difference is a formula used to determine the difference between two values in terms of percentage. It involves calculating the absolute difference, dividing by the average, and then converting it to a percentage by multiplying by 100.

Explanation

Percent difference is a formula used to determine the difference between two values in terms of percentage. It involves calculating the absolute difference, dividing by the average, and then converting it to a percentage by multiplying by 100.

12. What is the process for writing a number in scientific notation?

Add a comma after every three digits and add the appropriate power of ten.

Multiply the number by 10 and add 'x 10' along with the exponent.

Place a decimal after the first digit and count the number of places the original decimal needs to be moved. The number of places will be the positive exponent for large numbers, and it will be the negative exponent for numbers less than 1.58,300,000 = 5.83 x 1070.00000124 = 1.24 x 10-6

Round the number to the nearest whole number and express it in exponential form.

13. Rewrite x-a with a positive exponent.

X^-a

X/a

A^x

When writing an expression with a negative exponent, it is equivalent to moving the term to the denominator with a positive exponent. Therefore, x-a can be rewritten as x^(-a).

Explanation

When writing an expression with a negative exponent, it is equivalent to moving the term to the denominator with a positive exponent. Therefore, x-a can be rewritten as x^(-a).

14. What does the acronym FOIL stand for?

To multiply two binomialsFOIL stands for First, Outer, Inner, Last.

To divide two binomials

To find the square root of a number

To simplify algebraic expressions

FOIL is a method used to multiply two binomials by multiplying the First terms, then the Outer terms, then the Inner terms, and finally the Last terms.

Explanation

FOIL is a method used to multiply two binomials by multiplying the First terms, then the Outer terms, then the Inner terms, and finally the Last terms.

15. Which terms in the expression 3xy^2 + 6xy - 3y^2 - xy^2 can be added?

6xy and - xy^2

3xy2 and - xy2Only terms with the same variables can be added.

6xy and - 3y^2

3xy^2 and 6xy

In the given expression, terms with similar variables (in this case, xy^2) can be added together. Therefore, 3xy^2 and - xy^2 can be added as they have the same variable components, while the other listed combinations do not.

Explanation

In the given expression, terms with similar variables (in this case, xy^2) can be added together. Therefore, 3xy^2 and - xy^2 can be added as they have the same variable components, while the other listed combinations do not.

16. Factor x^2 - y^2.

(x + y)^2

X^2 + y^2

X2 - y2 = (x - y)(x + y)

(x - y)^2

To factor the expression x^2 - y^2, we use the difference of squares formula which states that a^2 - b^2 = (a - b)(a + b). In this case, x^2 - y^2 = (x - y)(x + y).

Explanation

To factor the expression x^2 - y^2, we use the difference of squares formula which states that a^2 - b^2 = (a - b)(a + b). In this case, x^2 - y^2 = (x - y)(x + y).

17. What is the slope of a horizontal line?

1

Undefined

Infinite

0

The slope of a horizontal line is always 0 because a horizontal line has a constant y value and no change in the y-axis for any change in the x-axis.

Explanation

The slope of a horizontal line is always 0 because a horizontal line has a constant y value and no change in the y-axis for any change in the x-axis.

18. Which of the following numbers satisfies the inequality 0 < 8? 0, 4, 8, 12

12

4 and 8

0

16

In order to satisfy the inequality 0

Explanation

In order to satisfy the inequality 0

19. When graphing the inequality y > 4x - 1, which side of the line will be shaded?

Below the line

What is the y-intercept form of a linear equation?y-intercept form: y = mx + b

To the left of the line

To the right of the line

In inequalities involving y >, the area above the line is shaded to indicate where y values are greater than those on the line.

Explanation

In inequalities involving y >, the area above the line is shaded to indicate where y values are greater than those on the line.

20. What is the definition of a function?

A mathematical equation

A random set of numbers

A sequence of events

A relationship where each input value has only one output value

In mathematics, a function defines a particular relationship between a set of inputs and a set of outputs, where each input value maps to only one output value. This definition is fundamental in understanding the behavior of functions.

Explanation

In mathematics, a function defines a particular relationship between a set of inputs and a set of outputs, where each input value maps to only one output value. This definition is fundamental in understanding the behavior of functions.

21. What determines whether the graph of an inequality is a solid or dashed line?

If the inequality is > or <, the line will be solid. If the inequality is either < or >, the line will be dashed.

If the inequality is ≤ or ≥, the line will be solid.

If the inequality is > or

If the inequality is = or ≠, the line will be solid.

The correct answer is based on the inequality symbols used in mathematical representation, where > and

Explanation

The correct answer is based on the inequality symbols used in mathematical representation, where > and

22. What are domain and range in the context of functions?

Domain refers to the outputs, or y-values, of a given function. Range refers to the inputs, or x-values, for a given function.

Domain refers to acceptable inputs, or x-values, for a given function. Range refers to the outputs, or y-values, of a given function.

Domain is a term used only in geometry, while range is a concept used in statistics.

Domain and range both refer to the same set of values in a function.

Domain and range are terms used interchangeably in mathematics and have no specific meaning in relation to functions.

The domain of a function is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values). It is important to understand this distinction in order to analyze and describe functions accurately.

Explanation

The domain of a function is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values). It is important to understand this distinction in order to analyze and describe functions accurately.

23. What are the sides of a 45 - 45 - 90 right triangle?

3:4:5

1:2:√3

2:3:4

In a 45 - 45 - 90 right triangle, the two legs are congruent to each other, and the hypotenuse is √2 times the length of either leg. This relationship between the sides is what defines a 45 - 45 - 90 triangle.

Explanation

In a 45 - 45 - 90 right triangle, the two legs are congruent to each other, and the hypotenuse is √2 times the length of either leg. This relationship between the sides is what defines a 45 - 45 - 90 triangle.

24. How many points are needed to draw a straight line?

4

2

3

1

In order to draw a straight line, at least two distinct points are needed to determine the slope and direction of the line.

Explanation

In order to draw a straight line, at least two distinct points are needed to determine the slope and direction of the line.

25. Two lines that intersect to form a 90° angle are _______.

Obtuse

Parallel

Perpendicular

Acute

When two lines intersect to form a 90° angle, they are considered perpendicular. Parallel lines never intersect, obtuse angles are greater than 90°, and acute angles are less than 90°.

Explanation

When two lines intersect to form a 90° angle, they are considered perpendicular. Parallel lines never intersect, obtuse angles are greater than 90°, and acute angles are less than 90°.

26. Two lines that lie in the same plane but never intersect are _________.

Intersecting

Perpendicular

Parallel

Skew

When two lines lie in the same plane and never intersect, they are considered parallel. Parallel lines have the same slope and will never converge or meet.

Explanation

When two lines lie in the same plane and never intersect, they are considered parallel. Parallel lines have the same slope and will never converge or meet.

27. What do we call an angle that is greater than 90°?

Acute

Obtuse

Straight

Right

An angle that is greater than 90° but less than 180° is considered an obtuse angle. It is more than a right angle (90°) but less than a straight angle (180°).

Explanation

An angle that is greater than 90° but less than 180° is considered an obtuse angle. It is more than a right angle (90°) but less than a straight angle (180°).

28. Complementary angles add to ____ degrees?

180

90

45

60

Complementary angles are two angles that add up to 90 degrees when combined.

Explanation

Complementary angles are two angles that add up to 90 degrees when combined.

29. In a circle, what is the relationship between the diameter and the radius?

The diameter and radius have no relationship.

The diameter is half the length of the radius.

The diameter is twice the length of the radius.

The diameter is equal to the length of the radius.

In a circle, the diameter is always twice the length of the radius since the diameter is a straight line passing through the center of the circle and connecting two points on the circle's circumference.

Explanation

In a circle, the diameter is always twice the length of the radius since the diameter is a straight line passing through the center of the circle and connecting two points on the circle's circumference.