| {"id": "math-001", "category": "math", "question": "What is 12 multiplied by 13?", "answer": "12 multiplied by 13 equals 156."} | |
| {"id": "math-002", "category": "math", "question": "What is 144 divided by 12?", "answer": "144 divided by 12 equals 12."} | |
| {"id": "math-003", "category": "math", "question": "What is the sum of 17 and 25?", "answer": "The sum of 17 and 25 is 42."} | |
| {"id": "math-004", "category": "math", "question": "What is 100 minus 37?", "answer": "100 minus 37 equals 63."} | |
| {"id": "math-005", "category": "math", "question": "What is 7 times 8?", "answer": "7 times 8 equals 56."} | |
| {"id": "math-006", "category": "math", "question": "What is 81 divided by 9?", "answer": "81 divided by 9 equals 9."} | |
| {"id": "math-007", "category": "math", "question": "What is 15 percent of 200?", "answer": "15 percent of 200 is 30."} | |
| {"id": "math-008", "category": "math", "question": "What is three-quarters of 60?", "answer": "Three-quarters of 60 equals 45."} | |
| {"id": "math-009", "category": "math", "question": "What is two-fifths of 100?", "answer": "Two-fifths of 100 equals 40."} | |
| {"id": "math-010", "category": "math", "question": "What is 0.75 expressed as a fraction in lowest terms?", "answer": "0.75 expressed as a fraction in lowest terms is 3/4."} | |
| {"id": "math-011", "category": "math", "question": "What is the area of a rectangle that is 12 units long and 5 units wide?", "answer": "The area is 60 square units, found by multiplying length by width."} | |
| {"id": "math-012", "category": "math", "question": "What is the perimeter of a rectangle that is 12 units long and 5 units wide?", "answer": "The perimeter is 34 units, calculated as twice the length plus twice the width."} | |
| {"id": "math-013", "category": "math", "question": "What is the area of a triangle with a base of 10 and a height of 6?", "answer": "The area is 30 square units, calculated as one-half times base times height."} | |
| {"id": "math-014", "category": "math", "question": "What is the circumference of a circle with a radius of 7, in terms of pi?", "answer": "The circumference is 14 times pi, since circumference equals 2 times pi times the radius."} | |
| {"id": "math-015", "category": "math", "question": "What is the value of 5 factorial?", "answer": "5 factorial equals 120, calculated as 5 times 4 times 3 times 2 times 1."} | |
| {"id": "math-016", "category": "math", "question": "What is 2 to the power of 10?", "answer": "2 to the power of 10 equals 1024."} | |
| {"id": "math-017", "category": "math", "question": "What is 3 to the power of 4?", "answer": "3 to the power of 4 equals 81."} | |
| {"id": "math-018", "category": "math", "question": "What is the greatest common divisor of 18 and 24?", "answer": "The greatest common divisor of 18 and 24 is 6."} | |
| {"id": "math-019", "category": "math", "question": "What is the least common multiple of 4 and 6?", "answer": "The least common multiple of 4 and 6 is 12."} | |
| {"id": "math-020", "category": "math", "question": "How many prime numbers are there between 1 and 20?", "answer": "There are 8 prime numbers between 1 and 20: 2, 3, 5, 7, 11, 13, 17, and 19."} | |
| {"id": "math-021", "category": "math", "question": "Is 1 considered a prime number?", "answer": "No, 1 is not a prime number; by definition a prime must have exactly two distinct positive divisors, which 1 does not have."} | |
| {"id": "math-022", "category": "math", "question": "What is the smallest prime number?", "answer": "The smallest prime number is 2, since it is the first positive integer with exactly two distinct divisors, namely 1 and itself."} | |
| {"id": "math-023", "category": "math", "question": "What is the sum of the first 10 positive integers?", "answer": "The sum of the first 10 positive integers is 55, following the formula n times n plus 1 divided by 2."} | |
| {"id": "math-024", "category": "math", "question": "What is the average of the numbers 5, 7, 9, and 11?", "answer": "The average (mean) is 8, found by summing the four numbers and dividing by 4."} | |
| {"id": "math-025", "category": "math", "question": "What is the median of the numbers 3, 5, 7, 9, and 11?", "answer": "The median is 7, because it is the middle value when the numbers are arranged in order."} | |
| {"id": "math-026", "category": "math", "question": "What is 60 percent expressed as a fraction in lowest terms?", "answer": "60 percent equals 3/5 as a fraction in lowest terms."} | |
| {"id": "math-027", "category": "math", "question": "What is 125 percent expressed as a decimal?", "answer": "125 percent expressed as a decimal is 1.25."} | |
| {"id": "math-028", "category": "math", "question": "What is 0.0625 expressed as a fraction in lowest terms?", "answer": "0.0625 equals 1/16 as a fraction in lowest terms."} | |
| {"id": "math-029", "category": "math", "question": "How many degrees are in a right angle?", "answer": "A right angle measures exactly 90 degrees."} | |
| {"id": "math-030", "category": "math", "question": "How many degrees are in a straight line?", "answer": "A straight line measures 180 degrees."} | |
| {"id": "math-031", "category": "math", "question": "How many degrees are in a complete circle?", "answer": "A complete circle measures 360 degrees."} | |
| {"id": "math-032", "category": "math", "question": "How many degrees are in the interior angles of a triangle?", "answer": "The interior angles of any triangle sum to 180 degrees."} | |
| {"id": "math-033", "category": "math", "question": "How many degrees are in the interior angles of a quadrilateral?", "answer": "The interior angles of any quadrilateral sum to 360 degrees."} | |
| {"id": "math-034", "category": "math", "question": "How many degrees are in the interior angles of a regular pentagon?", "answer": "The interior angles of a regular pentagon sum to 540 degrees."} | |
| {"id": "math-035", "category": "math", "question": "How many sides does a hexagon have?", "answer": "A hexagon has 6 sides."} | |
| {"id": "math-036", "category": "math", "question": "How many sides does an octagon have?", "answer": "An octagon has 8 sides."} | |
| {"id": "math-037", "category": "math", "question": "What is the name of a polygon with 12 sides?", "answer": "A polygon with 12 sides is called a dodecagon."} | |
| {"id": "math-038", "category": "math", "question": "In a right triangle, what does the Pythagorean theorem state?", "answer": "The Pythagorean theorem states that the square of the hypotenuse equals the sum of the squares of the other two sides, written a squared plus b squared equals c squared."} | |
| {"id": "math-039", "category": "math", "question": "What is the length of the hypotenuse of a right triangle whose legs are 3 and 4?", "answer": "The hypotenuse is 5, since 3 squared plus 4 squared equals 9 plus 16 equals 25, and the square root of 25 is 5."} | |
| {"id": "math-040", "category": "math", "question": "How many vertices does a cube have?", "answer": "A cube has 8 vertices."} | |
| {"id": "math-041", "category": "math", "question": "How many edges does a cube have?", "answer": "A cube has 12 edges."} | |
| {"id": "math-042", "category": "math", "question": "How many faces does a cube have?", "answer": "A cube has 6 faces."} | |
| {"id": "math-043", "category": "math", "question": "What is the formula for the area of a circle?", "answer": "The area of a circle equals pi times the radius squared."} | |
| {"id": "math-044", "category": "math", "question": "What is the formula for the volume of a rectangular box?", "answer": "The volume equals length times width times height."} | |
| {"id": "math-045", "category": "math", "question": "How many feet are in one mile?", "answer": "There are 5,280 feet in one mile."} | |
| {"id": "math-046", "category": "math", "question": "How many grams are in one kilogram?", "answer": "There are 1,000 grams in one kilogram."} | |
| {"id": "math-047", "category": "math", "question": "How many inches are in one foot?", "answer": "There are 12 inches in one foot."} | |
| {"id": "math-048", "category": "math", "question": "How many centimeters are in one inch?", "answer": "There are 2.54 centimeters in one inch."} | |
| {"id": "math-049", "category": "math", "question": "How many milliliters are in one liter?", "answer": "There are 1,000 milliliters in one liter."} | |
| {"id": "math-050", "category": "math", "question": "How many minutes are in one hour?", "answer": "There are 60 minutes in one hour."} | |
| {"id": "math-051", "category": "math", "question": "How many seconds are in one day?", "answer": "There are 86,400 seconds in one day, since 24 times 60 times 60 equals 86,400."} | |
| {"id": "math-052", "category": "math", "question": "How many ounces are in one pound?", "answer": "There are 16 ounces in one pound."} | |
| {"id": "math-053", "category": "math", "question": "What is the freezing point of water in degrees Celsius?", "answer": "Water freezes at 0 degrees Celsius."} | |
| {"id": "math-054", "category": "math", "question": "What is the boiling point of water in degrees Celsius?", "answer": "Water boils at 100 degrees Celsius at standard atmospheric pressure."} | |
| {"id": "math-055", "category": "math", "question": "What is the freezing point of water in degrees Fahrenheit?", "answer": "Water freezes at 32 degrees Fahrenheit."} | |
| {"id": "math-056", "category": "math", "question": "What is the boiling point of water in degrees Fahrenheit?", "answer": "Water boils at 212 degrees Fahrenheit at standard atmospheric pressure."} | |
| {"id": "math-057", "category": "math", "question": "At what temperature in degrees Fahrenheit are the Celsius and Fahrenheit scales equal?", "answer": "The Celsius and Fahrenheit scales are equal at negative 40 degrees."} | |
| {"id": "math-058", "category": "math", "question": "If a car travels at 60 miles per hour for 4 hours, how far does it travel?", "answer": "The car travels 240 miles, since distance equals speed multiplied by time."} | |
| {"id": "math-059", "category": "math", "question": "If you run 3 miles in 30 minutes, what is your average speed in miles per hour?", "answer": "Your average speed is 6 miles per hour, since 3 miles divided by 0.5 hour equals 6."} | |
| {"id": "math-060", "category": "math", "question": "What is a tip of 20 percent on a $45 restaurant bill?", "answer": "A 20 percent tip on $45 is $9."} | |
| {"id": "math-061", "category": "math", "question": "In the equation y equals 3x plus 2, what is the slope?", "answer": "The slope is 3, since in slope-intercept form y equals mx plus b, m represents the slope."} | |
| {"id": "math-062", "category": "math", "question": "In the equation y equals 3x plus 2, what is the y-intercept?", "answer": "The y-intercept is 2, since the constant term in slope-intercept form is the y-intercept."} | |
| {"id": "math-063", "category": "math", "question": "What is a variable in algebra?", "answer": "A variable is a symbol, usually a letter, that represents an unknown or changeable numerical value."} | |
| {"id": "math-064", "category": "math", "question": "What is a coefficient in an algebraic expression?", "answer": "A coefficient is the numerical factor that multiplies a variable, such as the 5 in the term 5x."} | |
| {"id": "math-065", "category": "math", "question": "What does it mean to solve an equation?", "answer": "To solve an equation means to find the value or values of the variable that make the equation true."} | |
| {"id": "math-066", "category": "math", "question": "What is the value of x in the equation 2x plus 6 equals 14?", "answer": "The value of x is 4, found by subtracting 6 from both sides and then dividing by 2."} | |
| {"id": "math-067", "category": "math", "question": "What is a monomial in algebra?", "answer": "A monomial is an algebraic expression consisting of a single term, such as 5x, 3x squared, or 7."} | |
| {"id": "math-068", "category": "math", "question": "What is the value of pi to two decimal places?", "answer": "Pi is approximately 3.14 to two decimal places."} | |
| {"id": "math-069", "category": "math", "question": "What is the approximate value of the mathematical constant e?", "answer": "The constant e, the base of natural logarithms, is approximately 2.71828."} | |
| {"id": "math-070", "category": "math", "question": "What is the approximate value of the golden ratio?", "answer": "The golden ratio is approximately 1.618, often denoted by the Greek letter phi."} | |
| {"id": "math-071", "category": "math", "question": "Who is known as the father of geometry?", "answer": "The ancient Greek mathematician Euclid is known as the father of geometry for his work The Elements."} | |
| {"id": "math-072", "category": "math", "question": "Which Greek mathematician is famous for the theorem about right triangles?", "answer": "Pythagoras is the Greek mathematician traditionally credited with the Pythagorean theorem about right triangles."} | |
| {"id": "math-073", "category": "math", "question": "What famous constant is associated with the mathematician Leonhard Euler?", "answer": "Euler is associated with the constant e, the base of natural logarithms, as well as many theorems and notations used in mathematics."} | |
| {"id": "math-074", "category": "math", "question": "Which mathematician is famous for summing the integers from 1 to 100 as a schoolboy?", "answer": "Carl Friedrich Gauss reportedly summed the integers from 1 to 100 as a schoolboy by pairing numbers to total 101."} | |
| {"id": "math-075", "category": "math", "question": "Which mathematician is famous for inventing calculus along with Leibniz?", "answer": "Isaac Newton is credited, along with Gottfried Wilhelm Leibniz, with independently inventing calculus in the 17th century."} | |
| {"id": "math-076", "category": "math", "question": "Which ancient Greek mathematician is famous for shouting 'Eureka'?", "answer": "Archimedes is the ancient Greek mathematician famously associated with shouting Eureka when he discovered a principle of buoyancy."} | |
| {"id": "math-077", "category": "math", "question": "Who is often regarded as the first computer programmer?", "answer": "Ada Lovelace is often regarded as the first computer programmer for her work on Charles Babbage's proposed analytical engine in the 19th century."} | |
| {"id": "math-078", "category": "math", "question": "Who proved Fermat's Last Theorem in 1994?", "answer": "The British mathematician Andrew Wiles proved Fermat's Last Theorem in 1994, completing work he first announced in 1993."} | |
| {"id": "math-079", "category": "math", "question": "Who is credited with discovering the law of gravity and co-inventing calculus?", "answer": "Isaac Newton is credited with discovering the law of universal gravitation and co-inventing calculus."} | |
| {"id": "math-080", "category": "math", "question": "Who wrote the book The Elements, a foundational geometry textbook?", "answer": "The Greek mathematician Euclid wrote The Elements, a foundational geometry textbook used for centuries."} | |
| {"id": "math-081", "category": "math", "question": "Which mathematician developed the field of analytic geometry?", "answer": "The French mathematician René Descartes developed analytic geometry, which combines algebra and geometry using coordinates."} | |
| {"id": "math-082", "category": "math", "question": "Who is famous for the Fermat's Last Theorem?", "answer": "Pierre de Fermat is famous for Fermat's Last Theorem, a statement he wrote in the margin of a book claiming he had a proof that was too large to fit."} | |
| {"id": "math-083", "category": "math", "question": "Which number is known as the additive identity?", "answer": "The number zero is known as the additive identity, because adding zero to any number leaves it unchanged."} | |
| {"id": "math-084", "category": "math", "question": "What is a rational number?", "answer": "A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not zero."} | |
| {"id": "math-085", "category": "math", "question": "What is an irrational number?", "answer": "An irrational number is a real number that cannot be expressed as a ratio of two integers, such as pi or the square root of 2."} | |
| {"id": "math-086", "category": "math", "question": "What does it mean for a number to be even?", "answer": "A number is even if it is divisible by 2 with no remainder."} | |
| {"id": "math-087", "category": "math", "question": "What does it mean for a number to be odd?", "answer": "A number is odd if it is not divisible by 2, meaning dividing by 2 leaves a remainder of 1."} | |
| {"id": "math-088", "category": "math", "question": "What is the Fibonacci sequence's first six terms starting with 1, 1?", "answer": "The first six terms of the Fibonacci sequence starting with 1, 1 are 1, 1, 2, 3, 5, and 8, where each term is the sum of the two previous terms."} | |
| {"id": "math-089", "category": "math", "question": "What is a prime factor of 60?", "answer": "A prime factor of 60 is one of the prime numbers 2, 3, or 5, since 60 equals 2 times 2 times 3 times 5."} | |
| {"id": "math-090", "category": "math", "question": "What is the probability of flipping a fair coin and getting heads?", "answer": "The probability is 1/2 or 50 percent, since a fair coin has two equally likely outcomes."} | |
| {"id": "math-091", "category": "math", "question": "What is the probability of rolling a 6 on a standard six-sided die?", "answer": "The probability is 1/6, since a fair die has six equally likely outcomes and only one face is six."} | |
| {"id": "math-092", "category": "math", "question": "What type of graph is best for showing parts of a whole?", "answer": "A pie chart is best for showing parts of a whole, with each slice representing a proportion of the total."} | |
| {"id": "math-093", "category": "math", "question": "What type of graph is best for showing how a value changes over time?", "answer": "A line graph is best for showing how a value changes over time, since it connects data points to reveal trends."} | |
| {"id": "math-094", "category": "math", "question": "What type of graph uses rectangular bars to compare categories?", "answer": "A bar graph uses rectangular bars, with length proportional to the value being represented, to compare categories."} | |
| {"id": "math-095", "category": "math", "question": "What is meant by mean in statistics?", "answer": "The mean is the arithmetic average of a set of numbers, found by summing them and dividing by how many numbers there are."} | |
| {"id": "math-096", "category": "math", "question": "What is meant by mode in a set of numbers?", "answer": "The mode is the number that appears most frequently in a set, such as 5 in the set 2, 3, 5, 5, 7."} | |
| {"id": "math-097", "category": "math", "question": "How many vertices does a triangle have?", "answer": "A triangle has 3 vertices."} | |
| {"id": "math-098", "category": "math", "question": "What is the relationship between radius and diameter of a circle?", "answer": "The diameter of a circle is twice the radius, since the diameter passes through the center and equals the longest chord."} | |
| {"id": "math-099", "category": "math", "question": "What is a prime factorization?", "answer": "A prime factorization is the expression of a number as a product of prime numbers, such as 12 equals 2 times 2 times 3."} | |
| {"id": "math-100", "category": "math", "question": "What is the sum of the angles around a single point?", "answer": "The sum of the angles around a single point is 360 degrees."} | |