AYT Flashcards
What is the Pythagorean Theorem?
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
True or False: The sum of the angles in any triangle is 180 degrees.
True
Fill in the blank: The formula for the area of a circle is _____.
πr²
What is the Quadratic Formula?
The solutions to the equation ax² + bx + c = 0 are given by x = (-b ± √(b² - 4ac)) / (2a).
True or False: The sum of the interior angles of a polygon with n sides is (n-2) × 180 degrees.
True
What is the formula for the volume of a cylinder?
V = πr²h
Fill in the blank: The distance formula in a coordinate plane is _____.
d = √((x₂ - x₁)² + (y₂ - y₁)²)
What is the definition of a function?
A relation that assigns exactly one output for each input.
True or False: A linear function has a constant rate of change.
True
What is the slope-intercept form of a linear equation?
y = mx + b
Fill in the blank: The sum of the exterior angles of any polygon is _____.
360 degrees
What is the difference between a permutation and a combination?
A permutation is an arrangement of objects where order matters, while a combination is a selection of objects where order does not matter.
True or False: In a normal distribution, about 68% of the data falls within one standard deviation of the mean.
True
What is the Fundamental Theorem of Algebra?
Every non-constant polynomial equation has at least one complex root.
Fill in the blank: The area of a triangle can be calculated using the formula _____.
A = 1/2 × base × height
What is the definition of a rational number?
A number that can be expressed as a fraction p/q, where p and q are integers and q ≠ 0.
True or False: The product of two negative numbers is positive.
True
What is the Law of Cosines?
c² = a² + b² - 2ab cos(C) for any triangle.
Fill in the blank: The formula for the surface area of a sphere is _____.
4πr²
What is an asymptote?
A line that a graph approaches but never touches.
True or False: The roots of a quadratic equation can be real or complex.
True
What does it mean for two lines to be parallel?
Two lines are parallel if they have the same slope and never intersect.
Fill in the blank: The equation of a circle with center (h, k) and radius r is _____.
(x - h)² + (y - k)² = r²
What is the definition of an irrational number?
A number that cannot be expressed as a fraction of two integers.
True or False: The median of a set of numbers is the middle value when the numbers are arranged in order.
True
What is the formula for the perimeter of a rectangle?
P = 2(l + w), where l is the length and w is the width.
Fill in the blank: The sum of the first n natural numbers is given by the formula _____.
n(n + 1) / 2
What is the definition of a vertical asymptote?
A vertical line x = a where the function approaches infinity as x approaches a.
True or False: A circle is a type of ellipse.
True
What is the difference between dependent and independent events in probability?
Dependent events are affected by each other, while independent events are not.
Fill in the blank: The formula for the area of a trapezoid is _____.
A = 1/2 × (b₁ + b₂) × h
What is the definition of a composite number?
A natural number greater than 1 that is not prime, meaning it has factors other than 1 and itself.
True or False: The range of a function is the set of all possible output values.
True
What is the definition of a radius?
The distance from the center of a circle to any point on the circle.
Fill in the blank: The formula for the volume of a rectangular prism is _____.
V = l × w × h
What is the definition of a system of equations?
A set of two or more equations with the same variables.
True or False: The x-intercept of a graph is where the graph crosses the x-axis.
True
What is the definition of a bijective function?
A function that is both injective (one-to-one) and surjective (onto).
Fill in the blank: The formula for the area of a parallelogram is _____.
A = base × height
What is the definition of a linear equation?
An equation that graphs a straight line.
True or False: The sum of two odd numbers is even.
True
What is the definition of a trapezoid?
A quadrilateral with at least one pair of parallel sides.
Fill in the blank: The formula for the circumference of a circle is _____.
C = 2πr
What is the definition of an acute angle?
An angle that measures less than 90 degrees.
True or False: An obtuse angle measures more than 90 degrees.
True
What is the definition of a right angle?
An angle that measures exactly 90 degrees.
Fill in the blank: The formula for the area of a sector of a circle is _____.
A = (θ/360) × πr²
What is the definition of a reflex angle?
An angle that measures more than 180 degrees but less than 360 degrees.
True or False: The diameter of a circle is twice the radius.
True
What is the definition of a congruent figure?
Figures that have the same shape and size.
Fill in the blank: The formula for the distance between two points (x₁, y₁) and (x₂, y₂) is _____.
d = √((x₂ - x₁)² + (y₂ - y₁)²)
What is the definition of complementary angles?
Two angles that add up to 90 degrees.
True or False: Two lines that intersect form four angles.
True
What is the definition of supplementary angles?
Two angles that add up to 180 degrees.
Fill in the blank: The formula for the area of a rectangle is _____.
A = length × width
What is the definition of a polynomial?
An algebraic expression consisting of variables and coefficients, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
True or False: The highest degree of a polynomial determines its classification (linear, quadratic, cubic, etc.).
True
What is the definition of a perfect square trinomial?
A polynomial that can be factored into the square of a binomial.
Fill in the blank: The formula for the difference of squares is _____.
a² - b² = (a + b)(a - b)
What is the definition of a rational expression?
A fraction where the numerator and denominator are both polynomials.
True or False: A quadratic function can have at most two real roots.
True
What is the definition of the vertex of a parabola?
The highest or lowest point on the graph of a quadratic function.
Fill in the blank: The formula for the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is _____.
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
What is the definition of an exponential function?
A function in which the variable is in the exponent.
True or False: An exponential function grows faster than a linear function.
True
What is the definition of a logarithm?
The inverse operation to exponentiation, answering the question: to what exponent must a base be raised, to produce a given number?
Fill in the blank: The change of base formula for logarithms is _____.
log_b(a) = log_k(a) / log_k(b)
What is the definition of a binomial?
A polynomial with exactly two terms.
True or False: The sum of two even numbers is odd.
False
What is the definition of a mean in statistics?
The average of a set of numbers, calculated by dividing the sum of the numbers by the count of the numbers.
Fill in the blank: The formula for the standard deviation is _____.
σ = √(Σ(x - μ)² / N)
What is the definition of a histogram?
A graphical representation of the distribution of numerical data, using bars to show frequency.
True or False: A box plot displays the five-number summary of a data set.
True
What is the definition of a scatter plot?
A graph that uses dots to represent the values obtained for two different variables, showing potential relationships.
Fill in the blank: The formula for the probability of an event A is _____.
P(A) = Number of favorable outcomes / Total number of outcomes
What is the definition of mutually exclusive events?
Events that cannot occur at the same time.
True or False: The probability of certain events is always 1.
True
What is the definition of a sample space in probability?
The set of all possible outcomes of a random experiment.
Fill in the blank: The formula for combinations is _____.
C(n, r) = n! / [r!(n - r)!]
