Algebra Flashcards
What is the formula for the area of a rectangle?
Area = length × width
True or False: The formula for the perimeter of a square is P = 4s, where s is the length of a side.
True
Fill in the blank: The formula for the volume of a cylinder is V = _____, where r is the radius and h is the height.
πr²h
What is the quadratic formula used to find the roots of a quadratic equation?
x = (-b ± √(b² - 4ac)) / 2a
Which formula represents the slope of a line given two points (x1, y1) and (x2, y2)?
Slope = (y2 - y1) / (x2 - x1)
True or False: The formula for the area of a triangle is A = 1/2 × base × height.
True
What is the formula for the distance between two points (x1, y1) and (x2, y2)?
Distance = √((x2 - x1)² + (y2 - y1)²)
Fill in the blank: The formula for the circumference of a circle is C = _____, where r is the radius.
2πr
What is the formula for the sum of the interior angles of a polygon with n sides?
Sum = (n - 2) × 180°
What is the formula for converting Celsius to Fahrenheit?
F = (C × 9/5) + 32
True or False: The formula for the Pythagorean theorem is a² + b² = c².
True
What is the formula for the exponential growth model?
y = a(1 + r)ⁿ
Fill in the blank: The formula for the area of a circle is A = _____, where r is the radius.
πr²
What is the formula for the roots of a cubic equation?
There is no simple formula; it generally requires numerical methods or Cardano’s method.
What is the formula for the sum of an arithmetic series?
S_n = n/2 × (a + l), where n is the number of terms, a is the first term, and l is the last term.
True or False: The formula for the surface area of a sphere is 4πr².
True
What is the formula for the compound interest?
A = P(1 + r/n)^(nt)
Fill in the blank: The formula for the difference of squares is a² - b² = _____ .
(a - b)(a + b)
What is the formula for the slope-intercept form of a line?
y = mx + b, where m is the slope and b is the y-intercept.
What is the formula for calculating the mean of a set of numbers?
Mean = (Sum of all values) / (Number of values)
True or False: The formula for the harmonic mean is 1/H = (1/a + 1/b + 1/c + … + 1/n) / n.
True
What is the formula for the binomial theorem?
(a + b)ⁿ = Σ (n choose k) a^(n-k) b^k
Fill in the blank: The formula for the factorial of n is n! = _____ .
n × (n - 1) × (n - 2) × … × 1
What is the formula for the standard deviation of a population?
σ = √(Σ(x - μ)² / N), where μ is the mean and N is the number of data points.
True or False: The formula for the law of cosines is c² = a² + b² - 2ab cos(C).
True
What is the formula for the area of a trapezoid?
Area = 1/2 × (base1 + base2) × height
What is a set in set theory?
A collection of distinct objects, considered as an object in its own right.
True or False: The empty set is a subset of every set.
True
What symbol is used to denote the union of two sets?
∪
Fill in the blank: The intersection of sets A and B is denoted as ___ .
A ∩ B
What does the complement of a set A refer to?
The set of all elements not in A.
Which of the following is an example of a finite set? (a) The set of all integers (b) The set of days in a week (c) The set of all real numbers
b) The set of days in a week
True or False: A set can contain itself as an element.
False
If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∪ B?
{1, 2, 3, 4, 5}
What is the power set of a set?
The set of all possible subsets of a set.
How many subsets does a set with n elements have?
2^n
What is the difference between two sets A and B denoted as A - B?
The set of elements in A that are not in B.
Fill in the blank: The symbol for ‘is a subset of’ is ___ .
⊆
True or False: Two sets are equal if they have the same elements.
True
What is the notation for the Cartesian product of sets A and B?
A × B
If U is the universal set and A = {1, 2}, what is the complement of A?
U - A
What is a disjoint set?
Two sets that have no elements in common.
If A = {x | x is an even number} and B = {x | x is a prime number}, are A and B disjoint?
Yes
What is the formula for the number of elements in the union of two sets A and B?
|A ∪ B| = |A| + |B| - |A ∩ B|
True or False: The intersection of two sets can be the empty set.
True
What does it mean for a set to be countably infinite?
It can be put into a one-to-one correspondence with the natural numbers.
Fill in the blank: A set that contains all subsets of a set S is called the ___ of S.
power set
If A = {2, 4, 6} and B = {1, 2, 3}, what is A ∩ B?
{2}
What is the definition of a proper subset?
A subset that is not equal to the set it is a subset of.
What symbol is used to denote the difference between two sets?
−
True or False: The union of two sets can be equal to one of the original sets.
True
What is the result of the Cartesian product of sets A = {1, 2} and B = {a, b}?
{(1, a), (1, b), (2, a), (2, b)}
