Mathematics Flashcards
scalar
a quantity with magnitude but without direction
vector
a quantity with direction and magnitude
Heron’s area formula
can solve for the area of any triangle ABC given the sides S=Perimeter/2 Area = square root of (s(s-a)(s-b)(s-c))
Conditional probability
The probability of an event A given hat event B has already occured
A matrix with 1’s on the main diagonal and 0’s everywhere else is:
An Identity matrix
A matrix formed by a single row is called a
row matrix
In a _____ matrix, the elements located below the main diagonal are zeros.
upper triangular matrix
A ______ matrix is a diagonal matrix in which the diagonal elements are equal.
scalar
A column matrix is a matrix with:
a single column
In a lower triangular matrix, the elements ______ are zeros
above the main diagonal
Name the trigonometrical functions and their inverses.
Sine - Cosecant Cosine - Secant Tangent - Cotangent
Convert 101100101₂ to base ten (Use a piece of paper. Don’t just guess.)
357
An _____ Sequence is made by adding the same value each time.
Arithmetic
A _______ Sequence is made by multiplying by the same value each time.
Geometric
The ______ Sequence is found by adding the two numbers before it together.
Fibonacci
A branch of mathematics related to determining the the number of elements of a set or the number of ways objects can be arranged or combined.
Combinatorics
What is an Augmented Matrix?
A matrix that represents a system of equations.
What are the two separate curves that make up a hyperbola called?
Branches
Continuously compounding equation
A = Pe^(rt) Where A is the amount, P is the initial value, r is the rate, and t is the time for which P has been compounding.
What is a dihedral angle?
An angle formed by two intersecting planes.
A perfect correlation coefficient is?
-1 or 1
What are coterminal angles?
Two angles having the same initial side and the same terminal side.
What is the equation for the difference of two complex numbers?
(a+bi) - (c+di) = (a-c) + (b-d)i
What is an infinite sequence?
A function whose domain is the set of all natural numbers.
Order of matrix =
R•C where R is the number of rows and C is the number of columns.
What is the Fundamental Theorem of Algebra?
A polynomial functional of degree n > 0 has n complex zeros (counting multiplicity)
What are the identity properties?
Additive Identity: a + 0 Multiplicative Identity: a ∙ 1 (Subtraction would be a - 0, but that is the same as a + -0 and -0 doesn’t exist. Division would be a/1, but that is the same as a ∙ 1/1, which simplifies to a ∙ 1)
What is an extraneous solution?
A solution of the resulting equation that is not a solution of the original equation.
What is an inverse matrix?
The inverse of a square matrix of matrix A, if it exists, is a square matrix B, such that AB = BA = I, where I is an identity matrix.
What is the Law of Cosines?
a² = b² + c² - 2bc(Cos(A)), b² = a² + c² - 2ac(Cos(B)), c² = a² + b² - 2ab(Cos(C))
What is the main diagonal of a matrix?
The diagonal going from upper left to lower right.
What is a modified boxplot?
A box plot with the extremes removed.
What is permutation?
An arrangement of elements in a set in which order is important.
What is the polar distance formula?
What is a rose curve?
A graph of the polar equation:
r = a ∙ (cos(nӨ))
or
r = a ∙ (sin(nӨ))
The graph of f(x) = ax+a, when a is negative, has to cross what two parts of the cartesian plain? Why?
Negative x-axis and negative y-axis.
Explainations may vary, but must include the following:
a is both the slope and y intercept, meaining it must cross the y axis below the origin and it must increase as x approaches -∞, whenever a is negative.
What is the Spiral of Archimedes?
The graph of the polar curve r = Ө
What is the standard form equation for a circle?
(x-h)² + (y-k)² = r²
What is the standard form equation for an ellipse?
What is the standard form equation for a hyperbola?
What is the standard form equation for a parabola?
(x-h)² = 4p(y-k)²
or
(y-k)² = 4p(x-h)²
Solve for the Sine of all the following angles (without the use of a calculator or reference sheet)
0
π /6
π /4
π /3
π
0
1/2
√ (2)/2
√ (3)/2
0
Solve for the Secant of all the following angles (without the use of a calculator or reference sheet)
0
π /6
π /4
π /3
π
1
(2√ (3)) /3
(2√ (2)) /2
2
-1
Following the trichotomy property, for the real numbers a and b, exactly one of the following is true:
a < b
a = b
a > b
What is the equation for calculating standard deviation?
Where μ is the mean, xi are the individual x values, and n is the quantity of x values:
What is variance?
The square of the standard deviation.
What German mathematician in 1865 cut a long rectangular strip of paper, gave the paper a half-twist, and pasted the ends together, to show that a sheet can have only one side?
Augustus Mobius
What is the longest chord of a circle also known as?
The diameter
What is the equation for the area of a section of a circe?
(In radians)
What is the specific name for a common tangent that intersects the segment joining the centers of 2 circles?
Internal Common Tangent
What is the determinate of the matrix
|A| = a(ei - fh) - b(di - fg) + c(dh - eg)
The pattern is this:
(Red is negative, blue is positive)
To find the geometric mean of a set of n numbers….
Multiply the numbers and then take the nth root of the product
What is the polar equation for the rose curve with n petals and just y axis symmetry?
r = a(sin(nӨ))
where n is odd
What are the two different equations of the two rose curves with 2n petals, and both y and x axis symmetry?
r = a(sin(nӨ))
and
r = a(cos(nӨ))
when n is even
What is the equation of the polar function which has n petals and only x axis symmetry?
r = a(cos(nӨ))
and n is odd
What are the equations for the Lemniscate Curves?
r² = a²(sin(2Ө))
or
r² = a²(cos(2Ө))
What are the two equations for Limacon Curves?
r = a±b(sin(Ө))
and
r = a±b(cos(Ө))
Where a>0 and b>0
Which Limacon Curve equation is symmetrical to the x axis?
r = a±b(cos(Ө))
Which Limacon Curve equation is symmetrical to the y axis?
r = a±b(sin(Ө))
What is the equation for the Limacon Curve with loop?
r = a±b(sin(Ө))
or
r = a±b(cos(Ө))
when a/b < 1
What is the equation for the Cardioid Limacon Curve?
r = a±b(cos(Ө))
or
r = a±b(sin(Ө))
When a/b = 1
What is the equation for the Dimpled Limacon Loop?
r = a±b(sin(Ө))
or
r = a±b(cos(Ө))
When 1 < a/b < 2
What is the equation for the convex limacon?
r = a±b(sin(Ө))
or
r = a±b(cos(Ө))
a/b ≥ 2
