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Science Bowl > Mathematics > Flashcards

Mathematics Flashcards

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1
Q

scalar

A

a quantity with magnitude but without direction

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2
Q

vector

A

a quantity with direction and magnitude

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3
Q

Heron’s area formula

A

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))

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4
Q

Conditional probability

A

The probability of an event A given hat event B has already occured

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5
Q

A matrix with 1’s on the main diagonal and 0’s everywhere else is:

A

An Identity matrix

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6
Q

A matrix formed by a single row is called a

A

row matrix

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7
Q

In a _____ matrix, the elements located below the main diagonal are zeros.

A

upper triangular matrix

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8
Q

A ______ matrix is a diagonal matrix in which the diagonal elements are equal.

A

scalar

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9
Q

A column matrix is a matrix with:

A

a single column

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10
Q

In a lower triangular matrix, the elements ______ are zeros

A

above the main diagonal

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11
Q

Name the trigonometrical functions and their inverses.

A

Sine - Cosecant Cosine - Secant Tangent - Cotangent

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12
Q

Convert 101100101₂ to base ten (Use a piece of paper. Don’t just guess.)

A

357

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13
Q

An _____ Sequence is made by adding the same value each time.

A

Arithmetic

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14
Q

A _______ Sequence is made by multiplying by the same value each time.

A

Geometric

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15
Q

The ______ Sequence is found by adding the two numbers before it together.

A

Fibonacci

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16
Q

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.

A

Combinatorics

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17
Q

What is an Augmented Matrix?

A

A matrix that represents a system of equations.

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18
Q

What are the two separate curves that make up a hyperbola called?

A

Branches

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19
Q

Continuously compounding equation

A

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.

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20
Q

What is a dihedral angle?

A

An angle formed by two intersecting planes.

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21
Q

A perfect correlation coefficient is?

A

-1 or 1

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22
Q

What are coterminal angles?

A

Two angles having the same initial side and the same terminal side.

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23
Q

What is the equation for the difference of two complex numbers?

A

(a+bi) - (c+di) = (a-c) + (b-d)i

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24
Q

What is an infinite sequence?

A

A function whose domain is the set of all natural numbers.

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25
Q

Order of matrix =

A

R•C where R is the number of rows and C is the number of columns.

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26
Q

What is the Fundamental Theorem of Algebra?

A

A polynomial functional of degree n > 0 has n complex zeros (counting multiplicity)

27
Q

What are the identity properties?

A

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)

28
Q

What is an extraneous solution?

A

A solution of the resulting equation that is not a solution of the original equation.

29
Q

What is an inverse matrix?

A

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.

30
Q

What is the Law of Cosines?

A

a² = b² + c² - 2bc(Cos(A)), b² = a² + c² - 2ac(Cos(B)), c² = a² + b² - 2ab(Cos(C))

31
Q

What is the main diagonal of a matrix?

A

The diagonal going from upper left to lower right.

32
Q

What is a modified boxplot?

A

A box plot with the extremes removed.

33
Q

What is permutation?

A

An arrangement of elements in a set in which order is important.

34
Q

What is the polar distance formula?

A
35
Q

What is a rose curve?

A

A graph of the polar equation:

r = a ∙ (cos(nӨ))

or

r = a ∙ (sin(nӨ))

36
Q

The graph of f(x) = ax+a, when a is negative, has to cross what two parts of the cartesian plain? Why?

A

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.

37
Q

What is the Spiral of Archimedes?

A

The graph of the polar curve r = Ө

38
Q

What is the standard form equation for a circle?

A

(x-h)² + (y-k)² = r²

39
Q

What is the standard form equation for an ellipse?

A
40
Q

What is the standard form equation for a hyperbola?

A
41
Q

What is the standard form equation for a parabola?

A

(x-h)² = 4p(y-k)²

or

(y-k)² = 4p(x-h)²

42
Q

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

A

0

1/2

√ (2)/2

√ (3)/2

0

43
Q

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

A

1

(2√ (3)) /3

(2√ (2)) /2

2

-1

44
Q

Following the trichotomy property, for the real numbers a and b, exactly one of the following is true:

A

a < b

a = b

a > b

45
Q

What is the equation for calculating standard deviation?

A

Where μ is the mean, xi are the individual x values, and n is the quantity of x values:

46
Q

What is variance?

A

The square of the standard deviation.

47
Q

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?

A

Augustus Mobius

48
Q

What is the longest chord of a circle also known as?

A

The diameter

49
Q

What is the equation for the area of a section of a circe?

A

(In radians)

50
Q

What is the specific name for a common tangent that intersects the segment joining the centers of 2 circles?

A

Internal Common Tangent

51
Q

What is the determinate of the matrix

A

|A| = a(ei - fh) - b(di - fg) + c(dh - eg)

The pattern is this:

(Red is negative, blue is positive)

52
Q

To find the geometric mean of a set of n numbers….

A

Multiply the numbers and then take the nth root of the product

53
Q

What is the polar equation for the rose curve with n petals and just y axis symmetry?

A

r = a(sin(nӨ))

where n is odd

54
Q

What are the two different equations of the two rose curves with 2n petals, and both y and x axis symmetry?

A

r = a(sin(nӨ))

and

r = a(cos(nӨ))

when n is even

55
Q

What is the equation of the polar function which has n petals and only x axis symmetry?

A

r = a(cos(nӨ))

and n is odd

56
Q

What are the equations for the Lemniscate Curves?

A

r² = a²(sin(2Ө))

or

r² = a²(cos(2Ө))

57
Q

What are the two equations for Limacon Curves?

A

r = a±b(sin(Ө))

and

r = a±b(cos(Ө))

Where a>0 and b>0

58
Q

Which Limacon Curve equation is symmetrical to the x axis?

A

r = a±b(cos(Ө))

59
Q

Which Limacon Curve equation is symmetrical to the y axis?

A

r = a±b(sin(Ө))

60
Q

What is the equation for the Limacon Curve with loop?

A

r = a±b(sin(Ө))

or

r = a±b(cos(Ө))

when a/b < 1

61
Q

What is the equation for the Cardioid Limacon Curve?

A

r = a±b(cos(Ө))

or

r = a±b(sin(Ө))

When a/b = 1

62
Q

What is the equation for the Dimpled Limacon Loop?

A

r = a±b(sin(Ө))

or

r = a±b(cos(Ө))

When 1 < a/b < 2

63
Q

What is the equation for the convex limacon?

A

r = a±b(sin(Ө))

or

r = a±b(cos(Ө))

a/b ≥ 2

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