Mathematics

Question 1

scalar

Answer 1

a quantity with magnitude but without direction

Question 2

vector

Answer 2

a quantity with direction and magnitude

Question 3

Heron’s area formula

Answer 3

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))

Question 4

Conditional probability

Answer 4

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

Question 5

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

Answer 5

An Identity matrix

Question 6

A matrix formed by a single row is called a

Answer 6

row matrix

Question 7

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

Answer 7

upper triangular matrix

Question 8

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

Answer 8

scalar

Question 9

A column matrix is a matrix with:

Answer 9

a single column

Question 10

In a lower triangular matrix, the elements ______ are zeros

Answer 10

above the main diagonal

Question 11

Name the trigonometrical functions and their inverses.

Answer 11

Sine - Cosecant Cosine - Secant Tangent - Cotangent

Question 12

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

Answer 12

357

Question 13

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

Answer 13

Arithmetic

Question 14

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

Answer 14

Geometric

Question 15

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

Answer 15

Fibonacci

Question 16

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.

Answer 16

Combinatorics

Question 17

What is an Augmented Matrix?

Answer 17

A matrix that represents a system of equations.

Question 18

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

Answer 18

Branches

Question 19

Continuously compounding equation

Answer 19

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.

Question 20

What is a dihedral angle?

Answer 20

An angle formed by two intersecting planes.

Question 21

A perfect correlation coefficient is?

Answer 21

-1 or 1

Question 22

What are coterminal angles?

Answer 22

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

Question 23

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

Answer 23

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

Question 24

What is an infinite sequence?

Answer 24

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

Question 25

Order of matrix =

Answer 25

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

Question 26

What is the Fundamental Theorem of Algebra?

Answer 26

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

Question 27

What are the identity properties?

Answer 27

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)

Question 28

What is an extraneous solution?

Answer 28

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

Question 29

What is an inverse matrix?

Answer 29

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.

Question 30

What is the Law of Cosines?

Answer 30

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

Question 31

What is the main diagonal of a matrix?

Answer 31

The diagonal going from upper left to lower right.

Question 32

What is a modified boxplot?

Answer 32

A box plot with the extremes removed.

Question 33

What is permutation?

Answer 33

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

Question 34

What is the polar distance formula?

Answer 34

Question 35

What is a rose curve?

Answer 35

A graph of the polar equation: r = a ∙ (cos(nӨ)) or r = a ∙ (sin(nӨ))

Question 36

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

Answer 36

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.

Question 37

What is the Spiral of Archimedes?

Answer 37

The graph of the polar curve r = Ө

Question 38

What is the standard form equation for a circle?

Answer 38

(x-h)² + (y-k)² = r²

Question 39

What is the standard form equation for an ellipse?

Answer 39


Question 40

What is the standard form equation for a hyperbola?

Answer 40


Question 41

What is the standard form equation for a parabola?

Answer 41

(x-h)² = 4p(y-k)² or (y-k)² = 4p(x-h)²

Question 42

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

Answer 42

0 1/2 √ (2)/2 √ (3)/2 0

Question 43

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

Answer 43

1 (2√ (3)) /3 (2√ (2)) /2 2 -1

Question 44

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

Answer 44

a \< b a = b a \> b

Question 45

What is the equation for calculating standard deviation?

Answer 45

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

Question 46

What is variance?

Answer 46

The square of the standard deviation.

Question 47

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?

Answer 47

Augustus Mobius

Question 48

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

Answer 48

The diameter

Question 49

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

Answer 49

(In radians)

Question 50

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

Answer 50

Internal Common Tangent

Question 51

What is the determinate of the matrix 

Answer 51

|A| = a(ei - fh) - b(di - fg) + c(dh - eg) The pattern is this: (Red is negative, blue is positive) 

Question 52

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

Answer 52

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

Question 53

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

Answer 53

r = a(sin(nӨ)) where n is odd

Question 54

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

Answer 54

r = a(sin(nӨ)) and r = a(cos(nӨ)) when n is even

Question 55

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

Answer 55

r = a(cos(nӨ)) and n is odd

Question 56

What are the equations for the Lemniscate Curves?

Answer 56

r² = a²(sin(2Ө)) or r² = a²(cos(2Ө))

Question 57

What are the two equations for Limacon Curves?

Answer 57

r = a±b(sin(Ө)) and r = a±b(cos(Ө)) Where a\>0 and b\>0

Question 58

Which Limacon Curve equation is symmetrical to the x axis?

Answer 58

r = a±b(cos(Ө))

Question 59

Which Limacon Curve equation is symmetrical to the y axis?

Answer 59

r = a±b(sin(Ө))

Question 60

What is the equation for the Limacon Curve with loop?

Answer 60

r = a±b(sin(Ө)) or r = a±b(cos(Ө)) when a/b \< 1

Question 61

What is the equation for the Cardioid Limacon Curve?

Answer 61

r = a±b(cos(Ө)) or r = a±b(sin(Ө)) When a/b = 1

Question 62

What is the equation for the Dimpled Limacon Loop?

Answer 62

r = a±b(sin(Ө)) or r = a±b(cos(Ө)) When 1 \< a/b \< 2

Question 63

What is the equation for the convex limacon?

Answer 63

r = a±b(sin(Ө)) or r = a±b(cos(Ө)) a/b ≥ 2