Math History
Which ancient Greek philosopher and mathematician is most famous for the theorem relating the sides of a right-angled triangle a^2 + b^2 = c^2?
Pythagoras
In the slope-intercept linear equation (y = mx + b), what does the letter m represent?
The slope
What is the Area of a triangle with b=3 and h=5?
A=(bh)/2=15/2
What foundational concept is used to define continuity, derivatives, and limits?
The limit
An equation is a differential equation if it contains what?
At least one derivative (such as y')
Which ancient civilization is credited with first developing the modern mathematical concept and symbol for zero as both a placeholder and an operational number
Ancient India
What shape is the graph of a quadratic function like f(x) = ax^2 + bx + c?
A parabola
A quadrilateral with exactly one pair of parallel sides is called a
Trapezoid
What is the power rule for derivatives?
(d/dx)x^n=nx^(n-1)
In the expression dy/dx, what does the term represent in a physical or real-world context?
The rate of change of y with respect to x
The famous integer sequence where each number is the sum of the two preceding ones (0, 1, 1, 2, 3, 5, 8...) is named after which 13th-century Italian mathematician?
Fibonacci
The Pythagorean Identity states that sin^2(x)+cos^2(x) equals a specific constant? What is that constant?
1
If two angles are complementary and one of them measures 35 degrees, what is the measure of the other angle?
55 degrees
What is the derivative of sin(x)
cos(x)
What is the order of the following differential equation?
(x^3)*y'' + 2y' = y^4 + sin(x)
The order is 2
Which 17th-century French philosopher and mathematician gave his name to the standard two-dimensional grid system x and y axes used in algebra and geometry?
René Descartes
What is the formula for finding the straight-line distance between two coordinates in 2D space?
the formula
What is a straight line segment whose two endpoints both lie on the circumference (edge) of the circle called?
A chord
The net signed area between the curve f(x) and the (x) from x=a to x=b is measured by?
The integral
Is the following differential equation linearly independent or not?
(x^3)*y'' + 2y' = y^4 + sin(x)
It is not linearly independent
Who is widely celebrated as the world's first computer programmer for writing an algorithm to calculate Bernoulli numbers on Charles Babbage’s mechanical computer?
Ada Lovelace
If the center of a circle is at the origin (0,0) and the radius is r, what is the standard equation of the circle?
x^2 + y^2 = r^2
What do you call a line that touches a curve or circle at exactly one point without crossing it?
A tangent line
What is the integral of f(x) when f(x)=x/(x-4)
x+4*ln(x-4)
Is the following equation an exact differential equations or not? If so, what is the value of M_y or N_x?
(2xy+3)dx+((x^2)-1)dy=0
It is exact, and M_y=N_x=2x