Algebra
{5x-2y+9z=-7
{-2x+y-4z=5
{3x-10y-8z=0
What is x=194/31, y=139/31, and z=-101/31?
Betty travels 6 parsecs north and 8 parsecs west to get to school. August leaves from the same location as Betty except he travels in a straight line directly to school. How much more distance did Betty travel than August?
What is 4?
The formula for the circumference of a circle.
What is 2πr?
Mental Math:
Solve the lattice point.
(44*44, 111111111*111111111)
What is (1936, 12345678987654321)?
Order of operations PEMDAS.
What are parentheses, exponents, multiplication, division, addition, and subtraction?
Solve the quadratic equation x² + 5x + 6 = 0.
What is x1=-3, x2=-2?
In triangle XYZ, two sides are 5 and 10 units long, and the angle between them is 60 degrees. Find the area of the triangle.
What is 25√3/2?
Slope-intercept form.
What is y=mx+b?
Solve the equation for x.
log2(7x+3)/x=3
What is 3?
Inventor of calculus.
Who is Isaac Newton? and/or Who is Gottfried Willhelm Leibniz?
Let f be a linear function (f(x) = ax + b for some a and b). If f (z) = 8, f (f (z)) = 20, and f (f (f (z))) = 44, what is the value of z?
What is 2?
Arnold the Ant starts at the top of a regular octahedron with side length 2. What is the shortest distance Arnold needs to walk to reach the opposite corner, given that he can only travel along the surface of the octahedron?
What is 2√3?
The Pythagorean Theorem.
What is a2+b2=c2?
If sin𝐴+sin2𝐴=1 and 𝑎 cos12 A+b cos8 A+c cos6 A−1=0 then 𝑏+𝑐/𝑎+𝑏=?
What is 3?
Inventor of Geometry. (Last name)
Who is Euclid?
For real a and b, let f(x) = (2a − x)(x + 3). f(x) has a maximum value of 2b. Furthermore, let g(x) = bx2 + 8x − 6, where g(x) has a vertex with y-coordinate −b. Find the maximum value of a2b.
What is 242?
What is the area of the region of all points that are of distance at most 1 from (0, 0) or (1, 0)?
What is 4π/3-√3/2?
The volume of a cone.
What is ⅓πr2h?
The real value of x if √(4x2+9=2).
What is no solution?
Inventor of combinatorics (last name).
Who is Pascal? and/or Who is Fermat?
There exists an angle x between 0 and π/2 exclusive, such that 4sin(2x) + 4sin(x) + 12sin2(x/2)=9. Find cos(x).
What is √7/4?
Triangle ABC has AB = 5, AC = 6, BC = 7. The circumcenter of the triangle has center O. Segment BO is extended through side AC to meet the circumcircle at point B’. What is the length of B’C?
What is 7√6/12?
Quadratic equation formula.
What is ax2+bx+c=0?
Use the Baire Category Theorem together with the completeness of C(I, R) to show that there is a dense Gδ, B ⊂ C(I, R) such that every function f ∈ B not differentiable at any point.
What is there exists a dense Gδ set B⊂C(I,R) such that every function f∈Bf is nowhere differentiable.
...and it was delicious!
What is √-1 23 Σ π?