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  1. anemone

    Challenge Determine the minimum value

    Determine the minimum value of the function f(x)=x^4-6x^2+8x-3 .
  2. anemone

    Challenge Evaluate the sum

    Given that abx^2=(a-b)^2(x+1). Find 1+\dfrac{4}{x}+\dfrac{4}{x^2}.
  3. anemone

    Challenge Quadratic equation that has two roots

    Find all integer valuse of k such that the quadratic expression (x+k)(x+1991)+1 can be factored as a product of (x+p)(x+q), where p and q are integers.
  4. anemone

    Challenge Simplify a sum

    Simplify \tan x \cos 1 ^\circ + \sin 1^\circ.
  5. anemone

    Challenge Find the sum of squares

    If x^3=12x+7y and y^3=7x+12y, evaluate x^2+y^2.
  6. anemone

    Challenge Solve for x

    Solve the equation x^{\log x}=\dfrac{x^3}{100}.
  7. anemone

    Challenge Find the sum to infinity of a sequence

    If \dfrac{1}{1^2}+\dfrac{1}{2^2}+\dfrac{1}{3^2}+\cdots=\dfrac{\pi^2}{6}, evaluate the exact value of \dfrac{1}{1^2}+\dfrac{1}{3^2}+\dfrac{1}{5^2}+\cdots
  8. anemone

    Practice Find derivative of the sum of two quotients

    Find the derivative of \dfrac{\sin^2 x}{1+\cot x}+\dfrac{\cos^2 x}{1+\tan x}.
  9. anemone

    Challenge Logarithmic Challenge

    Given that \log_{4n} 40\sqrt{3}=\log_{3n} 45, find n^3.
  10. anemone

    Challenge Find the area of the shaded region

    Points P and Q are centers of the circles as shown below. Chord AB is tangent to the circle with center P. Given that the line PQ is parallel to chord AB and AB=x units, find the area of the shaded region.
  11. anemone

    Challenge Simplifying a quotient

    Simplify \dfrac{2020^3-2002^3-18^3}{2020\cdot 2002 \cdot 18}.
  12. anemone

    Challenge Evaluation of a sum

    Evaluate a^{a^8}+a^{a^2} if a^{a^4}=4 and a is real.
  13. anemone

    Good versus Bad, Very Bad Practice Questions

    There is huge difference between good practice questions and bad practice questions. Bad practice questions, especially the one made up by anyone who knows nothing or just a little of mathematics can make a forum looks in a very bad taste. :confused: On the other hand, good practice problems...
  14. anemone

    Optimization problem

    Suppose a and b are the values of x that satisfy the equation x^2-2px+p^2+2p+3=0 for some real number p. Minimize the expression of a^2+b^2.
  15. anemone

    Challenge Prove a sum identity

    Prove that 1^2-2^2+3^2-4^2+\cdots+(-1)^{n-1}n^2=(-1)^{n-1}\dfrac{n(n+1)}{2}.
  16. anemone

    Science teacher

  17. anemone

    Product over Sum Problem

    Evaluate \dfrac{1\cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8}{1+2+3+4+5+6+7+8}.
  18. anemone

    Challenge Solve for a side of triangle

    In a triangle ABC, it is given that \sin(A+B)+\cos(2A-B)=2 and AB=4. Find BC.
  19. anemone

    Challenge Evaluate P(3)+P(9)

    Evaluate P(3)+P(9) if P(x)=\dfrac{(x-\sqrt{2})(x-\sqrt{3})}{(1-\sqrt{2})(1-\sqrt{3})}+2\left(\dfrac{(x-1)(x-\sqrt{3})}{(\sqrt{2}-1)(\sqrt{2}-\sqrt{3})}\right)+3\left(\dfrac{(x-1)(x-\sqrt{2})}{(\sqrt{3}-1)(\sqrt{3}-\sqrt{2})}\right).
  20. anemone

    Challenge Evaluation of an expression

    What is the value of 2(2(2(2(2(2+1)+1)+1)+1)+1)+1?