MathDB

2

Part of 2018 Hanoi Open Mathematics Competitions

Problems(4)

2f(x) + f(2 - x) = 5 + x, f(0) + f(2) wanted (HOMC 2018 Ind. p2)

Source:

1/31/2020
Let f(x)f(x) be a polynomial such that 2f(x)+f(2−x)=5+x2f(x) + f(2 - x) = 5 + x for any real number x. Find the value of f(0)+f(2)f(0) + f(2).
A. 44 B. 00 C.2 2 D. 33 E. 11
polynomialfunctional equation
area of rectangle (HOMC 2018 Team j2)

Source:

1/31/2020
Let ABCDABCD be a rectangle with \angle ABD = 15^o, BD = 6 cm. Compute the area of the rectangle.
A. 99 cm2^2 B. 939 \sqrt3 cm2^2 C. 1818 cm2^2 D. 18318 \sqrt3 cm2^2 E. 24324 \sqrt3 cm2^2
geometryrectangle
max area of regular hexagon inside equliateral (HOMC 2018 ind. sen2)

Source:

2/2/2020
What is the largest area of a regular hexagon that can be drawn inside the equilateral triangle of side 33?
A. 373\sqrt7 B. 332\frac{3 \sqrt3}{2} C. 252\sqrt5 D. 338\frac{3\sqrt3}{8} E. 353\sqrt5
areamaximumhexagonEquilateralgeometry
computanional in a triangle (HOMC 2018 S Team 2)

Source:

2/16/2020
In triangle ABC,∠BAC=60o,AB=3aABC,\angle BAC = 60^o, AB = 3a and AC=4a,(a>0)AC = 4a, (a > 0). Let MM be point on the segment ABAB such that AM=13AB,NAM =\frac13 AB, N be point on the side ACAC such that AN=12ACAN =\frac12AC. Let II be midpoint of MNMN. Determine the length of BIBI.
A. a219\frac{a\sqrt2}{19} B. 2a19\frac{2a}{\sqrt{19}} C. 19a192\frac{19a\sqrt{19}}{2} D. 19a2\frac{19a}{\sqrt2} E. a192\frac{a\sqrt{19}}{2}
geometryTriangle