World Mathematics Invitational (WMI) is the first international competition founded by Taiwan. It gathers institutes and organizations worldwide that make efforts in promoting and popularizing mathematics. Through interacting with other math-loving students that represent their countries, students can expand their worldview, experience different cultures, and thus their horizon as well as their future will be broaden. (sc : http://www.wminv.org/)
Berikut ini soal dan solusi WMI grade 8A tahun 2022
1) Given that \(40^2=1600\) and \(50^2=2500\). If \(n\) is an integer, and \(n<\sqrt{2022}<n+1\), find \(n\).
(A) 47
(B) 45
(C) 44
(D) 43
2) Find the hundreds digit of \(9999.98Γ9999.98\)
(A) 4
(B) 5
(C) 6
(D) 8
3) Which option below is the factor of \(2(x-1)^2+5(x-1)+3\)?
(A) x
(B) x-1
(C) x+1
(D) 2x+3
4) In the picture a rectangle ABCD is \(3x+1\) in lenght and \(2x+1\) in width. If a square whose side length is 3 is cut from the rectangle, find the perimeter of the remaining part.
(A) 10x
(B) 10x-2
(C) 10x-4
(D) 10x+4
5) A pair of set squares are placed as below. If \(β I=80ΒΊ\), find \(β 2=?\)
(A) 80ΒΊ
(B) 95ΒΊ
(C) 100ΒΊ
(D) 105ΒΊ
6) In \(Ξπ΄π΅πΆ, AB= \sqrt{6} + 1, BC = 2 + \sqrt{3}\), and \(AC= \sqrt{2} + \sqrt{5}\), Find the relation among \(β π΄,β π΅,\) and \(β πΆ\).
(A) \(β A>β B>β C\)
(B) \(β B>β A>β C\)
(C) \(β C>β B>β A\)
(D) \(β A>β C>β B\)
7) Supose \(π, π, 48, π, π\) and \(30\) make an arithmetic sequence; \(π, π₯, π,\) and \(π¦\) make a geometric
sequence. Find \(π¦\).
(A) \(12\sqrt{3}\)
(B) \(12\sqrt{6}\)
(C) \(18\sqrt{2}\)
(D) \(18\sqrt{6}\)
8) As shown in the picture, \(πΏ//π, β 1 = β 3 = 35Β°\). Find \(β 1 + β 2 + β 3 + β 4 + β 5\).
(A) 180ΒΊ
(B) 200ΒΊ
(C) 210ΒΊ
(D) 240ΒΊ
9) Two grid points A and B are on a piece of \(4Γ4\) square paper. Find a grid point C to make \(ΞABC\) an isosceles right triangle. How many such points C’s are there?
(A) 1
(B) 2
(C) 3
(D) 4
10) Company W uses the linear function to adjust employees’ salary. Below shows the monthly salary of three employees in 2021 and 2022. How much is Max’ monthly salary in 2021?
(A) $700
(B) $750
(C) $800
(D) $900
11. In the picture, \(ABCD\) is a square, and \(AP = 7, BP = 13\). Find the area of \(ABCD\)
(A) 240
(B) 256
(C) 288
(D) 289
12. Set \(f(n)οΌ4nοΌ90\), in which n is a positive integer. If \(f(1)οΌf(2)οΌf(3)οΌβ¦οΌf(n)οΌ0\), find \(n\).
(A) 34
(B) 36
(C) 44
(D) 46
13) Set the median of the ten numbers 1, 3, 3, 4, 5, 5, 6, 7, 7, and 9 to be \(a\). If a number is taken out at will from these ten numbers, find the probability that such number is larger than \(a\).
(A) \(\frac{2}{5}\)
(B) \(\frac{3}{5}\)
(C) \(\frac{1}{4}\)
(D) \(\frac{2}{3}\)
14) Given that \(π\) is a root of the quadratic equation \(π₯^2 + 2π₯ β 21 = 0\). Find \((π β 3)(π + 3)(π β1)(π + 5)\)
(A) 20
(B) -15
(C) -20
(D) -35
15) Given a rhombus \(ABCD\) on the rectangular coordinate plane. Suppose its side \(AD β₯ y-axis\) on \(E\), point \(B\) is on \(y-axis, BC οΌ5, BE οΌ2 DE\) , and the graph of the inverse function \(yοΌ\frac{k}{x}(xοΌ0)\) passes through points \(C\) and \(D\) at the same time. Find \(k\).
(A) \(\frac{20}{3}\)
(B) \(\frac{40}{3}\)
(C) \(\frac{5}{2}\)
(D) \(\frac{5}{4}\)