SEAMO PAPER D 2019 [PROBLEM And SOLUTION]

19. In sector AOB , segment AB has length 18 cm. OA and OB are tangent to the two circles and arc AB is tangent to the circle with centre C . Given that the circle with centre C has a radius of 6 cm, find the radius for the circle with centre D.

(A) 2
(B) 3
(C) 4
(D) 5
(E) None of the above

20. The side length of square ABCD is 2√15 . E and F are midpoints of
AB and BC, respectively. AF intersects DE and DB at M and N. Find the area of ΔDMN.

(A) 8
(B) 9
(C) 10
(D) 11
(E) None of the above

21. Let \(a_n\) be the number of ways to climb up a flight of \(n\) steps by taking either 1 or 2 steps at a time.
Find the remainder when `\(a_{2019}\) is
divided by 7.

23. Find the sum of all the positive integral values of \(n\) for which the fraction \(\frac{7n+15}{n-3}\) is also an integer.

24. \(α\) and \(β\) satisfy the conditions

\(\frac{α^2-αβ+β^2}{α^2+αβ+β^2}=\frac{31}{43}\)
\(\frac{1}{α}+\frac{1}{β}=\frac{7}{2}\)

The quadratic equation with \(α\) and \(β\) as roots and \(p\) is positive is \(px^2+qx+r\),
where \(p\), \(q\) and \(r\) are integers with a greatest common divisor of 1.

Find \(p+q+r\).

25. Suppose \(n_1\) and \(n_2\) are positive integers where \(1≤n_1<n_2≤99\).

When all possible values of \(\frac{n_1}{n_2}\) are arranged in ascending order, find the fraction that comes after \(\frac{17}{76}\).

baca juga Soal Lomba Matematika SMP PEMNAS UB