# SEAMO PAPER D 2019 [PROBLEM And SOLUTION]

Problem and Solution SEAMO 2019 paper D. Soal ini bersumber dari seamo-official.org

1.Given $$(a+b)^3=a^3 + 3a^2b + 3ab^2 +b^3$$, find the $$2^{nd}$$ and $$3^{rd}$$terms in the expansion of $$(2x+3y)^3$$.

(A) $$18x^2y+54xy^2$$
(B) $$24x^2y+54xy^2$$
(C) $$36x^2y+54xy^2$$
(D) $$24x^2y+27xy^2$$
(E) None of the above

Suku kedua dari $$(2𝑥 + 3𝑦)^3$$ adalah $$3(2𝑥)^2(3𝑦) = 36𝑥^2𝑦$$
Suku ketiga dari $$(2𝑥 + 3𝑦)^3$$ adalah $$3(2𝑥)(3𝑦)^2 =54𝑥𝑦^2$$

2. Evaluate

$$\frac{20192018^2+1}{20192017^2+20192019^2}$$

(A) $$\frac{1}{4}$$
(B) $$\frac{1}{3}$$
(C) $$\frac{1}{2}$$
(D) $$1$$
(E) None of the above

Ingat !!
$$(𝑎+𝑏)^2=𝑎^2+2𝑎𝑏+𝑏^2$$
$$(𝑎−𝑏)^2=𝑎^2+2𝑎𝑏+𝑏^2$$
$$𝑎^2−𝑏^2=(𝑎−𝑏)(𝑎+𝑏)$$

Misalkan $$𝑥=20192018$$

$$\frac{20192018^2+1}{20192017^2+20192019^2}$$

$$=\frac{𝑥^2+1}{(𝑥−1)^2+(𝑥+1)^2}=\frac{𝑥^2+1}{𝑥^2−2𝑥+1+𝑥^2+2𝑥+1}$$

$$={𝑥^2+1}{2𝑥^2+2}=\frac{𝑥^2+1}{2(𝑥^2+1)}=\frac{1}{2}$$

3. It is known that $$ABCDE$$ is a regular pentagon. O is a point in $$ABCDE$$ such that $$ΔDOE$$ is equilateral. Find $$∠AOC$$.

(A) 108°
(B) 128°
(C) 138°
(D) 168°
(E) None of the above $$∠𝐴 = ∠𝐵 = ∠𝐶 = ∠𝐷 = ∠𝐸 = 108°$$
$$∠𝐶𝐷𝑂 = 108 − 60 = 48°$$
Karena segitiga $$OCD$$ sama kaki maka $$∠𝐷𝐶𝑂 = ∠𝐷𝑂𝐶 = 𝑎$$

perhatikan $$ΔCOD$$
$$∠𝐶𝐷𝑂 + ∠𝐷𝐶𝑂 + ∠𝐷𝑂𝐶 = 180°$$
$$𝑎 + 𝑎 + 48° = 180° ⟹ 2𝑎 = 132° ⟹ a=66°$$
Jadi $$∠𝐶𝐴𝑂 = 360° − 60° − 66° − 66° = 168°$$

4. Given that 2016 is a leap year and Sonia’s birthday fell on Sunday, $$24^{th}$$ of June, 2012. In which year will her birthday next fall on a Sunday?
(A) 2017
(B) 2018
(C) 2019
(D) 2020
(E) None of the above

Bukan tahun kabisat 365 mod 7 = 1, tahun kabisat 366 mod 7 = 2
24 Juni 2012 hari Senin
24 Juni 2013 hari Selasa
24 Juni 2014 hari Rabu
24 Juni 2015 hari Kamis
24 Juni 2016 hari Sabtu  (tahun kabisat)
24 Juni 2017 hari Minggu
24 Juni 2018 hari Senin

Jadi di tahun 2018 Sonia berulang tahun lagi di hari Senin

5. Which of the following statements is true about the expressions

$$\sqrt{5} + \sqrt{8}$$ and $$\sqrt{4} + \sqrt{10}$$ ?

(A) $$\sqrt{4} + \sqrt{10}>\sqrt{5} + \sqrt{8}$$
(B) $$\sqrt{4} + \sqrt{10}<\sqrt{5} + \sqrt{8}$$
(C) $$\sqrt{4} + \sqrt{10}=\sqrt{5} + \sqrt{8}$$
(D) They are both rational
(E) None of the above

$$(\sqrt{5} + \sqrt{8})^2=5+8+2\sqrt{40}=13+2\sqrt{40}$$
$$(\sqrt{4} + \sqrt{10})^2=4+10+2\sqrt{40}=14+2\sqrt{40}$$

dari keterangan di atas dapat disimpulkan bahwa $$\sqrt{4} + \sqrt{10}>\sqrt{5} + \sqrt{8}$$

6. A batch of berries has mass 100 kg. 1% of its mass is flesh and 99% is water. After a few hours in the sun, the water content reduced to 98%. How much does the batch weigh now?
(A) 98 kg
(B) 97 kg
(C) 48 kg
(D) 49 kg
(E) None of the above

Diketahui berat air seluruhnya adalah 99 kg, setelah dijemur berat airnyanya menjadi 98% atau 99 × 98% = 97,02 kg