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Daftar Materi OSN Matematika SMA/MA 2018

Bagi Anda yang biasa mengikuti seleksi Olimpiade Siswa Nasional (OSN) sejak dini hingga ke SMA/MA tentu tidak merasa asing lagi dengan materi-materi atau soal-soal yang akan diujikan. Anda minimal sudah tahu bagaimana tingkat kesulitannya dan bagaimana strategi yang jitu dalam menyelesaikan soal-soal tersebut. Namun, bagi mereka yang baru ingin mencoba mengikuti seleksi pada tahun ini atau tahun depan, blog Matematika Ku Bisa berikut ini memberikan  Daftar Materi OSN Matematika SMA/MA 2018 (sebaran dari kemendikbud) yang bisa dijadikan acuan bagi Anda untuk mempersiapkan diri.

A. Bidang Aljabar

1. Sistem bilangan real
o Himpunan bilangan real dilengkapi dengan operasi tambah dan kali
beserta sifat-sifatnya.
o Sifat urutan (sifat trikotomi, relasi lebih besar/kecil dari, beserta sifat-

2. Ketaksamaan
o Penggunaan sifat urutan untuk menyelesaikan soal-soal ketaksamaan.
o Penggunaan sifat bahwa kuadrat bilangan real selalu non negatif
untuk menyelesaikan soal-soal ketaksamaan.
o Ketaksamaan yang berkaitan dengan rataan kuadratik, rataan
aritmatika, rataan geometri, dan rataan harmonik.

3. Nilai mutlak
o Pengertian nilai mutlak dan sifat-sifatnya
o Aspek geometri nilai mutlak
o Persamaan dan ketaksamaan yang melibatkan nilai mutlak

4. Sukubanyak (polinom)
o Algoritma pembagian
o Teorema sisa
o Teorema faktor
o Teorema Vieta (sifat simetri akar)

5. Fungsi
o Pengertian dan sifat-sifat fungsi
o Komposisi fungsi
o Fungsi invers
o Pencarian fungsi yang memenuhi sifat tertentu

6. Sistem koordinat bidang
o Grafik fungsi
o Persamaan dan grafik fungsi irisan kerucut (lingkaran, ellips, parabola,
dan hiperbola)

7. Barisan dan deret
o Suku ke-n suatu barisan
o Jumlah n suku pertama suatu deret
o Deret tak hingga
o Notasi sigma

8. Persamaan dan sistem persamaan
o Penggunaan sifat-sifat fungsi untuk menyelesaikan persamaan dan
sistem persamaan
o Penggunaan ketaksamaan untuk menyelesaikan persamaan dan sistem

B. Bidang Geometri

1. Hubungan antara garis dan titik

2. Hubungan antara garis dan garis

3. Bangun-bangun bidang datar
o Segitiga
o Segiempat
o Segibanyak beraturan
o Lingkaran

4. Kesebangunan dan kekongruenan

5. Sifat-sifat segitiga: garis istimewa (garis berat, garis bagi, garis tinggi, garis

6. Dalil Menelaus

7. Dalil Ceva

8. Dalil Stewart

9. Relasi lingkaran dengan titik
o Titik kuasa (power point)

10. Relasi lingkaran dengan garis:
o Bersinggungan
o Berpotongan
o Tidak berpotongan

11. Relasi lingkaran dengan segitiga:
o Lingkaran dalam
o Lingkaran luar

12. Relasi lingkaran dengan segiempat:
o Segi empat tali busur (beserta sifat-sifatnya)
o Dalil Ptolomeus

13. Relasi lingkaran dengan lingkaran:
o Dua lingkaran tidak beririsan: baik salah satu di dalam atau di luar
yang lain
o Dua lingkaran beririsan di satu titik (bersinggungan): dari dalam atau
dari luar
o Dua lingkaran beririsan di dua titik
o Lingkaran-lingkaran sepusat

14. Garis-garis yang melalui satu titik (konkuren), titik-titik yang segaris

15. Trigonometri (perbandingan, fungsi, persamaan, dan identitas)

16. Bangun-bangun ruang sederhana

C. Bidang Kombinatorika

1. Prinsip pencacahan
o Prinsip penjumlahan
o Prinsip perkalian
o Permutasi dan kombinasi
o Penggunaan prinsip pencacahan untuk menghitung peluang suatu

2. Prinsip rumah merpati (pigeonhole principle, prinsip Dirichlet)

3. Prinsip paritas

D. Bidang Teori Bilangan

1. Sistem bilangan bulat (himpunan bilangan bulat dan sifat-sifat operasinya)
2. Keterbagian (pengertian, sifat-sifat elementer, algoritma pembagian)
3. Faktor persekutuan terbesar dan kelipatan persekutuan terkecil, relatif
prima, algoritma Euklid
4. Bilangan prima
5. Teorema dasar aritmatika (faktorisasi prima)
6. Persamaan dan sistem persamaan bilangan bulat
7. Fungsi tangga

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