
Asesmen Diagnostik Kognitif
Authored by Wa Fitriani
Mathematics
11th Grade
Used 1+ times

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7 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 5 pts
Ada tiga langkah dalam induksi matematika yang diperlukan untuk membuktikan suatu rumus atau pernyataan. Langkah kedua yang kita pelajari adalah ...
Membuktikan bahwa rumus atau pernyataan tersebut benar untuk n = 1
Membuktikan bahwa rumus atau pernyataan tersebut benar untuk n = 0
Mengasumsikan bahwa rumus atau pernyataan tersebut benar untuk n = k
Membuktikan bahwa rumus atau pernyataan tersebut benar untuk n = ~
Membuktikan bahwa rumus atau pernyataan tersebut benar untuk n = k + 1
2.
MULTIPLE CHOICE QUESTION
30 sec • 5 pts
Jumlah n bilangan ganjil pertama dapat dinyatakan sebagai berikut:
1 + 3 + 5 + 7 + . . . + (2n − 1) = n2
Untuk membuktikan kebenaran pernyataan tersebut dengan induksi matematika, maka diperlukan pemisalan/asumsi langkah ke tiga yaitu ...
pernyataan tersebut benar untuk n = k, dengan k bilangan asli.
1 + 3 + 5 + 7 + . . . + (2k − 1) = k2
Pernyataan tersebut benar untuk n = 1:
2(1) − 1 = 12
Pernyataan tersebut benar untuk n = k + 1:
1 + 3 + 5 + 7 + . . . + (2k − 1) + (2k + 1) = (k + 1)2
Pernyataan tersebut bernilai salah.
Pernyataan tersebut benar untuk n = k + 1:
1 + 3 + 5 + 7 + . . . + (2k − 1) = (k + 1)2
3.
MULTIPLE CHOICE QUESTION
30 sec • 5 pts
Diketahui S(n) adalah rumus dari:
1+5+9+...+(4n−3)=2n2−n
Andaikan S(n) benar untuk n = k, maka...
1+5+9+...+(4k−3)=2n2−2
(4k−3)=2k2−k
(4k−3)=2n2−n
(4n−3)=2k2−k
1+5+9+...+(4k−3)=2k2−k
4.
MULTIPLE CHOICE QUESTION
30 sec • 5 pts
Misalkan S(n) = 2n − 1, dengan n anggota himpunan bilangan asli. Untuk sebarang bilangan bulat k, tentukan:
a) S(k)
b) S(k + 1)
a) S(k) = 2k − 1
b) S(k + 1) = 2n + 1
a) S(k) = 2k + 1
b) S(k + 1) = 2k + 1
a) S(k) = 2k − 1
b) S(k + 1) = 2k + 1
a) S(k) = 2k − 1
b) S(k + 1) = 2k - 1
5.
MULTIPLE CHOICE QUESTION
30 sec • 5 pts
Pernyataan
1+2+3+...+ n = ½ n (n+1) bernilai...
Benar
Salah
6.
MULTIPLE CHOICE QUESTION
30 sec • 5 pts
Pernyataan
1.2+2.3+3.4+...+n(n+1)=⅓n(n+1)(n+2)bernilai...
Benar
Salah
7.
MULTIPLE CHOICE QUESTION
30 sec • 5 pts
Jika n = 10 maka dari: 1+3+6+10+...+½n(n+1)=...
220
110
66
330
660
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