中学受験生の暗記すべき計算160選

目次

平方数(30)
平方数の応用1(20)
平方数の応用2(20)
15の倍数(20)
25の倍数(20)
12の倍数(20)
三角数(15)
円周率(18)

平方数(30)

11 × 11 = 121
12 × 12 = 144
13 × 13 = 169
14 × 14 = 196
15 × 15 = 225
16 × 16 = 256
17 × 17 = 289
18 × 18 = 324
19 × 19 = 361
20 × 20 = 400
21 × 21 = 441
22 × 22 = 484
23 × 23 = 529
24 × 24 = 576
25 × 25 = 625
26 × 26 = 676
27 × 27 = 729
28 × 28 = 784
29 × 29 = 841
30 × 30 = 900
31 × 31 = 961
32 × 32 = 1024
33 × 33 = 1089
34 × 34 = 1156
35 × 35 = 1225
36 × 36 = 1296
37 × 37 = 1369
38 × 38 = 1444
39 × 39 = 1521
40 × 40 = 1600

平方数の応用1(20)

10 × 12 = 120 = 11 × 11 - 1
11 × 13 = 143 = 12 × 12 - 1
12 × 14 = 168 = 13 × 13 - 1
13 × 15 = 195 = 14 × 14 - 1
14 × 16 = 224 = 15 × 15 - 1
15 × 17 = 255 = 16 × 16 - 1
16 × 18 = 288 = 17 × 17 - 1
17 × 19 = 323 = 18 × 18 - 1
18 × 20 = 360 = 19 × 19 - 1
19 × 21 = 399 = 20 × 20 - 1
20 × 22 = 440 = 21 × 21 - 1
21 × 23 = 483 = 22 × 22 - 1
22 × 24 = 528 = 23 × 23 - 1
23 × 25 = 575 = 24 × 24 - 1
24 × 26 = 624 = 25 × 25 - 1
25 × 27 = 675 = 26 × 26 - 1
26 × 28 = 728 = 27 × 27 - 1
27 × 29 = 783 = 28 × 28 - 1
28 × 30 = 840 = 29 × 29 - 1
29 × 31 = 899 = 30 × 30 - 1

平方数の応用2(20)

10 × 14 = 140 = 12 × 12 - 4
11 × 15 = 165 = 13 × 13 - 4
12 × 16 = 192 = 14 × 14 - 4
13 × 17 = 221 = 15 × 15 - 4
14 × 18 = 252 = 16 × 16 - 4
15 × 19 = 285 = 17 × 17 - 4
16 × 20 = 320 = 18 × 18 - 4
17 × 21 = 357 = 19 × 19 - 4
18 × 22 = 396 = 20 × 20 - 4
19 × 23 = 437 = 21 × 21 - 4
20 × 24 = 480 = 22 × 22 - 4
21 × 25 = 525 = 23 × 23 - 4
22 × 26 = 572 = 24 × 24 - 4
23 × 27 = 621 = 25 × 25 - 4
24 × 28 = 672 = 26 × 26 - 4
25 × 29 = 725 = 27 × 27 - 4
26 × 30 = 780 = 28 × 28 - 4
27 × 31 = 857 = 29 × 29 - 4
28 × 32 = 896 = 30 × 30 - 4

15の倍数(20)

15の倍数は15にかける数を半分した値をその数に足して10倍すると求まります。例えば15に18をかける場合、18に18を半分した9を足して27にします。それを10倍して270が求まります。

15 × 11 = 165
15 × 12 = 180
15 × 13 = 195
15 × 14 = 210
15 × 15 = 225
15 × 16 = 240
15 × 17 = 255
15 × 18 = 270
15 × 19 = 285
15 × 20 = 300
15 × 21 = 315
15 × 22 = 330
15 × 23 = 345
15 × 24 = 360
15 × 25 = 375
15 × 26 = 390
15 × 27 = 405
15 × 28 = 420
15 × 29 = 435
15 × 30 = 450

25の倍数(20)

25の倍数は、25にかける数を4で割って100倍すると求まります。例えば25に16をかける場合、16を4で割って4にして100倍すると400になります。

25 × 11 = 275
25 × 12 = 300
25 × 13 = 325
25 × 14 = 350
25 × 15 = 375
25 × 16 = 400
25 × 17 = 425
25 × 18 = 450
25 × 19 = 475
25 × 20 = 500
25 × 21 = 525
25 × 22 = 550
25 × 23 = 575
25 × 24 = 600
25 × 25 = 625
25 × 26 = 650
25 × 27 = 675
25 × 28 = 700
25 × 29 = 725
25 × 30 = 750

12の倍数(20)

12 × 11 = 132
12 × 12 = 144
12 × 13 = 156
12 × 14 = 168
12 × 15 = 180
12 × 16 = 192
12 × 17 = 204
12 × 18 = 216
12 × 19 = 228
12 × 20 = 240
12 × 21 = 252
12 × 22 = 264
12 × 23 = 276
12 × 24 = 288
12 × 25 = 300
12 × 26 = 312
12 × 27 = 324
12 × 28 = 336
12 × 29 = 348
12 × 30 = 360

三角数(15)

□個の中から△個選ぶ組み合わせを□C△と書くことにします。これを三角数と言います。

※Cは当ページ独自の表記です。受験本番で絶対に使わないでください。

2 C 2 = 1
3 C 2 = 3
4 C 2 = 6
5 C 2 = 10
6 C 2 = 15
7 C 2 = 21
8 C 2 = 28
9 C 2 = 36
10 C 2 = 45
11 C 2 = 55
12 C 2 = 66
13 C 2 = 78
14 C 2 = 91
15 C 2 = 105
16 C 2 = 120

円周率(18)

3.14 × 2 = 6.28
3.14 × 3 = 9.42
3.14 × 4 = 12.56
3.14 × 5 = 15.7
3.14 × 6 = 18.84
3.14 × 7 = 21.98
3.14 × 8 = 25.12
3.14 × 9 = 28.26
3.14 × 10 = 31.4
3.14 × 12 = 37.68
3.14 × 15 = 47.1
3.14 × 16 = 50.24
3.14 × 18 = 56.52
3.14 × 20 = 62.8
3.14 × 24 = 75.36
3.14 × 25 = 78.5
3.14 × 30 = 94.2
3.14 × 32 = 100.48

(追加)

分数の足し算

分数の足し算は、分数を二つの分数の足し算に分解できるようにします。

※分解の仕方はいろいろあるので、次の例はあくまでも一例。

$\dfrac{ 5 }{ 6 } = \dfrac{ 1 }{ 2 } + \dfrac{ 1 }{ 3 }$

$\dfrac{ 3 }{ 4 } = \dfrac{ 1 }{ 2 } + \dfrac{ 1 }{ 4 }$

$\dfrac{ 7 }{ 10 } = \dfrac{ 1 }{ 2 } + \dfrac{ 1 }{ 5 }$

$\dfrac{ 2 }{ 3 } = \dfrac{ 1 }{ 2 } + \dfrac{ 1 }{ 6 }$

$\dfrac{ 7 }{ 12 } = \dfrac{ 1 }{ 3 } + \dfrac{ 1 }{ 4 }$

$\dfrac{ 8 }{ 15 } = \dfrac{ 1 }{ 3 } + \dfrac{ 1 }{ 5 }$

$\dfrac{ 1 }{ 2 } = \dfrac{ 1 }{ 3 } + \dfrac{ 1 }{ 6 }$

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