| 1 × 1 = 1 | ||||||||
| 1 × 2 = 2 | 2 × 2 = 4 | |||||||
| 1 × 3 = 3 | 2 × 3 = 6 | 3 × 3 = 9 | ||||||
| 1 × 4 = 4 | 2 × 4 = 8 | 3 × 4 = 12 | 4 × 4 = 16 | |||||
| 1 × 5 = 5 | 2 × 5 = 10 | 3 × 5 = 15 | 4 × 5 = 20 | 5 × 5 = 25 | ||||
| 1 × 6 = 6 | 2 × 6 = 12 | 3 × 6 = 18 | 4 × 6 = 24 | 5 × 6 = 30 | 6 × 6 = 36 | |||
| 1 × 7 = 7 | 2 × 7 = 14 | 3 × 7 = 21 | 4 × 7 = 28 | 5 × 7 = 35 | 6 × 7 = 42 | 7 × 7 = 49 | ||
| 1 × 8 = 8 | 2 × 8 = 16 | 3 × 8 = 24 | 4 × 8 = 32 | 5 × 8 = 40 | 6 × 8 = 48 | 7 × 8 = 56 | 8 × 8 = 64 | |
| 1 × 9 = 9 | 2 × 9 = 18 | 3 × 9 = 27 | 4 × 9 = 36 | 5 × 9 = 45 | 6 × 9 = 54 | 7 × 9 = 63 | 8 × 9 = 72 | 9 × 9 = 81 |
质数（素数）是大于 1 的自然数，除了 1 和它自身外，不能被其他自然数整除的数。
| 质数区间 | 质数列表 |
|---|---|
| 0 - 99 | 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 |
| 100 - 199 | 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199 |
| 200 - 299 | 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293 |
| 300 - 399 | 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397 |
| 400 - 499 | 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499 |
| 500 - 599 | 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599 |
| 600 - 699 | 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691 |
| 700 - 799 | 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797 |
| 800 - 899 | 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887 |
| 900 - 999 | 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997 |
| \(1^2=1\) | \(2^2=4\) | \(3^2=9\) | \(4^2=16\) | \(5^2=25\) | \(6^2=36\) | \(7^2=49\) | \(8^2=64\) | \(9^2=81\) | \(10^2=100\) |
| \(11^2=121\) | \(12^2=144\) | \(13^2=169\) | \(14^2=196\) | \(15^2=225\) | \(16^2=256\) | \(17^2=289\) | \(18^2=324\) | \(19^2=361\) | \(20^2=400\) |
| \(21^2=441\) | \(22^2=484\) | \(23^2=529\) | \(24^2=576\) | \(25^2=625\) | \(26^2=676\) | \(27^2=729\) | \(28^2=784\) | \(29^2=841\) | \(30^2=900\) |
| \(31^2=961\) | \(32^2=1024\) | \(33^2=1089\) | \(34^2=1156\) | \(35^2=1225\) | \(36^2=1296\) | \(37^2=1369\) | \(38^2=1444\) | \(39^2=1521\) | \(40^2=1600\) |
| \(41^2=1681\) | \(42^2=1764\) | \(43^2=1849\) | \(44^2=1936\) | \(45^2=2025\) | \(46^2=2116\) | \(47^2=2209\) | \(48^2=2304\) | \(49^2=2401\) | \(50^2=2500\) |
| \(51^2=2601\) | \(52^2=2704\) | \(53^2=2809\) | \(54^2=2916\) | \(55^2=3025\) | \(56^2=3136\) | \(57^2=3249\) | \(58^2=3364\) | \(59^2=3481\) | \(60^2=3600\) |
| \(61^2=3721\) | \(62^2=3844\) | \(63^2=3969\) | \(64^2=4096\) | \(65^2=4225\) | \(66^2=4356\) | \(67^2=4489\) | \(68^2=4624\) | \(69^2=4761\) | \(70^2=4900\) |
| \(71^2=5041\) | \(72^2=5184\) | \(73^2=5329\) | \(74^2=5476\) | \(75^2=5625\) | \(76^2=5776\) | \(77^2=5929\) | \(78^2=6084\) | \(79^2=6241\) | \(80^2=6400\) |
| \(81^2=6561\) | \(82^2=6724\) | \(83^2=6889\) | \(84^2=7056\) | \(85^2=7225\) | \(86^2=7396\) | \(87^2=7569\) | \(88^2=7744\) | \(89^2=7921\) | \(90^2=8100\) |
| \(91^2=8281\) | \(92^2=8464\) | \(93^2=8649\) | \(94^2=8836\) | \(95^2=9025\) | \(96^2=9216\) | \(97^2=9409\) | \(98^2=9604\) | \(99^2=9801\) | \(100^2=10000\) |
| \(1^3=1\) | \(2^3=8\) | \(3^3=27\) | \(4^3=64\) | \(5^3=125\) | \(6^3=216\) | \(7^3=343\) | \(8^3=512\) | \(9^3=729\) | \(10^3=1000\) |
| \(11^3=1331\) | \(12^3=1728\) | \(13^3=2197\) | \(14^3=2744\) | \(15^3=3375\) | \(16^3=4096\) | \(17^3=4913\) | \(18^3=5832\) | \(19^3=6859\) | \(20^3=8000\) |
| \(21^3=9261\) | \(22^3=10648\) | \(23^3=12167\) | \(24^3=13824\) | \(25^3=15625\) | \(26^3=17576\) | \(27^3=19683\) | \(28^3=21952\) | \(29^3=24389\) | \(30^3=27000\) |
| \(31^3=29791\) | \(32^3=32768\) | \(33^3=35937\) | \(34^3=39304\) | \(35^3=42875\) | \(36^3=46656\) | \(37^3=50653\) | \(38^3=54872\) | \(39^3=59319\) | \(40^3=64000\) |
| \(41^3=68921\) | \(42^3=74088\) | \(43^3=79507\) | \(44^3=85184\) | \(45^3=91125\) | \(46^3=97336\) | \(47^3=103823\) | \(48^3=110592\) | \(49^3=117649\) | \(50^3=125000\) |
| \(51^3=132651\) | \(52^3=140608\) | \(53^3=148877\) | \(54^3=157464\) | \(55^3=166375\) | \(56^3=175616\) | \(57^3=185193\) | \(58^3=195112\) | \(59^3=205379\) | \(60^3=216000\) |
| \(61^3=226981\) | \(62^3=238328\) | \(63^3=250047\) | \(64^3=262144\) | \(65^3=274625\) | \(66^3=287496\) | \(67^3=300763\) | \(68^3=314432\) | \(69^3=328509\) | \(70^3=343000\) |
| \(71^3=357911\) | \(72^3=373248\) | \(73^3=389017\) | \(74^3=405224\) | \(75^3=421875\) | \(76^3=438976\) | \(77^3=456533\) | \(78^3=474552\) | \(79^3=493039\) | \(80^3=512000\) |
| \(81^3=531441\) | \(82^3=551368\) | \(83^3=571787\) | \(84^3=592704\) | \(85^3=614125\) | \(86^3=636056\) | \(87^3=658503\) | \(88^3=681472\) | \(89^3=704969\) | \(90^3=729000\) |
| \(91^3=753571\) | \(92^3=778688\) | \(93^3=804357\) | \(94^3=830584\) | \(95^3=857375\) | \(96^3=884736\) | \(97^3=912673\) | \(98^3=941192\) | \(99^3=970299\) | \(100^3=1000000\) |
\(a, b, c, d\) 表示边长 \(h\) 表示高度 \(r\) 表示半径 \(\pi\) 是圆周率，约等于 \(3.14159\) \(a, b\) 表示椭圆的长半轴和短半轴 椭圆周长公式为近似公式（拉马努金公式） \(d_1, d_2\) 表示对角线长度 \(\theta\) 表示圆心角（度） \(R, r\) 表示外圆半径和内圆半径
| 几何图形 | 图形示例 | 周长公式 | 面积公式 | 备注说明 |
|---|---|---|---|---|
| 三角形 |
|
\(P = a + b + c\) | \(S = \dfrac{1}{2} b h\) | \(b\) = 底，\(h\) = 高，面积 \(= \dfrac{1}{2}\times \text{底} \times \text{高}\) |
| 正方形 |
|
\(P = 4a\) | \(S = a^2\) | \(a\) = 正方形边长 |
| 长方形 |
|
\(P = 2(a + b)\) | \(S = a b\) | \(a\) = 长，\(b\) = 宽 |
| 梯形 |
|
\(P = a + b + c + d\) | \(S = \dfrac{1}{2}(a + b)h\) | \(a\) = 上底，\(b\) = 下底，\(h\) = 高 |
| 平行四边形 |
|
\(P = 2(a + b)\) | \(S = b h\) | \(b\) = 底，\(h\) = 高 |
| 菱形 |
|
\(P = 4a\) | \(S = \dfrac{1}{2} d_1 d_2\) | \(a\) = 边长，\(d_1\) = 长对角线，\(d_2\) = 短对角线 |
| 筝形 |
|
\(P = 2(a + b)\) | \(S = \dfrac{1}{2} d_1 d_2\) | \(a, b\) = 边长，\(d_1, d_2\) = 对角线 |
| 扇形 |
|
\(P = 2r + \dfrac{\theta}{180}\pi r\) | \(S = \dfrac{\theta}{360}\pi r^2\) | \(r\) = 半径，\(\theta\) = 扇形夹角（度），\(\pi\) 是圆周率，约等于 \(3.14159\) |
| 圆形 |
|
\(P = 2\pi r\) | \(S = \pi r^2\) | \(r\) = 半径，\(\pi\) 是圆周率，约等于 \(3.14159\) |
| 圆环 |
|
\(P = 2\pi (R + r)\) | \(S = \pi (R^2 - r^2)\) | \(R\) = 大半径，\(r\) = 小半径，\(\pi\) 是圆周率 |
| 椭圆 |
|
\(P \approx \pi\left[3(a+b) - \sqrt{(3a+b)(a+3b)}\right]\) | \(S = \pi a b\) | \(a\) = 长半轴，\(b\) = 短半轴，\(\pi\) 是圆周率 |
| 正五边形 |
|
\(P = 5a\) | \(S = \dfrac{1}{4}\sqrt{5(5+2\sqrt{5})}\,a^2\) | \(a\) = 边长 |
| 正六边形 |
|
\(P = 6a\) | \(S = \dfrac{3\sqrt{3}}{2} a^2\) | \(a\) = 边长 |
| 正八边形 |
|
\(P = 8a\) | \(S = 2(1+\sqrt{2})\,a^2\) | \(a\) = 边长 |
\(a, b, c\) 表示边长 \(h\) 表示高度 \(r\) 表示半径 \(\pi\) 是圆周率，约等于 \(3.14159\) \(l\) 表示斜高（圆锥母线） \(\sqrt{2} \approx 1.414\)，\(\sqrt{3} \approx 1.732\)
| 立体图形 | 图形示例 | 表面积公式 | 体积公式 | 备注说明 |
|---|---|---|---|---|
| 立方体 |
|
\(S = 6a^2\) | \(V = a^3\) | \(a\) = 边长 |
| 长方体 |
|
\(S = 2(ab + bc + ac)\) | \(V = a b c\) | \(a\) = 长，\(b\) = 宽，\(c\) = 高 |
| 圆柱 |
|
\(S = 2\pi r^2 + 2\pi r h\) | \(V = \pi r^2 h\) | \(\pi\) = 圆周率，\(r\) = 底面半径，\(h\) = 高 |
| 球体 |
|
\(S = 4\pi r^2\) | \(V = \dfrac{4}{3}\pi r^3\) | \(\pi\) = 圆周率，\(r\) = 球体半径 |
| 椭圆球体 |
|
\(S = \pi r^2 + \pi r l\) | \(V = \dfrac{1}{3}\pi r^2 h\) | \(\pi\) = 圆周率，\(r\) = 底面半径，\(h\) = 高，\(l\) = 母线 |
| 圆锥 |
|
\(S = \pi r^2 + \pi r l\) | \(V = \dfrac{1}{3}\pi r^2 h\) | \(\pi\) = 圆周率，\(r\) = 底面半径，\(h\) = 高，\(l\) = 母线 |
| 三棱锥 |
|
\(S = 4 \times \dfrac{1}{2} a l = 2al\) | \(V = \dfrac{\sqrt{2}}{12} a^3\) | \(a\) = 棱长，\(l\) = 斜高，\(h\) = 高 |
| 四棱锥 |
|
\(S = 2al + a^2 = a^2 + 2a\sqrt{h^2 + \dfrac{a^2}{4}}\) | \(V = \dfrac{1}{3}a^2 h = \dfrac{1}{3}a^2\sqrt{l^2 - \left(\dfrac{a}{2}\right)^2}\) | \(a\) = 正方形边长，\(l\) = 斜高，\(h\) = 高 |
下表列出常见特殊角的三角函数精确值。
| 角度 | 弧度 | 图形实例 | \(\sin\theta\) | \(\cos\theta\) | \(\tan\theta\) | \(\cot\theta\) | \(\sec\theta\) | \(\csc\theta\) |
|---|---|---|---|---|---|---|---|---|
| \(0^\circ\) | \(0\) |
0°
|
\(0\) | \(1\) | \(0\) | \(\infty\) | \(1\) | \(\infty\) |
| \(15^\circ\) | \(\dfrac{\pi}{12}\) |
15°
|
\(\dfrac{\sqrt{6} - \sqrt{2}}{4}\) | \(\dfrac{\sqrt{6} + \sqrt{2}}{4}\) | \(2 - \sqrt{3}\) | \(2 + \sqrt{3}\) | \(\sqrt{6} - \sqrt{2}\) | \(\sqrt{6} + \sqrt{2}\) |
| \(30^\circ\) | \(\dfrac{\pi}{6}\) |
30°
|
\(\dfrac{1}{2}\) | \(\dfrac{\sqrt{3}}{2}\) | \(\dfrac{\sqrt{3}}{3}\) | \(\sqrt{3}\) | \(\dfrac{2\sqrt{3}}{3}\) | \(2\) |
| \(45^\circ\) | \(\dfrac{\pi}{4}\) |
45°
|
\(\dfrac{\sqrt{2}}{2}\) | \(\dfrac{\sqrt{2}}{2}\) | \(1\) | \(1\) | \(\sqrt{2}\) | \(\sqrt{2}\) |
| \(60^\circ\) | \(\dfrac{\pi}{3}\) |
60°
|
\(\dfrac{\sqrt{3}}{2}\) | \(\dfrac{1}{2}\) | \(\sqrt{3}\) | \(\dfrac{\sqrt{3}}{3}\) | \(2\) | \(\dfrac{2\sqrt{3}}{3}\) |
| \(75^\circ\) | \(\dfrac{5\pi}{12}\) |
75°
|
\(\dfrac{\sqrt{6} + \sqrt{2}}{4}\) | \(\dfrac{\sqrt{6} - \sqrt{2}}{4}\) | \(2 + \sqrt{3}\) | \(2 - \sqrt{3}\) | \(\sqrt{6} + \sqrt{2}\) | \(\sqrt{6} - \sqrt{2}\) |
| \(90^\circ\) | \(\dfrac{\pi}{2}\) |
90°
|
\(1\) | \(0\) | \(\infty\) | \(0\) | \(\infty\) | \(1\) |