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OxfordAQA · International GCSE · Mathematics الموضوع 1 5:29 سرد باللغة الإنجليزية · ترجمة مدمجة بالإنجليزية + الصينية
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Unit 3.1 has no formulae sheet: the specification is the recall list.
3.1 单元没有公式表：考纲本身就是要记的清单。
Know the compound interest formula, that a rounded value lies half a unit either side, how a recurring decimal becomes a fraction, and the exponential model.
要记住复利公式、近似值在上下各半个单位内、循环小数如何化为分数，以及指数模型。
To compare, convert to one form: three fifths is 0.6.
比较大小时先化成同一形式：3/5 = 0.6。
Add mixed numbers through improper fractions over a common denominator: 43 twelfths, which is 3 and 7 twelfths.
带分数相加先化成假分数并通分：43/12，即 3 又 7/12。
When multiplying, cancel the 7 and the 3 first, and the answer is already simple: 5 twelfths.
相乘时先约去 7 和 3，答案已是最简：5/12。
Write every number in index form first.
先把每个数写成指数形式。
504 is 2 cubed times 3 squared times 7, and 588 is 2 squared times 3 times 7 squared.
504 等于 2 的三次方乘 3 的平方乘 7，588 等于 2 的平方乘 3 乘 7 的平方。
The shared primes go in the overlap: 2, 2, 3 and 7.
共有的质因数放在重叠部分：2、2、3 和 7。
504 keeps an extra 2 and 3, and 588 keeps an extra 7.
504 多出一个 2 和一个 3，588 多出一个 7。
The highest common factor takes the lowest power of each common prime: 2 squared times 3 times 7, which is 84.
最大公因数取每个公共质因数的最低次幂：2 的平方乘 3 乘 7，等于 84。
The lowest common multiple takes the highest power of every prime: 3528.
最小公倍数取每个质因数 的最高次幂：3528。
Take the power apart.
把指数拆开。
The minus sign flips the fraction.
负号把分数颠倒。
The 4 in the denominator takes a fourth root: three halves.
分母的 4 表示开四次方：3/2。
The 3 on top cubes it: 27 over 8.
分子的 3 表示立方：27/8。
Root first, then power, keeps the numbers small.
先开方再乘方，数字保持很小。
Pull the square factors out: root 50 is 5 root 2, root 18 is 3 root 2, root 8 is 2 root 2.
提出平方因数：√50 = 5√2，√18 = 3√2，√8 = 2√2。
Now they are like terms: 4 root 2.
现在它们是同类项：4√2。
To rationalise 5 over 3 minus root 2, multiply by the conjugate, 3 plus root 2; the denominator becomes 9 minus 2, which is 7.
要使 5/(3 − √2) 分母有理化，乘以共轭 3 + √2；分母变成 9 − 2 = 7。
Keep full precision; let the Venn carry the counting.
全程保留精度，计数交给维恩图。
Every rounded value carries an interval of half a unit either side, and a bounds question chooses the extreme it needs.
每个近似值都带有左右各半个单位的区间，上下界的题目要选出它需要的极端值。
A floor of 96 square metres to 2 significant figures lies from 95.5 up to 96.5.
精确到两位有效数字的 96 平方米地面，范围是 95.5 到 96.5。
Each person needs 5.1 square metres to 1 decimal place, so at most 5.15.
每人 需要 5.1 平方米、精确到一位小数，所以最多 5.15。
The greatest number of people guaranteed room uses the smallest floor and the largest space: 95.5 divided by 5.15 is 18.5, so the answer rounds down to 18, because 19 people could need 97.85 square metres.
用最小的地面和最大的人均面积：95.5 除以 5.15 等于 18.5，答案要向下取整为 18，因为 19 个人可能需要 97.85 平方米。
Let x be 0.2777 recurring.
设 x = 0.2777…。
Ten x and a hundred x both end in the same string of sevens, so subtract those two, not x itself: 90x is 25, and x is 5 eighteenths.
10x 和 100x 的小数部分都是同样的一串 7，所以用这两行相减，而不是减 x 本身：90x = 25，x = 5/18。
Start at 300 yuan.
从 300 元开始。
Twenty percent off multiplies by 0.8: 240.
打八折即乘 0.8：240。
Twenty percent up multiplies by 1.2, but the 20 percent is of 240 now, so the price ends at 288, not 300.
再涨 20% 即乘 1.2，但这 20% 是 240 的，所以价格最后是 288，不是 300。
Compound interest repeats the same multiplier: 2000 times 1.03 to the 4.
复利就是重复同一个乘数：2000 × 1.03⁴。
A coat costs 68 pounds after 15 percent off, so 68 is 85 percent of the original.
大衣打 85 折后 68 英镑，所以 68 是原价的 85%。
Divide by 0.85: 80 pounds.
除以 0.85：80 英镑。
Adding 15 percent of 68 is the classic mistake, because the 15 percent was of the original.
在 68 上加 15% 是典型错误，因为这 15% 是原价的。
Amir and Bea share money in the ratio 3 to 5, and Bea gets 24 pounds more.
Amir 和 Bea 按 3:5 分钱，Bea 多得 24 英镑。
The difference is 2 parts, so 2 parts are 24 and one part is 12.
差是 2 份，所以 2 份是 24，1 份是 12。
Amir gets 36 and Bea gets 60.
Amir 得 36，Bea 得 60。
y is inversely proportional to x squared, and y is 5 when x is 2.
y 与 x² 成反比，x = 2 时 y = 5。
Write y equals k over x squared, so k is 20.
写成 y = k/x²，得 k = 20。
When x is 4, y is 20 over 16, 1.25.
x = 4 时 y = 20/16 = 1.25。
Check: doubling x divides y by 4.
检验：x 加倍，y 除以 4。
In y equals a times b to the t, b bigger than 1 grows and b between 0 and 1 decays.
在 y 等于 a 乘 b 的 t 次方中，b 大于 1 是增长，b 在 0 和 1 之间是衰减。
Data of 240, 192 and 153.6 share a ratio of 0.8, so the model is 240 times 0.8 to the t.
数据 240、192、153.6 的比都是 0.8，所以模型是 240 乘 0.8 的 t 次方。
A machine worth 12000 that keeps 0.8 of its value each year first falls below 2500 when t is greater than about 7.0, so during the 8th year.
一台价值 12000 的机器每年保留价值的 0.8，当 t 大于约 7.0 时第一次低于 2500，也就是在第 8 年中。
Growth runs the other way: 240 times 1.35 to the 5 is about 1076.2.
增长则相反：240 乘 1.35 的 5 次方 约为 1076.2。
Check yourself.
自我检测。
8 to the two thirds is 4.
8^{2/3} = 4。
0.45 recurring is 5 elevenths.
0.45 循环是 5/11。
A 17 percent decrease multiplies by 0.83.
减少 17% 乘以 0.83。
96 to 2 significant figures has lower bound 95.5.
96（两位有效数字）的下界是 95.5。
And doubling x divides y by 4.
x 加倍，y 除以 4。