📚 Year 8 Higher Maths Answers | 八年级数学提高版答案解析
This revision guide explains how to approach and check Year 8 Higher Maths answers. It covers the main topics, worked examples and common mistakes, so you can improve accuracy and confidence.
这份复习指南讲解如何作答与检查八年级数学提高版的答案。它涵盖主要专题、例题和常见错误，帮助你提高准确性和信心。
1. Number and Place Value | 数与位值
Ordering decimals requires comparing place values from left to right. Write 0.7, 0.67 and 0.607 with the same number of decimal places: 0.700, 0.670, 0.607.
小数排序需要从左到右比较位值。把 0.7、0.67 和 0.607 写成相同的小数位数：0.700、0.670、0.607。
The correct ascending order is 0.607, 0.67, 0.7. A common error is to think 0.607 is larger than 0.67 because it has more digits.
正确的升序是 0.607、0.67、0.7。常见错误是认为 0.607 比 0.67 大，因为它的位数更多。
Negative numbers follow the opposite order: -7 < -3 < -1. When adding or subtracting, use a number line to avoid sign errors.
负数遵循相反的顺序：-7 < -3 < -1。做加减法时，使用数轴以避免符号错误。
For rounding, identify the place value required. Round 3.746 to 2 decimal places: the hundredths digit is 4, the thousandths digit is 6, so round up to 3.75.
四舍五入时，先确定所需的位值。将 3.746 保留两位小数：百分位是 4，千分位是 6，因此向上舍入为 3.75。
2. Fractions, Decimals and Percentages | 分数、小数与百分比
, divide 3 by 5: 3 ÷ 5 = 0.6. To write it as a percentage, multiply by 100: 0.6 × 100 = 60%.
将 3/5 转换为小数，用 3 除以 5：3 ÷ 5 = 0.6。写成百分比时乘以 100：0.6 × 100 = 60%。
To find 15% of 240, convert 15% to 0.15 and multiply: 0.15 × 240 = 36. You can also find 10% (24) and 5% (12), then add them.
求 240 的 15%，把 15% 转换为 0.15 再相乘：0.15 × 240 = 36。也可以先求 10%（24）和 5%（12），然后相加。
Percentage increase: increase 80 by 25%. Find 25% of 80 = 20, then add: 80 + 20 = 100. The new value is 100.
百分比增加：把 80 增加 25%。求 80 的 25% = 20，再加起来：80 + 20 = 100。新值是 100。
ommon denominator. For 1/3 + 1/4, the lowest common denominator is 12: 4/12 + 3/12 = 7/12.
分数相加需要公分母。对于 1/3 + 1/4，最小公分母是 12：4/12 + 3/12 = 7/12。
3. Ratio and Proportion | 比与比例
To simplify a ratio, divide all parts by the highest common factor. For example, 24:36:60 divides by 12 to give 2:3:5.
化简比时，用最大公因数除以所有部分。例如 24:36:60 除以 12 得到 2:3:5。
Sharing £450 in the ratio 2:3:4 means there are 2 + 3 + 4 = 9 parts. One part is £450 ÷ 9 = £50. The shares are £100, £150 and £200.
按 2:3:4 分配 £450，表示共有 2 + 3 + 4 = 9 份。一份是 £450 ÷ 9 = £50。分配结果分别是 £100、£150 和 £200。
Direct proportion: if 5 pens cost £3.50, one pen costs £0.70, so 8 pens cost 8 × £0.70 = £5.60.
正比例：如果 5 支笔售价 £3.50，一支笔售价 £0.70，那么 8 支笔售价为 8 × £0.70 = £5.60。
| Question | Working | Answer |
| Share £450 in the ratio 2:3:4 | 2 + 3 + 4 = 9 parts; £450 ÷ 9 = £50 | £100, £150, £200 |
4. Algebraic Expressions | 代数表达式
Simplify expressions by collecting like terms. For 4a + 3b - 2a + 5b, collect a terms and b terms: 2a + 8b.
通过合并同类项化简表达式。对于 4a + 3b - 2a + 5b，合并 a 项和 b 项：2a + 8b。
ultiply the outside term by each term inside. Expand 3(2x - 5) = 3 × 2x - 3 × 5 = 6x - 15.
去括号：用外面的一项乘以括号内的每一项。展开 3(2x - 5) = 3 × 2x - 3 × 5 = 6x - 15。
Factorising is the reverse of expanding. Factorise 6x + 9 by taking out the common factor 3: 3(2x + 3).
因式分解是去括号的逆运算。因式分解 6x + 9，提取公因数 3：3(2x + 3)。
Remember that x² means x × x, not 2x. So 3x² + 5x² = 8x², while 3x + 5x = 8x.
记住 x² 表示 x × x，而不是 2x。因此 3x² + 5x² = 8x²，而 3x + 5x = 8x。
5. Solving Equations | 解方程
lve 2x + 5 = 17: subtract 5 from both sides to get 2x = 12, then divide by 2 to get x = 6.
对于两步方程，按相反顺序逆运算。解 2x + 5 = 17：两边同时减 5 得到 2x = 12，然后两边除以 2 得到 x = 6。
x + 9: subtract 2x from both sides to get 3x - 3 = 9, then add 3 to get 3x = 12, so x = 4.
如果未知数在两边，先移较小的含未知数项。解 5x - 3 = 2x + 9：两边同时减 2x 得到 3x - 3 = 9，再加 3 得到 3x = 12，所以 x = 4。
answer back into the original equation. For 2x + 5 = 17, substitute x = 6: 2(6) + 5 = 17.
始终把答案代回原方程检验。对于 2x + 5 = 17，代入 x = 6：2(6) + 5 = 17。
ly every term by the denominator. Solve x/3 + 2 = 6: subtract 2, then multiply by 3 to get
Published by TutorHao | Year 8 Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图