📚 Year 7 Higher Homework Answers | 七年级高阶作业答案与解析
Welcome to this Year 7 Higher homework answer guide. It covers the core topics that usually appear in higher-tier homework for 11-12 year olds, including number, algebra, geometry and statistics. Each section gives a worked question followed by the answer and a short explanation so that you can check your own reasoning.
欢迎使用这篇七年级高阶作业答案指南。它涵盖了 11-12 岁高阶作业中常见的核心主题，包括数、代数、几何和统计。每一节都提供一道例题、答案和简要解析，帮助你核对自己的解题思路。
1. Place Value and Rounding | 位值与四舍五入
Worked example: Write 3 047.805 in words and round it to 2 decimal places.
例题：用文字写出 3 047.805，并将其四舍五入到两位小数。
The number is three thousand and forty-seven point eight zero five. To round to 2 decimal places, look at the third decimal digit, which is 5. Because it is 5 or more, we round the hundredths digit up: 3 047.81.
这个数读作三千零四十七点八零五。四舍五入到两位小数时，看第三位小数，即 5。由于是 5 或更大，我们把百分位向上进位，得到 3 047.81。
Common mistake: do not say 'and' before the decimal part; use 'point'. Also, keep the zero after the decimal point when it is needed for place value, as in 3 047.80.
常见错误：小数点前不要用 'and' 来连接小数部分，应读作 'point'。另外，在需要表示位值时，小数点后的零要保留，例如 3 047.80。
Quick check: Round 2.396 to 1 decimal place. The first decimal digit is 3, the next digit is 9, so we round up to 2.4.
快速检测：将 2.396 四舍五入到一位小数。第一位小数是 3，下一位是 9，因此向上进位为 2.4。
2. Negative Numbers | 负数
Worked example: Evaluate -6 + 4 - (-3).
例题：计算 -6 + 4 - (-3)。
Subtracting negative three is the same as adding three. So -6 + 4 + 3 = 1.
减去负三等于加上三。所以 -6 + 4 + 3 = 1。
Second example: Calculate -5 × 4 and (-5) × (-4).
第二个例子：计算 -5 × 4 和 (-5) × (-4)。
a positive is negative. (-5) × (-4) = 20 because a negative times a negative is positive.
-5 × 4 = -20。负数乘正数得负数。(-5) × (-4) = 20，因为负数乘负数得正数。
Quick check: Work out 10 - 12 + (-3). 10 - 12 = -2, and -2 + (-3) = -5.
快速检测：计算 10 - 12 + (-3)。10 - 12 = -2，-2 + (-3) = -5。
3. Fractions, Decimals and Percentages | 分数、小数与百分比
Worked example: Write 3/8 as a decimal and as a percentage.
例题：将 3/8 写成小数和百分数。
3 ÷ 8 = 0.375. To change to a percentage, multiply by 100: 0.375 × 100 = 37.5%.
3 ÷ 8 = 0.375。转换为百分数时乘以 100：0.375 × 100 = 37.5%。
Second example: Find 15% of 60.
第二个例子：求 60 的 15%。
15% = 0.15, so 0.15 × 60 = 9.
15% = 0.15，所以 0.15 × 60 = 9。
Third example: Convert 0.125 to a fraction in its simplest form.
第三个例子：将 0.125 转换为最简分数。
0.125 = 125/1000 = 1/8.
0.125 = 125/1000 = 1/8。
4. Ratio and Proportion | 比与比例
Worked example: Divide £45 between A and B in the ratio 2 : 3.
例题：将 45 英镑按 2 : 3 的比例分给 A 和 B。
Total parts = 2 + 3 = 5. One part = £45 ÷ 5 = £9. A gets 2 × £9 = £18 and B gets 3 × £9 = £27.
总份数 = 2 + 3 = 5。一份 = £45 ÷ 5 = £9。A 得到 2 × £9 = £18，B 得到 3 × £9 = £27。
Second example: A recipe uses 200 g flour for 4 people. How much flour is needed for 10 people?
第二个例子：一份食谱为 4 人准备需要 200 克面粉。10 人需要多少面粉？
One person needs 200 ÷ 4 = 50 g. Ten people need 50 × 10 = 500 g.
每人需要 200 ÷ 4 = 50 克。十人需要 50 × 10 = 500 克。
ick check: If a map scale is 1 : 50 000, what real distance does 3 cm on the map represent? 3 × 50 000 = 150 000 cm = 1.5 km.
快速检测：如果地图比例尺为 1 : 50 000，地图上 3 厘米代表实际距离是多少？3 × 50 000 = 150 000 厘米 = 1.5 千米。
5. Algebraic Expressions | 代数表达式
Worked example: Simplify 3a + 5b - 2a + 7b.
例题：化简 3a + 5b - 2a + 7b。
Collect like terms: 3a - 2a = a and 5b + 7b = 12b, so the answer is a + 12b.
合并同类项：3a - 2a = a，5b + 7b = 12b，因此答案是 a + 12b。
Second example: Expand 4(x + 3) - 2(x - 5).
第二个例子：展开 4(x + 3) - 2(x - 5)。
Multiply out: 4x + 12 - 2x + 10 = 2x + 22. Be careful: -2 × -5 = +10.
去括号：4x + 12 - 2x + 10 = 2x + 22。注意：-2 × -5 = +10。
Quick check: Simplify 7m - 3n - 4m + n. The answer is 3m - 2n.
快速检测：化简 7m - 3n - 4m + n。答案是 3m - 2n。
6. Solving Linear Equations | 解一元一次方程
Worked example: Solve 3x + 5 = 20.
例题：解方程 3x + 5 = 20。
Subtract 5 from both sides: 3x = 15. Divide both sides by 3: x = 5.
两边同时减去 5：3x = 15。两边同时除以 3：x = 5。
tituting x = 5 back into the equation: 3(5) + 5 = 15 + 5 = 20, so the solution is correct.
将 x = 5 代回原方程检验：3(5) + 5 = 15 + 5 = 20，因此解是正确的。
Second example: Solve 2(x - 4) = 10.
第二个例子：解方程 2(x - 4) = 10。
Expand first: 2x - 8 = 10. Add 8 to both sides: 2x = 18. Divide by 2: x = 9.
先展开：2x - 8 = 10。两边同时加上 8：2x = 18。再除以 2：x = 9。
Check: 2(9 - 4) = 2 × 5 = 10, so the solution is correct.
检验：2(9 - 4) = 2 × 5 = 10，因此解是正确的。
7. Angles and Shapes | 角与图形
Worked example: Find the missing angle in a triangle with angles 43° and 27°.
例题：一个三角形的两个角分别为 43° 和 27°，求缺失的角。
The angles in a triangle add up to 180°. Missing angle = 180 - 43 - 27 = 110°.
三角形内角和为 180°。缺失角 = 180 - 43 - 27 = 110°。
Second example: Find the exterior angle of a regular pentagon.
第二个例子：求正五边形的一个外角。
entagon has 5 equal exterior angles summing to 360°. Each exterior angle = 360° ÷ 5 = 72°.
正五边形的 5 个外角相等且总和为 360°。每个外角 = 360° ÷ 5 = 72°。
ilateral, three angles are 90°, 80° and 70°. The fourth angle = 360 - 90 - 80 - 70 = 120°.
快速检测：一个四边形中，三个角分别是 90°、80° 和 70°。第四个角 = 360 - 90 - 80 - 70 = 120°。
8. Area and Perimeter | 面积与周长
Worked example: Find the area and perimeter of a rectangle with length 8 cm and width 5 cm.
例题：求一个长 8 厘米、宽 5 厘米的长方形的面积和周长。
Area = length × width = 8 × 5 = 40 cm². Perimeter = 2(length + width) = 2(8 + 5) = 26 cm.
面积 = 长 × 宽 = 8 × 5 = 40 平方厘米。周长 = 2(长 + 宽) = 2(8 + 5) = 26 厘米。
Second example: Find the area of a triangle with base 12 cm and height 7 cm.
第二个例子：求一个底为 12 厘米、高为 7 厘米的三角形的面积。
Area = ½ × base × height = ½ × 12 × 7 = 42 cm².
面积 = ½ × 底 × 高 = ½ × 12 × 7 = 42 平方厘米。
Third example: A 6 cm by 4 cm rectangle has a 2 cm by 2 cm square cut out from it. Find the shaded area.
第三个例子：一个 6 厘米 × 4 厘米的长方形中挖去一个 2 厘米 × 2 厘米的正方形。求阴影部分面积。
ngle area = 6 × 4 = 24 cm². Square removed = 2 × 2 = 4 cm². Shaded area = 24 - 4 = 20 cm².
长方形面积 = 6 × 4 = 24 平方厘米。挖去的正方形面积 = 2 × 2 = 4 平方厘米。阴影面积 = 24 - 4 = 20 平方厘米。
9. Averages and Range | 平均数与极差
Worked example: Find the mean, median, mode and range of 4, 7, 2, 7, 5.
例题：求数据 4、7、2、7、5 的平均数、中位数、众数和极差。
n order: 2, 4, 5, 7, 7. Median = 5. Mode = 7, because it appears twice. Range = 7 - 2 = 5.
平均数 = (4 + 7 + 2 + 7 + 5) ÷ 5 = 25 ÷ 5 = 5。从小到大排列：2、4、5、7、7。中位数 = 5。众数 = 7，因为它出现两次。极差 = 7 - 2 = 5。
Second example: Find the mean from the frequency table: 2 appears 1 time, 4 appears 1 time, 5 appears 1 time, 7 appears 2 times.
第二个例子：根据频率表求平均数：2 出现 1 次，4 出现 1 次，5 出现 1 次，7 出现 2 次。
+ 7×2 = 2 + 4 + 5 + 14 = 25. The frequency total is 1 + 1 + 1 + 2 = 5. Mean = 25 ÷ 5 = 5.
总和为 2×1 + 4×1 + 5×1 + 7×2 = 2 + 4 + 5 + 14 = 25。频数总和为 1 + 1 + 1 + 2 = 5。平均数 = 25 ÷ 5 = 5。
10. Problem Solving | 问题解决
Worked example: A train leaves at 09:15 and takes 2 hours 45 minutes. Find the arrival time.
例题：一列
Published by TutorHao | Year 7 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