📚 9H Homework Answers: November 2nd | 9H 作业答案解析（11月2日）
This article explains the answers and methods for the Year 9 Higher mathematics homework set on 2 November. The focus is on clear step-by-step reasoning so you can check your work and understand the key techniques.
本文解析 11 月 2 日布置的九年级高阶数学作业答案。重点在于给出清晰的逐步推理，帮助你核对作业并理解关键方法。
1. Solving Linear Equations | 解一元一次方程
Worked example: solve 3(x − 2) = 2x + 5.
例题：解方程 3(x − 2) = 2x + 5。
Expand the bracket to get 3x − 6 = 2x + 5.
展开括号得 3x − 6 = 2x + 5。
Subtract 2x from both sides: x − 6 = 5.
两边同时减去 2x：x − 6 = 5。
Add 6 to both sides: x = 11.
两边同时加 6：x = 11。
l equation: left side 3(11 − 2) = 27, right side 2(11) + 5 = 27, so the answer is correct.
将 x = 11 代入原方程检验：左边 3(11 − 2) = 27，右边 2(11) + 5 = 27，因此答案正确。
2. Expanding and Factorising | 展开与因式分解
To expand (x + 4)(x − 3), multiply each term in the first bracket by each term in the second bracket.
展开 (x + 4)(x − 3) 时，将第一个括号中的每一项分别乘以第二个括号中的每一项。
This gives x² − 3x + 4x − 12, which simplifies to x² + x − 12.
得到 x² − 3x + 4x − 12，化简为 x² + x − 12。
To factorise x² − 7x + 12, find two numbers that multiply to 12 and add to −7: they are −3 and −4.
因式分解 x² − 7x + 12 时，找两个数，它们的乘积为 12，和为 −7：这两个数是 −3 和 −4。
Therefore x² − 7x + 12 = (x − 3)(x − 4).
因此 x² − 7x + 12 = (x − 3)(x − 4)。
3. Fractions, Decimals and Percentages | 分数、小数与百分数
Convert the decimal 0.375 to a fraction by writing it as 375/1000 and simplifying.
将小数 0.375 转化为分数，写成 375/1000 后化简。
de the numerator and denominator by 125: 375 ÷ 125 = 3 and 1000 ÷ 125 = 8, so 0.375 = 3/8.
分子分母同时除以 125：375 ÷ 125 = 3，1000 ÷ 125 = 8，所以 0.375 = 3/8。
To find 15% of 240, multiply 240 by 0.15, which gives 36.
求 240 的 15%，用 240 乘以 0.15，得到 36。
To increase 80 by 25%, first find 25% of 80 = 20, then add it to 80: 80 + 20 = 100.
将 80 增加 25%，先求 80 的 25% 为 20，再加到 80 上：80 + 20 = 100。
4. Ratio and Proportion | 比与比例
Divide £120 in the ratio 2 : 3 : 5. First add the parts: 2 + 3 + 5 = 10.
将 120 英镑按 2 : 3 : 5 的比例分配。先求出总份数：2 + 3 + 5 = 10。
One part is £120 ÷ 10 = £12.
一份为 120 ÷ 10 = 12 英镑。
Therefore the shares are 2 × £12 = £24, 3 × £12 = £36, and 5 × £12 = £60.
因此各部分为 2 × 12 = 24 英镑，3 × 12 = 36 英镑，5 × 12 = 60 英镑。
Check: £24 + £36 + £60 = £120, so the division is complete.
检验：24 + 36 + 60 = 120 英镑，因此分配完整。
5. Angles in Polygons | 多边形内角
The sum of the interior angles of a polygon with n sides is (n − 2) × 180°.
n 边形的内角和为 (n − 2) × 180°。
For a decagon, n = 10, so the sum is (10 − 2) × 180° = 8 × 180° = 1440°.
十边形 n = 10，因此内角和为 (10 − 2) × 180° = 8 × 180° = 1440°。
The exterior angle of a regular nonagon is found by dividing 360° by 9, which gives 40°.
正九边形的一个外角等于 360° 除以 9，得到 40°。
Each interior angle is then 180° − 40° = 140°.
每个内角则为 180° − 40° = 140°。
6. Area and Volume | 面积与体积
given by A = 1/2 × (a + b) × h, where a and b are the parallel sides and h is the height.
梯形的面积公式为 A = 1/2 × (a + b) × h，其中 a 和 b 是平行边，h 是高。
es 8 cm and 12 cm and height 5 cm, the area is 1/2 × (8 + 12) × 5 = 1/2 × 20 × 5 = 50 cm².
若平行边为 8 cm 和 12 cm，高为 5 cm，则面积为 1/2 × (8 + 12) × 5 = 1/2 × 20 × 5 = 50 cm²。
. If the cross-section is 20 cm² and the length is 15 cm, the volume is 20 × 15 = 300 cm³.
棱柱的体积等于横截面积 × 长度。若横截面积为 20 cm²，长度为 15 cm，则体积为 20 × 15 = 300 cm³。
7. Linear Graphs | 一次函数图像
For the line y = 2x − 1, the gradient is the coefficient of x, which is 2.
对于直线 y = 2x − 1，斜率为 x 的系数，即 2。
The y-intercept is the constant term, which is −1.
y 轴截距为常数项，即 −1。
To find x when y = 7, substitute y = 7 into the equation: 7 = 2x − 1.
当 y = 7 时求 x，将 y = 7 代入方程：7 = 2x − 1。
Add 1 to both sides: 8 = 2x, then divide by 2: x = 4.
两边加 1：8 = 2x，再除以 2：x = 4。
The line passes through (0, −1) and (4, 7).
这条直线经过点 (0, −1) 和 (4, 7)。
8. Inequalities | 不等式
Solve the inequality 4x − 3 > 2x + 5.
解不等式 4x − 3 > 2x + 5。
Subtract 2x from both sides: 2x − 3 > 5.
两边同时减去 2x：2x − 3 > 5。
Add 3 to both sides: 2x > 8.
两边同时加 3：2x > 8。
Divide both sides by 2: x > 4.
两边同时除以 2：x > 4。
On a number line, draw an open circle at 4 and shade to the right.
在数轴上，在 4 处画空心圆，并向右画阴影。
9. Standard Form | 科学记数法
Standard form is written as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.
科学记数法写作 a × 10ⁿ，其中 1 ≤ a < 10，n 为整数。
0.00052 in standard form by moving the decimal point four places to the right: 5.2 × 10⁻⁴.
将 0.00052 写成科学记数法，小数点向右移动四位：5.2 × 10⁻⁴。
tiply (3 × 10²)(4 × 10³), first multiply 3 × 4 = 12, then add the powers: 10² × 10³ = 10⁵.
计算 (3 × 10²)(4 × 10³) 时，先算 3 × 4 = 12，再将指数相加：10² × 10³ = 10⁵。
This gives 12 × 10⁵, which must be written as 1.2 × 10⁶ in proper standard form.
得到 12 × 10⁵，必须写成标准的 1.2 × 10⁶。
10. Averages and Range | 平均数与极差
For the data set 8, 11, 7, 15, 9, the mean is found by adding all values and dividing by 5.
对于数据组 8、11、7、15、9，平均数是将所有数值相加后除以 5。
Sum = 8 + 11 + 7 + 15 + 9 = 50, so the mean is 50 ÷ 5 = 10.
总和 = 8 + 11 + 7 + 15 + 9 = 50，因此平均数为 50 ÷ 5 = 10。
Put the data in order: 7, 8, 9, 11, 15. The median is the middle value, which is 9.
将数据按顺序排列：7、8、9、11、15。中位数是中间值，即 9。
The mode is the most frequent value; here there is no mode because all values appear once.
众数是出现次数最多的值；这里没有众数，因为所有值都只出现一次。
The range is the largest value minus the smallest value: 15 − 7 = 8.
极差是最大值减最小值：15 − 7 = 8。
11. Pythagoras' Theorem | 勾股定理
Pythagoras' theorem states that in a right-angled triangle, a² + b² = c², where c is the hypotenuse.
勾股定理指出，在直角三角形中，a² + b² = c²，其中 c 是斜边。
For legs of 6 cm and 8 cm, calculate c² = 6² + 8² = 36 + 64 = 100.
若两条直角边为 6 cm 和 8 cm，则 c² = 6² + 8² = 36 + 64 = 100。
Taking the square root gives c = √100 = 10 cm.
开平方得 c = √100 = 10 cm。
Therefore the hypotenuse is 10 cm, and the triangle is a 3-4-5 enlarged triangle.
因此斜边为 10 cm，这个三角形是一个放大的 3-4-5 三角形。
12. Probability | 概率
ntains 3 red, 5 blue and 2 green counters. The total number of counters is 3 + 5 + 2 = 10.
一个袋子里有 3 个红色、5 个蓝色和 2 个绿色筹码。筹码总数为 3 + 5 + 2 = 10。
The probability of picking a blue counter is 5/10, which simplifies to 1/2.
抽到蓝色筹码的概率为 5/10，化简为 1/2。
The probability of not picking a red counter is 1 − P(red) = 1 − 3/10 = 7/10.
没有抽到红色筹码的概率为 1 − P(红色) = 1 − 3/10 = 7/10。
Remember that all probabilities must be between 0 and 1.
请记住所有概率都必须在 0 和 1 之间。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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