📚 Year 11 Eduqas Maths: Unit Test Mock Paper Walkthrough | Year 11 Eduqas 数学：单元测试模拟卷解析
This walkthrough breaks down a typical Year 11 Eduqas unit test, covering algebra, ratio, geometry, trigonometry, statistics and compound interest. Each question is followed by clear step-by-step reasoning to help you master the skills needed for your GCSE exams.
本文对一份典型的 Year 11 Eduqas 单元测试模拟卷进行逐题解析，涵盖代数、比率、几何、三角学、统计和复利等主题。每道题都配有清晰的分步推理，帮助你掌握 GCSE 考试所需的技能。
1. Question 1: Solving Linear Equations and Inequalities | 第1题：解线性方程与不等式
Question: Solve 3x + 5 = 20. Hence, or otherwise, solve the inequality 2x – 3 > 5 and represent the solution on a number line.
题目：求解 3x + 5 = 20。然后，或用其他方法，解不等式 2x – 3 > 5，并在数轴上表示解集。
Step 1: Solve the equation. Subtract 5 from both sides: 3x = 15.
步骤1：解方程。两边同时减去 5：3x = 15。
Step 2: Divide both sides by 3 to find x = 5.
步骤2：两边除以 3，得到 x = 5。
Step 3: For the inequality, add 3 to both sides: 2x > 8. Then divide by 2: x > 4.
步骤3：对于不等式，两边同时加 3：2x > 8。再除以 2：x > 4。
Step 4: On a number line, draw an open circle at 4 and shade to the right, indicating all numbers greater than 4.
步骤4：在数轴上，在 4 处画一个空心圆，向右画阴影，表示所有大于 4 的数。
2. Question 2: Expanding and Simplifying Algebraic Expressions | 第2题：展开并化简代数式
Question: Expand and simplify fully: 3(2x + 4) – 2(x – 1).
题目：完全展开并化简：3(2x + 4) – 2(x – 1)。
Step 1: Multiply out the first bracket: 3 × 2x = 6x, and 3 × 4 = 12, giving 6x + 12.
步骤1：展开第一个括号：3 × 2x = 6x，3 × 4 = 12，得到 6x + 12。
Step 2: Multiply out the second bracket, remembering the minus sign: -2 × x = -2x, and -2 × (-1) = +2. So the second part is -2x + 2.
步骤2：展开第二个括号，注意负号：-2 × x = -2x，-2 × (-1) = +2。因此第二部分是 -2x + 2。
Step 3: Combine like terms: 6x – 2x = 4x, and 12 + 2 = 14. The simplified expression is 4x + 14.
步骤3：合并同类项：6x – 2x = 4x，12 + 2 = 14。化简后的代数式为 4x + 14。
3. Question 3: Ratio and Proportion – Best Value | 第3题：比率与比例 – 最优价
Question: A shop sells apples in two pack sizes: 6 apples for £2.40, or 10 apples for £3.80. Which pack gives better value for money? Show your working.
题目：一家商店销售两种包装的苹果：6个苹果售价£2.40，或10个苹果售价£3.80。哪种包装更划算？请展示计算过程。
Step 1: Find the price per apple for the smaller pack: £2.40 ÷ 6 = £0.40 per apple.
步骤1：计算小包装的单价：£2.40 ÷ 6 = 每个苹果£0.40。
Step 2: Find the price per apple for the larger pack: £3.80 ÷ 10 = £0.38 per apple.
步骤2：计算大包装的单价：£3.80 ÷ 10 = 每个苹果£0.38。
Step 3: Compare unit costs. £0.38 is less than £0.40, so the pack of 10 offers better value.
步骤3：比较单价。£0.38 小于 £0.40，因此 10 个装的苹果更划算。
4. Question 4: Pythagoras’ Theorem | 第4题：勾股定理
Question: A right-angled triangle has legs of length 6 cm and 8 cm. Calculate the length of the hypotenuse, giving your answer correct to 2 decimal places if necessary.
题目：一个直角三角形的两条直角边分别为 6 cm 和 8 cm。计算斜边的长度，如有需要，答案保留两位小数。
Step 1: Write Pythagoras’ theorem: c² = a² + b², where c is the hypotenuse.
步骤1：写出勾股定理：c² = a² + b²，其中 c 为斜边。
Step 2: Substitute the given lengths: c² = 6² + 8² = 36 + 64 = 100.
步骤2：代入已知边长：c² = 6² + 8² = 36 + 64 = 100。
Step 3: Take the square root: c = √100 = 10 cm. The answer is exact, so no rounding needed.
步骤3：开平方根：c = √100 = 10 cm。答案是精确值，无需四舍五入。
Step 4: Always remember to include the unit (cm) and check if the triangle satisfies the 3-4-5 ratio (6, 8, 10).
步骤4：务必记得带上单位（cm），并检查是否符合 3-4-5 比例（6, 8, 10 是该比例的倍数）。
5. Question 5: Trigonometry – Finding a Side | 第5题：三角学 – 求边长
Question: In a right-angled triangle, the hypotenuse is 10 cm and one of the acute angles is 30°. Calculate the length of the side opposite the 30° angle.
题目：在一个直角三角形中，斜边为 10 cm，一个锐角为 30°。计算 30° 角所对的边长。
Step 1: Identify the sides relative to the angle. We know the hypotenuse (H) and want the opposite (O). Use sine: sin θ = O / H.
步骤1：确定相对于该角的边。已知斜边（H），要求对边（O）。使用正弦：sin θ = O / H。
Step 2: Substitute: sin 30° = O / 10. Recall that sin 30° = 0.5.
步骤2：代入：sin 30° = O / 10。记住 sin 30° = 0.5。
Step 3: Solve for O: O = 10 × sin 30° = 10 × 0.5 = 5 cm.
步骤3：求解 O：O = 10 × sin 30° = 10 × 0.5 = 5 cm。
Step 4: The opposite side is exactly 5 cm. Always check if the triangle could be a 30-60-90 special triangle.
步骤4：对边正好是 5 cm。可以检查一下这是否符合 30-60-90 特殊三角形的比例。
6. Question 6: Averages and Range from a Data Set | 第6题：数据集的平均数与极差
Question: Here are the scores of seven students in a maths quiz: 5, 8, 9, 5, 7, 4, 5. Find the mean, median, mode and range.
题目：以下是七名学生在一次数学测验中的分数：5, 8, 9, 5, 7, 4, 5。求平均数、中位数、众数和极差。
Step 1: Arrange the data in ascending order: 4, 5, 5, 5, 7, 8, 9.
步骤1：将数据按升序排列：4, 5, 5, 5, 7, 8, 9。
| Scores (有序) | 4 | 5 | 5 | 5 | 7 | 8 | 9 |
Step 2: Mean = sum of scores ÷ number of scores. Sum = 4+5+5+5+7+8+9 = 43. Mean = 43 ÷ 7 ≈ 6.14 (to 2 d.p.).
步骤2：平均数 = 总分 ÷ 个数。总和 = 4+5+5+5+7+8+9 = 43。平均数 = 43 ÷ 7 ≈ 6.14（保留两位小数）。
Step 3: Median is the middle value. With 7 items, the 4th value is 5. So median = 5.
步骤3：中位数是中间的数。有 7 个数据，第 4 个值是 5。所以中位数 = 5。
Step 4: Mode is the value that appears most often. The number 5 appears three times, so mode = 5.
步骤4：众数是出现次数最多的值。数字 5 出现了三次，所以众数 = 5。
Step 5: Range = largest value – smallest value = 9 – 4 = 5.
步骤5：极差 = 最大值 – 最小值 = 9 – 4 = 5。
7. Question 7: Straight Line Graphs – Drawing and Intercepts | 第7题：直线图 – 绘图与截距
Question: On the coordinate grid, plot the graph of y = 2x + 1 for x-values from -2 to 2. Write down the coordinates of the y-intercept and the x-intercept.
题目：在坐标格纸上，绘制一次函数 y = 2x + 1 在 x 取值 -2 到 2 的图像。写出 y 轴截距和 x 轴截距的坐标。
Step 1: Create a table of values. Substitute x = -2, -1, 0, 1, 2 into y = 2x + 1.
步骤1：列出数值表格。分别将 x = -2, -1, 0, 1, 2 代入 y = 2x + 1。
| x | -2 | -1 | 0 | 1 | 2 |
| y = 2x+1 | -3 | -1 | 1 | 3 | 5 |
Step 2: Plot the points (-2,-3), (-1,-1), (0,1), (1,3), (2,5) and draw a straight line through them.
步骤2：在坐标平面上标出这些点，并过点画一条直线。
Step 3: The y-intercept is where x = 0. From the table, (0,1) is on the line, so y-intercept = (0, 1).
步骤3：y 轴截距是 x = 0 时的点。查表得 (0,1) 在线上，因此 y 轴截距为 (0, 1)。
Step 4: The x-intercept is where y = 0. Set 2x + 1 = 0 → 2x = -1 → x = -0.5. The x-intercept is (-0.5, 0).
步骤4：x 轴截距是 y = 0 时的点。令 2x + 1 = 0 → 2x = -1 → x = -0.5。x 轴截距为 (-0.5, 0)。
8. Question 8: Compound Interest | 第8题：复利计算
Question: Julia invests £500 in a savings account that pays 4% compound interest per annum. How much will she have in total after 3 years? Give your answer to the nearest penny.
题目：Julia 将 £500 存入一个年利率 4% 的复利储蓄账户。3 年后她将拥有多少总金额？答案精确到便士。
Step 1: Write the compound interest formula: Total = P (1 + r/100)ⁿ, where P is the principal, r the rate, and n the number of years.
步骤1：写出复利公式：总额 = P (1 + r/100)ⁿ，其中 P 为本金，r 为利率，n 为年数。
Step 2: Substitute the values: P = 500, r = 4, n = 3. Total = 500 × (1 + 0.04)³ = 500 × (1.04)³.
步骤2：代入数值：P = 500, r = 4, n = 3。总额 = 500 × (1 + 0.04)³ = 500 × (1.04)³。
Step 3: Calculate (1.04)³ step by step. 1.04² = 1.0816, then × 1.04 gives 1.124864.
步骤3：逐步计算 (1.04)³。1.04² = 1.0816，再乘以 1.04 得出 1.124864。
Step 4: Multiply by 500: 500 × 1.124864 = 562.432. Round to the nearest penny: £562.43.
步骤4：乘以 500：500 × 1.124864 = 562.432。四舍五入到便士：£562.43。
9. Exam Tips and Common Pitfalls | 考试技巧与常见失分点
Always show all your working, even if a calculation seems obvious. Marks are awarded for method, not just the final answer. In questions involving units, include them at every step to avoid losing marks.
始终展示完整的解题步骤，即使计算看起来很简单。评分不仅看最终答案，也看解题过程。涉及单位的题目，每一步都要带上单位，以免丢分。
Check the reasonableness of your answer. For example, a hypotenuse must be the longest side; a mean should lie within the data range. In compound interest, the final amount must be greater than the principal.
检查答案的合理性。例如，斜边一定是最长边；平均数应介于数据极差之间。在复利计算中，最终总额必定大于本金。
When drawing graphs, use a sharp pencil, label axes, and plot points accurately. For inequalities, ensure you use open or closed circles correctly. Practise reading wordy questions and underlining key information.
绘图时，使用削尖的铅笔，标注坐标轴，并精确描点。对于不等式，务必正确使用空心圆和实心圆。多练习阅读题干较长的题目，并划出关键信息。
Memorise the exact values of sin, cos and tan for 0°, 30°, 45°, 60° and 90°, as Eduqas often expects you to recall them without a calculator for certain questions.
牢记 0°、30°、45°、60° 和 90° 的正弦、余弦和正切精确值，因为 Eduqas 考试常要求在不使用计算器的情况下回答某些问题。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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