📚 Year 10 Eduqas Mathematics: Unit Test Mock Paper Walkthrough | Year 10 Eduqas 数学：单元测试模拟卷解析
This walkthrough takes you through a full mock paper designed for the Year 10 Eduqas Mathematics specification. Each question is carefully selected to reflect the style and demand of a typical unit test, and every solution is broken down into clear, examiner-friendly steps. Whether you are revising for an end-of-topic assessment or preparing for your summer mocks, this resource will help you deepen your understanding and avoid common mistakes.
本解析将带你逐题拆解一份为 Year 10 Eduqas 数学大纲设计的完整模拟试卷。每道题目都经过精心挑选，以反映单元测试的典型风格与要求，并且每一道解答都分解成清晰、符合评分标准步骤。无论你是在为主题末的测评复习，还是为夏季模拟考试做准备，这份资料都将帮助你加深理解并避开常见错误。
1. Mock Paper Structure | 模拟试卷结构
This mock paper consists of two sections: a non-calculator section worth 40 marks and a calculator section worth 60 marks. Questions cover the six main strands of the Eduqas GCSE Foundation tier: Number, Algebra, Ratio and Proportion, Geometry and Measures, Probability, and Statistics. You will be expected to show full working for all questions, as method marks are awarded even if the final answer is incorrect.
这份模拟卷由两部分组成：非计算器部分占40分，计算器部分占60分。题目覆盖Eduqas GCSE基础层级六大知识领域：数、代数、比率与比例、几何与测量、概率和统计。所有题目都要求写出完整的解题步骤，因为即使最终答案有误，正确的步骤也能获得方法分。
2. Q1: Order of Operations (Non-Calculator) | 第1题：运算顺序（非计算器）
Question: Work out the value of 2.5 × (3.6 + 1.4) ÷ 0.5. You must show each step.
题目：计算 2.5 × (3.6 + 1.4) ÷ 0.5 的值。必须展示每一步。
Step 1 English: Always start with the operation inside the brackets. Add 3.6 and 1.4 to get 5.
步骤1 中文：始终从括号内的运算开始。3.6 加 1.4 得 5。
ivision have equal priority, so work from left to right. First multiply 2.5 by 5 to get 12.5.
步骤2 中文：将表达式改写成 2.5 × 5 ÷ 0.5。乘法和除法优先级相同，因此从左到右计算。先算 2.5 乘 5 得 12.5。
Step 3 English: Now divide 12.5 by 0.5. Remember that dividing by 0.5 is the same as multiplying by 2, giving a final answer of 25.
步骤3 中文：现在计算 12.5 除以 0.5。记住，除以 0.5 等同于乘以 2，最终答案为 25。
3. Q2: Fractions and Percentages (Non-Calculator) | 第2题：分数与百分数（非计算器）
Question: Work out 2/3 + 1/4. Give your answer as a mixed number in its simplest form. Then express the result as a percentage, correct to one decimal place.
题目：计算 2/3 + 1/4。将答案写成最简带分数。然后将结果表示为百分数，精确到一位小数。
Step 1 English: To add fractions, find a common denominator. The lowest common multiple of 3 and 4 is 12. Write 2/3 as 8/12 and 1/4 as 3/12.
步骤1 中文：分数的加法要先找到公分母。3 和 4 的最小公倍数是 12。将 2/3 写成 8/12，1/4 写成 3/12。
eady a proper fraction and cannot be simplified further, so the mixed number is simply 11/12.
步骤2 中文：分子相加：8 + 3 = 11，因而和为 11/12。这已是一个真分数且不能再约分，因此带分数就是 11/12。
Step 3 English: To convert 11/12 to a percentage, divide 11 by 12 to get approximately 0.91666... Multiply by 100 to obtain 91.666...%, and round to one decimal place: 91.7%.
步骤3 中文：将 11/12 转换成百分数，先用 11 除以 12 得约 0.91666...，再乘以 100 得到 91.666...%，四舍五入至一位小数得 91.7%。
4. Q3: Algebraic Simplification (Non-Calculator) | 第3题：代数化简（非计算器）
Question: Simplify fully the expression 3x + 5y − 2x + 7y.
题目：完全化简表达式 3x + 5y − 2x + 7y。
Step 1 English: Identify and group the like terms. The x terms are 3x and −2x; the y terms are 5y and 7y.
步骤1 中文：识别并分组同类项。x 的同类项为 3x 和 −2x；y 的同类项为 5y 和 7y。
Step 2 English: Combine the x terms: 3x − 2x = 1x, which is simply written as x.
步骤2 中文：合并 x 项：3x − 2x = 1x，简写为 x。
3 English: Combine the y terms: 5y + 7y = 12y. The fully simplified expression is x + 12y.
步骤3 中文：合并 y 项：5y + 7y = 12y。完全化简后的表达式为 x + 12y。
5. Q4: Solving Linear Equations (Non-Calculator) | 第4题：解一元一次方程（非计算器）
Question: Solve the equation 5x − 3 = 2x + 9.
题目：解方程 5x − 3 = 2x + 9。
on one side. Subtract 2x from both sides: 5x − 2x − 3 = 9, which simplifies to 3x − 3 = 9.
步骤1 中文：将含未知数的项移到方程一边。两边同时减去 2x：5x − 2x − 3 = 9，化简得 3x − 3 = 9。
Step 2 English: Isolate the x-term by adding 3 to both sides: 3x = 12.
步骤2 中文：为分离出 x 项，两边同加 3：3x = 12。
al equation: 5(4) − 3 = 20 − 3 = 17 and 2(4) + 9 = 8 + 9 = 17, so the solution is correct.
步骤3 中文：两边同除以 3 得 x = 4。将解代回原方程检验：5×4 − 3 = 20 − 3 = 17，而 2×4 + 9 = 8 + 9 = 17，因此解正确。
6. Q5: Straight Line Graphs (Calculator) | 第5题：直线图（计算器）
Question: nts A(1, 2) and B(4, 8). Hence write down the equation of the line in the form y = mx + c.
题目：求经过 A(1, 2) 和 B(4, 8) 两点的直线的斜率。据此写出该直线在 y = mx + c 形式下的方程。
₁). Use A(1,2) as (x₁, y₁) and B(4,8) as (x₂, y₂). Then m = (8 − 2) / (4 − 1) = 6 / 3 = 2.
步骤1 中文：斜率 m 由公式 (y₂ − y₁) / (x₂ − x₁) 求得。取 A(1,2) 为 (x₁, y₁)，B(4,8) 为 (x₂, y₂)。则 m = (8 − 2) / (4 − 1) = 6 / 3 = 2。
ing point A: 2 = 2(1) + c, so 2 = 2 + c, giving c = 0. The equation of the line is y = 2x.
步骤2 中文：将斜率和其中一个点代入 y = mx + c。用点 A：2 = 2×1 + c，即 2 = 2 + c，得 c = 0。直线方程为 y = 2x。
7. Q6: Angles in Polygons (Non-Calculator) | 第6题：多边形内角（非计算器）
Question: (a) Calculate the sum of the interior angles of an octagon. (b) Find the size of one interior angle of a regular octagon.
题目：(a) 计算八边形的内角和。(b) 求正八边形一个内角的大小。
on: (n − 2) × 180°. For an octagon, n = 8, so the sum = (8 − 2) × 180° = 6 × 180° = 1080°.
步骤1 中文：使用 n 边形内角和公式：(n − 2) × 180°。八边形 n = 8，因此内角和 = (8 − 2) × 180° = 6 × 180° = 1080°。
gles equal. Divide the total sum by 8: 1080° ÷ 8 = 135°. Thus, one interior angle is 135°.
步骤2 中文：正八边形的所有内角相等。将总和除以 8：1080° ÷ 8 = 135°。因此一个内角为 135°。
8. Q7: Volume of a Cylinder (Calculator) | 第7题：圆柱体体积（计算器）
Question: Give your answer to one decimal place. (Use π = 3.14 or the π button on your calculator.)
题目：一个圆柱体底面半径为 3 cm，高为 10 cm。计算该圆柱体的体积，答案保留一位小数。（可使用 π = 3.14 或计算器上的 π 键。）
linder is V = πr²h. Substitute r = 3 cm and h = 10 cm into the formula: V = π × (3)² × 10.
步骤1 中文：圆柱体体积公式为 V = πr²h。将 r = 3 cm、h = 10 cm 代入公式：V = π × (3)² × 10。
, you may get a slightly more precise value, but rounded to one decimal place the answer is 282.7 cm³ (if using π = 3.14159...). Both 282.6 and 282.7 are accepted.
步骤2 中文：计算半径的平方：3² = 9。则 V = π × 9 × 10 = 90π。取 π ≈ 3.14，V ≈ 90 × 3.14 = 282.6 cm³。若使用计算器的 π 键，会得到更精确的值，四舍五入至一位小数后为 282.7 cm³（当 π = 3.14159...）。282.6 和 282.7 均接受。
9. Q8: Statistics – Mean from a Frequency Table (Calculator) | 第8题：统计 – 频数表求平均数（计算器）
Question: The frequency table below shows the number of books read by a group of students in one month. Estimate the mean number of books read.
| Number of books | Frequency |
| 0–4 | 5 |
| 5–9 | 12 |
| 10–14 | 8 |
| 15–19 | 5 |
题目：下面的频数表显示了一组学生在一个月内阅读的书籍数量。估计平均阅读书籍数。
| 书籍数量 | 频数 |
| 0–4 | 5 |
| 5–9 | 12 |
| 10–14 | 8 |
| 15–19 | 5 |
ass interval. The midpoints are: (0+4)÷2 = 2, (5+9)÷2 = 7, (10+14)÷2 = 12, (15+19)÷2 = 17.
步骤1 中文：要从分组数据估计平均数，首先求出每个区间的中点值。中点值为：(0+4)÷2 = 2，(5+9)÷2 = 7，(10+14)÷2 = 12，(15+19)÷2 = 17。
5 = 10, 7×12 = 84, 12×8 = 96, 17×5 = 85. Then sum these products: 10 + 84 + 96 + 85 = 275.
步骤2 中文：将每个中点值乘以其对应频数：2×5 = 10，7×12 = 84，12×8 = 96，17×5 = 85。然后将这些乘积相加：10 + 84 + 96 + 85 = 275。
ncy: 275 ÷ 30 = 9.166... Round to one decimal place to get an estimated mean of 9.2 books.
步骤3 中文：计算总频数：5 + 12 + 8 + 5 = 30。用乘积总和除以总频数：275 ÷ 30 = 9.166...，四舍五入至一位小数得估计平均值为 9.2 本书。
10. Q9: Ratio and Proportion (Non-Calculator) | 第9题：比率与比例（非计算器）
Question: Anna and Ben share a lottery prize of £350 in the ratio 2:3. How much does each person receive?
题目：安娜和本按 2:3 的比例分享 350 英镑的彩票奖金。每人各得多少？
arts of the ratio to find the total number of shares: 2 + 3 = 5 parts. The whole amount of £350 corresponds to these 5 parts.
步骤1 中文：将比例份数相加求出总份数：2 + 3 = 5 份。总额 350 英镑对应这 5 份。
Step 2 English: Calculate the value of one part: £350 ÷ 5 = £70. Then multiply by each part of the ratio: Anna receives 2 × £70 = £140, and Ben receives 3 × £70 = £210.
步骤2 中文：计算一份的价值：350 ÷ 5 = 70 英镑。然后乘以各自的份数：安娜得 2 × 70 = 140 英镑，本得 3 × 70 = 210 英镑。
Step 3 English: Always check that the two amounts add back to the total: £140 + £210 = £350, confirming the calculation.
步骤3 中文：务必验证两笔金额之和等于总额：140 + 210 = 350 英镑，确认计算无误。
11. Q10: Probability from a Two-Way Table (Calculator) | 第10题：双向表概率（计算器）
Question: The two-way table shows the number of students who prefer tea or coffee, by gender.
| Tea | Coffee | Total | |
| Male | 14 | 18 | 32 |
| Female | 21 | 7 | 28 |
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