📚 Year 7 WJEC Further Mathematics: Unit Test Mock Paper Walkthrough | Year 7 WJEC 进阶数学：单元测试模拟卷解析
This article provides a complete walkthrough of a typical Unit Test mock paper for Year 7 Further Mathematics under the WJEC specification. We will examine key question types, model answers, and common pitfalls to help students master essential skills and boost test confidence.
本文完整解析了 WJEC 大纲下的 Year 7 进阶数学单元测试模拟卷。我们会分析关键题型、示范解答与常见错误，帮助学生掌握核心技能，提升应试信心。
1. Structure of the Mock Test | 模拟卷结构
A standard WJEC Year 7 Further Mathematics unit test usually consists of 15 to 20 questions, worth a total of 50 to 60 marks. The test covers Number, Algebra, Geometry & Measures, Statistics, Ratio & Proportion, and Probability. The time allowed is typically 45 to 60 minutes. Questions often increase in difficulty, mixing fluency, reasoning, and problem-solving.
标准的 WJEC Year 7 进阶数学单元测试通常由 15 至 20 道题组成，总分 50 至 60 分。测试内容涵盖数字、代数、几何与度量、统计、比与比例以及概率。考试时间一般为 45 至 60 分钟。题目难度通常逐渐增加，综合考察熟练度、推理能力和问题解决能力。
You should expect both non-calculator and calculator sections if specified by your teacher. Many questions require you to show clear working steps to gain full marks.
根据老师的要求，试卷可能分为允许使用计算器和不允许使用计算器的部分。许多题目需要写出清晰的解题步骤才能拿到全部分数。
2. Number and Place Value | 数字与位值
This section tests operations with integers, negative numbers, powers, and roots. You may be asked to evaluate expressions involving multiple operations, using the correct order of operations (BIDMAS/BODMAS).
本节考查整数的运算、负数、乘方和开方。你可能会被要求计算包含多种运算的表达式，并正确使用运算顺序（括号、指数、乘除、加减）。
Mock question: Evaluate 20 - 3² × 2 + (-15) ÷ 5.
模拟题：计算 20 - 3² × 2 + (-15) ÷ 5。
0 - 18 + (-3). Finally, addition and subtraction left to right: 20 - 18 = 2, then 2 + (-3) = -1. Answer: -1.
解答：首先处理乘方：3² = 9。然后从左到右进行乘法和除法：9 × 2 = 18，(-15) ÷ 5 = -3。现在表达式变为 20 - 18 + (-3)。最后从左到右进行加法和减法：20 - 18 = 2，然后 2 + (-3) = -1。答案：-1。
Common mistake: Applying subtraction before division. Always follow the BIDMAS order. Also, be careful when adding a negative number.
常见错误：在除法之前先做减法。务必遵守 BIDMAS 运算顺序。另外，加负数时要格外小心。
3. Fractions, Decimals and Percentages | 分数、小数和百分数
Questions often involve converting between fractions, decimals, and percentages, and performing calculations with them. You need to be confident finding a fraction of an amount and adding/subtracting fractions with different denominators.
题目经常涉及分数、小数和百分数之间的转换以及相关计算。你需要熟练地求一个数量的几分之几，并能进行异分母分数的加减法。
Mock question: Work out 2/5 of 80, and write your answer as a percentage of 200.
模拟题：计算 80 的 2/5，并将结果写成 200 的百分之多少。
0 = (80 ÷ 5) × 2 = 16 × 2 = 32. Now express 32 as a percentage of 200: (32/200) × 100 = 16%. Answer: 16%.
解答：80 的 2/5 = (80 ÷ 5) × 2 = 16 × 2 = 32。然后将 32 表示成 200 的百分比：(32/200) × 100 = 16%。答案：16%。
ing fractions: 1/3 + 2/9. The common denominator is 9, so 1/3 = 3/9. Then 3/9 + 2/9 = 5/9.
另一项关键技能是分数加法：1/3 + 2/9。公分母是 9，所以 1/3 = 3/9。然后 3/9 + 2/9 = 5/9。
4. Algebra and Equations | 代数与方程
This section assesses your ability to simplify expressions, substitute values, and solve linear equations. You will also see basic expanding brackets and forming expressions from word problems.
本节考查你化简表达式、代入数值和解一元一次方程的能力。你还会遇到简单去括号和根据文字题列代数式。
Mock question: Solve the equation 4x + 7 = 31 - 2x.
模拟题：解方程 4x + 7 = 31 - 2x。
6x + 7 = 31. Then subtract 7 from both sides: 6x = 24. Divide by 6: x = 4. Answer: x = 4.
解答：两边同时加 2x 得 6x + 7 = 31。然后两边同时减去 7：6x = 24。两边除以 6：x = 4。答案：x = 4。
Simplifying expressions example: 3(a + 2) - a. Expand first: 3a + 6 - a, then combine like terms: 2a + 6.
化简表达式示例：3(a + 2) - a。先去括号：3a + 6 - a，然后合并同类项：2a + 6。
Notice that full marks require showing the balance method clearly. Always write what you do to both sides.
请注意，要拿全部分数必须清晰地写出平衡法步骤。始终写出你对等式两边所做的操作。
5. Sequences and Patterns | 数列与规律
WJEC often includes questions on finding the nth term of an arithmetic sequence and using it to find specific terms. You might also be given a pattern of shapes and asked to link it to the term number.
WJEC 经常考查找等差数列第 n 项的公式，并用它求指定项。你也可能看到图形规律题，需要把图形与项数建立联系。
Mock question: Here are the first four terms of a sequence: 6, 11, 16, 21. Find an expression for the nth term, and then work out the 50th term.
模拟题：一个数列的前四项为 6，11，16，21。写出第 n 项的表达式，然后计算第 50 项。
m the first term: 6 - 5 = 1. So the nth term is 5n + 1. The 50th term is 5 × 50 + 1 = 251.
解答：各项之间的差为 +5，因此乘数部分是 5n。为求出第零项，从第一项倒退：6 - 5 = 1。所以第 n 项表达式为 5n + 1。第 50 项为 5 × 50 + 1 = 251。
nth term = 5n + 1
when n = 1, 5(1)+1=6; n=2 gives 11; both correct. Always verify the rule with given terms.
验证：当 n = 1 时，5(1)+1=6；n=2 得 11；均正确。始终用已知项验证你找到的规律。
6. Geometry: Angles and Shapes | 几何：角度与图形
Angle facts are essential: angles on a straight line sum to 180°, angles around a point sum to 360°, and the sum of angles in a triangle is 180°. You should be able to work out missing angles using these rules.
角度定理至关重要：平角之和为 180°，周角之和为 360°，三角形内角和为 180°。你要能够运用这些规则求出未知角度。
Mock question: In a triangle, two angles are 43° and 78°. Find the third angle, and name the type of triangle based on its angles.
模拟题：一个三角形有两个角分别为 43° 和 78°。求第三个角，并根据角度命名该三角形的类型。
43° + 78°) = 180° - 121° = 59°. Since all angles are less than 90°, the triangle is acute.
解答：三角形内角和 = 180°，所以第三个角 = 180° - (43° + 78°) = 180° - 121° = 59°。因为所有角都小于 90°，该三角形是锐角三角形。
Another typical problem involves angles around parallel lines, though less common in Year 7. If it appears, remember alternate angles and corresponding angles are equal.
另一个典型题型涉及平行线中的角，不过在 Year 7 较少见。如果出现，记住内错角和同位角相等。
7. Perimeter and Area | 周长与面积
Be ready to calculate the perimeter and area of rectangles, triangles, and compound shapes made from rectangles. Knowing how to find the area of a triangle as half the base times height is crucial.
准备好计算矩形、三角形以及由矩形组合而成的复合图形的周长和面积。掌握三角形面积等于底乘高除以二的方法至关重要。
Mock question: A rectangle has length 8 cm and width 5 cm. A right-angled triangle sits on top of the rectangle, sharing the length, and has height 4 cm. Find the total area of the compound shape.
模拟题：一个长方形的长为 8 cm，宽为 5 cm。一个直角三角形放在该长方形上面，以长为公共边，三角形的高为 4 cm。求该复合图形的总面积。
ngle = (base × height) ÷ 2 = (8 × 4) ÷ 2 = 32 ÷ 2 = 16 cm². Total area = 40 + 16 = 56 cm².
解答：长方形面积 = 8 × 5 = 40 cm²。三角形面积 = (底 × 高) ÷ 2 = (8 × 4) ÷ 2 = 32 ÷ 2 = 16 cm²。总面积 = 40 + 16 = 56 cm²。
Always check units. If dimensions are in cm, area units must be cm². For perimeter, keep units as cm.
务必检查单位。如果尺寸单位是 cm，面积单位必须是 cm²。周长单位保留 cm。
8. Ratio and Proportion | 比与比例
Ratio questions may involve sharing amounts in a given ratio or scaling recipes. You might also need to simplify ratios or find an equivalent ratio.
比例题可能涉及按给定比例分配某个数量或调整配方比例。你可能还需要化简比或求等价比。
Mock question: Share £45 between Alice and Bob in the ratio 2 : 3. How much does each receive?
模拟题：将 £45 按 2:3 的比例分给 Alice 和 Bob。两人各得多少？
Solution: Total parts = 2 + 3 = 5. Value of one part = £45 ÷ 5 = £9. Alice gets 2 × £9 = £18. Bob gets 3 × £9 = £27.
解答：总份数 = 2 + 3 = 5。每一份的价值 = £45 ÷ 5 = £9。Alice 得到 2 × £9 = £18，Bob 得到 3 × £9 = £27。
ratio of boys to girls in a class is 4 : 5. If there are 20 boys, how many girls are there? Since boys correspond to 4 parts, 4 parts = 20, so 1 part = 5, girls = 5 × 5 = 25.
另一个例子：一个班级的男女生比例是 4:5。如果男生有 20 人，女生有多少人？因为男生对应 4 份，4 份 = 20，所以 1 份 = 5，女生 = 5 × 5 = 25。
9. Data Handling and Averages | 数据处理与平均数
Students should be able to find the mean, median, mode, and range of a dataset, and interpret simple charts like bar charts and pictograms.
学生应能求出一组数据的平均数（均值）、中位数、众数和极差，并能解读简单的图表，如条形图和象形图。
Mock question: The scores of a class in a test are: 7, 9, 6, 9, 5, 8. Calculate the mean, median, mode, and range.
模拟题：某班级的一次测验成绩为：7，9，6，9，5，8。计算平均数、中位数、众数和极差。
d 4th: (7+8) ÷ 2 = 7.5. Mode is the most frequent: 9. Range = highest - lowest = 9 - 5 = 4.
解答：平均数 = (7+9+6+9+5+8) ÷ 6 = 44 ÷ 6 = 7.33（或 7 1/3）。将数据排序：5，6，7，8，9，9。中位数是六个数的中间值，即第三和第四的平均值：(7+8) ÷ 2 = 7.5。众数是出现次数最多的：9。极差 = 最大值 - 最小值 = 9 - 5 = 4。
For an even number of data points, remember the median is the mean of the two central numbers. Don't just pick one.
当数据个数为偶数时，记住中位数是中间两个数的平均数，不要只选其中一个。
10. Probability | 概率
Simple probability is usually tested by asking for the chance of an event from a fair die, spinner, or bag of counters. Probability is always a fraction, decimal, or percentage between 0 and 1.
简单概率的测试通常要求从公平的骰子、转盘或袋子里的筹码中求某事件的可能性。概率总是介于 0 和 1 之间的分数、小数或百分数。
Mock question: A bag contains 3 red, 2 blue and 5 green counters. One counter is taken at random. What is the probability it is blue? What is the probability it is not red?
模拟题：一个袋子里有 3 个红色、2 个蓝色和 5 个绿色筹码。随机取出一个。取到蓝色的概率是多少？取不到红色的概率是多少？
favorable = 2 + 5 = 7, so probability = 7/10. Alternatively, 1 - P(red) = 1 - 3/10 = 7/10.
解答：筹码总数 = 3 + 2 + 5 = 10。取到蓝色的概率 = 2/10 = 1/5。取不到红色即取到蓝色或绿色，有利结果总数 = 2 + 5 = 7，所以概率 = 7/10。或者 1 - P(红) = 1 - 3/10 = 7/10。
Always simplify your fraction answer unless told otherwise.
如果没有特别说明，务必将分数答案化为最简形式。
11. Problem-Solving Strategies | 解题策略
Many marks are allocated to multi-step word problems. These require careful reading, identifying the relevant information, and breaking the problem into smaller steps. Drawing a diagram or using a bar model can be extremely helpful.
多步骤应用题往往占很多分数。这类题目需要仔细审题，找出相关信息，并把问题分解成小步骤。画示意图或使用条形模型会非常有帮助。
Mock question: A school hall has 24 rows of chairs with 15 chairs in each row. For a concert, 1/6 of the chairs are reserved for staff and guests. The remaining chairs are for students. 3/5 of the student chairs are taken by Year 7. How many chairs are left for other students?
模拟题：学校礼堂有 24 排椅子，每排 15 把。一场音乐会中，1/6 的椅子留给教职员工和嘉宾，剩下的给学生。学生椅子的 3/5 被 Year 7 占用。其余学生还有多少把椅子？
0. Year 7 chairs = 3/5 × 300 = 180. Remaining chairs for other students = 300 - 180 = 120.
解答：椅子总数 = 24 × 15 = 360。教职员工席 = 1/6 × 360 = 60。学生席 = 360 - 60 = 300。Year 7 占用 = 3/5 × 300 = 180。其余学生椅子数 = 300 - 180 = 120。
Notice how we tackled one step at a time. Writing it out clearly helped avoid confusion with fractions of different amounts.
请注意我们是怎样一步步解决的。清晰写出过程有助于避免把不同量的分数混在一起而出错。
12. Final Tips | 最后提示
Before the test, practice mental arithmetic and times tables to improve speed. In the exam, always show your working – a correct answer with no steps might lose marks if the method is required. Check your answers, especially for units and whether your answer is reasonable in context.
考试前，练习心算和乘法表以提高速度。考试中，始终写出解题步骤——如果要求写出方法，只给答案而无步骤可能会失分。检查你的答案，尤其要关注单位以及答案在实际情境中是否合理。
If stuck on a question, move on and return later. Manage your time so you attempt all questions. Remember to bring necessary equipment: pen, pencil, ruler, protractor, and a calculator if allowed.
如果遇到难题，先跳过，稍后再回来解答。合理分配时间，确保答完所有题目。记得携带必要文具：钢笔、铅笔、直尺、量角器，以及允许使用的计算器。
Finally, a positive mindset makes a big difference. Treat the mock as a chance to show what you know and to learn from any mistakes. Good luck!
最后，积极的心态至关重要。把模拟考看作展示你所学以及从错误中学习的机会。祝你好运！
Published by TutorHao | WJEC Further Mathematics 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