📚 Year 8 WJEC Maths: Case Study Practice | 八年级 WJEC 数学：案例分析实战演练
Welcome to this case study practice article designed for Year 8 students following the WJEC curriculum. Here, you will tackle real-world scenarios that require you to apply your maths skills, from fractions and percentages to algebra and geometry. Each case study is broken down step by step to help you build confidence and deepen your understanding.
欢迎阅读这篇为 WJEC 课程八年级学生设计的案例分析实战演练文章。在这里，你将解决需要运用数学技能的实际情景，从分数和百分数到代数和几何。每个案例都逐步分解，帮助你建立信心并加深理解。
1. Recipe Scaling with Fractions and Decimals | 运用分数和小数调整食谱配方
A recipe for 4 people needs 3/4 cup of sugar and 1.25 cups of flour. How much of each ingredient is needed for 6 people?
一份4人份的食谱需要3/4杯糖和1.25杯面粉。6人份需要每种原料多少？
First, find the scaling factor: 6 ÷ 4 = 1.5, or 3/2 as a fraction.
首先，找出比例因子：6 ÷ 4 = 1.5，或用分数表示为3/2。
Sugar: 3/4 × 1.5 = 3/4 × 3/2 = 9/8 = 1 1/8 cups. As a decimal, 1.125 cups.
糖：3/4 × 1.5 = 3/4 × 3/2 = 9/8 = 1 1/8 杯。用小数表示为1.125杯。
Flour: 1.25 × 1.5 = 1.875 cups.
面粉：1.25 × 1.5 = 1.875杯。
2. Percentage Discounts on Shopping | 购物中的百分数折扣
You buy a jacket priced at £45. The shop offers a 20% discount. Then an extra 10% off the reduced price is applied at the till. How much do you pay?
你买一件标价45英镑的夹克。商店提供20%折扣。然后在收银台对减价后的价格再打10%的额外折扣。你需要付多少钱？
Step 1: 20% of £45 = 0.2 × 45 = £9. Reduced price = 45 – 9 = £36.
步骤1：45英镑的20% = 0.2 × 45 = 9英镑。减后价 = 45 – 9 = 36英镑。
Step 2: 10% of £36 = 0.1 × 36 = £3.60. Final price = 36 – 3.60 = £32.40.
步骤2：36英镑的10% = 0.1 × 36 = 3.60英镑。最终价格 = 36 – 3.60 = 32.40英镑。
Alternatively, multiply by 0.8 then 0.9: 45 × 0.8 × 0.9 = 45 × 0.72 = £32.40.
或者，先乘以0.8再乘以0.9：45 × 0.8 × 0.9 = 45 × 0.72 = 32.40英镑。
3. Algebraic Expressions for Mobile Phone Costs | 用代数表达式表示手机费用
A mobile phone contract has a monthly fee of £6 plus £0.15 per minute of calls. If you talk for m minutes in a month, write an expression for the total cost C.
一个手机合约每月固定费用6英镑，另加每分钟通话费0.15英镑。如果你一个月通话m分钟，写出总费用C的表达式。
C = 6 + 0.15m. This is a linear expression.
C = 6 + 0.15m。这是一个一次表达式。
If you use 120 minutes in a month, substitute m = 120: C = 6 + 0.15 × 120 = 6 + 18 = £24.
如果你一个月用了120分钟，代入m = 120：C = 6 + 0.15 × 120 = 6 + 18 = 24英镑。
Find m when the bill is £30: 30 = 6 + 0.15m ⇒ 0.15m = 24 ⇒ m = 24 ÷ 0.15 = 160 minutes.
当账单为30英镑时求m：30 = 6 + 0.15m ⇒ 0.15m = 24 ⇒ m = 24 ÷ 0.15 = 160分钟。
4. Area and Perimeter for Fencing a Garden | 围花园的面积和周长
A rectangular lawn measures 8.5 m by 12 m. You need to buy fence panels for the perimeter and grass seed for the area. Calculate both.
一块长方形草坪长12米，宽8.5米。你需要为周长购买围栏板，为面积购买草籽。计算两者。
Perimeter = 2 × (length + width) = 2 × (12 + 8.5) = 2 × 20.5 = 41 m.
周长 = 2 × (长 + 宽) = 2 × (12 + 8.5) = 2 × 20.5 = 41 米。
Area = length × width = 12 × 8.5 = 102 m².
面积 = 长 × 宽 = 12 × 8.5 = 102 平方米。
covers 1.8 m, number of panels needed = 41 ÷ 1.8 ≈ 22.78, so buy 23 panels (rounding up).
如果一块围栏板覆盖1.8米，所需板数 = 41 ÷ 1.8 ≈ 22.78，因此买23块（向上取整）。
5. Ratio and Proportion in Mixing Paint | 混合油漆中的比和比例
To make a shade of purple, blue and red paint are mixed in the ratio 3:2. You have 2.4 litres of blue paint. How much red paint do you need, and what is the total volume of purple paint?
要调配一种紫色调，蓝色和红色油漆按3:2的比例混合。你有2.4升蓝漆。需要多少升红漆？配出的紫色油漆总体积是多少？
The ratio 3:2 means for every 3 parts blue, there are 2 parts red. Blue : Red = 3 : 2.
比例3:2意味着每3份蓝漆对应2份红漆。蓝 : 红 = 3 : 2。
Blue volume = 2.4 L, so 1 part = 2.4 ÷ 3 = 0.8 L. Red = 2 parts = 2 × 0.8 = 1.6 L.
蓝漆体积 = 2.4升，所以1份 = 2.4 ÷ 3 = 0.8升。红漆 = 2份 = 2 × 0.8 = 1.6升。
Total purple = 2.4 + 1.6 = 4.0 L.
紫色总体积 = 2.4 + 1.6 = 4.0升。
6. Mean, Median and Mode from Survey Data | 从调查数据中求平均数、中位数和众数
A class recorded the number of books read in a month: 3, 5, 2, 7, 5, 4, 5, 3, 6, 4. Find the mean, median and mode.
一个班级记录了一个月内阅读的书籍数量：3, 5, 2, 7, 5, 4, 5, 3, 6, 4。求平均数、中位数和众数。
Mean: sum = 3+5+2+7+5+4+5+3+6+4 = 44. Number of values = 10. Mean = 44 ÷ 10 = 4.4.
平均数：总和 = 3+5+2+7+5+4+5+3+6+4 = 44。数据个数 = 10。平均数 = 44 ÷ 10 = 4.4。
Median: order the data: 2, 3, 3, 4, 4, 5, 5, 5, 6, 7. Median = (4+5)/2 = 4.5.
中位数：将数据排序：2, 3, 3, 4, 4, 5, 5, 5, 6, 7。中位数 = (4+5)/2 = 4.5。
Mode: 5 appears most often (3 times), so mode = 5.
众数：5出现的次数最多（3次），因此众数 = 5。
7. Negative Numbers and Temperature Changes | 负数和温度变化
At midnight the temperature was -4°C. By 6 am it had dropped by 3°C. Then by noon it rose by 11°C. What was the temperature at noon?
午夜时温度为 -4°C。到早上6点下降了3°C。然后到中午上升了11°C。中午的温度是多少？
At 6 am: -4 – 3 = -7°C.
早上6点：-4 – 3 = -7°C。
At noon: -7 + 11 = 4°C.
中午：-7 + 11 = 4°C。
You can use a number line: starting at -4, move 3 left to -7, then 11 right to 4.
你可以使用数轴：从 -4 开始，向左移动3格到 -7，然后向右移动11格到4。
8. Solving Linear Equations in Budgeting | 用线性方程解预算问题
You have saved £40 and plan to save £5 per week. After how many weeks w will your total savings be £100? Write an equation and solve it.
你已经存了40英镑，并计划每周存5英镑。经过多少周w后，你的总储蓄将达到100英镑？写出方程并求解。
Equation: 40 + 5w = 100.
方程：40 + 5w = 100。
Subtract 40 from both sides: 5w = 60. Divide by 5: w = 12.
两边减去40：5w = 60。除以5：w = 12。
After 12 weeks you will have £100.
12周后你将有100英镑。
Check: 40 + 5 × 12 = 40 + 60 = 100. Correct.
检验：40 + 5 × 12 = 40 + 60 = 100。正确。
9. Time and Speed for a Journey | 旅行中的时间与速度
You travel 180 miles at an average speed of 50 mph. How long does the journey take? Give your answer in hours and minutes.
你以平均每小时50英里的速度行驶180英里。旅程需要多长时间？以小时和分钟给出答案。
Time = distance ÷ speed = 180 ÷ 50 = 3.6 hours.
时间 = 距离 ÷ 速度 = 180 ÷ 50 = 3.6 小时。
0.6 of an hour = 0.6 × 60 = 36 minutes. So journey time is 3 hours 36 minutes.
0.6小时 = 0.6 × 60 = 36分钟。因此行程时间为3小时36分钟。
If you leave at 10:15 am, arrival time = 10:15 + 3 h 36 min = 1:51 pm.
如果你上午10:15出发，到达时间 = 10:15 + 3小时36分钟 = 下午1:51。
10. Volume of Boxes for Packing | 打包箱子的体积
You are packing cube-shaped toys of side length 6 cm into a cardboard box measuring 30 cm by 24 cm by 18 cm. How many toys fit inside the box?
你将边长为6厘米的立方体玩具装入一个尺寸为30厘米×24厘米×18厘米的纸板箱。箱内能装下多少个玩具？
each dimension: Length-wise: 30 ÷ 6 = 5. Width-wise: 24 ÷ 6 = 4. Height-wise: 18 ÷ 6 = 3.
计算在每个维度上能放多少个玩具：长度方向：30 ÷ 6 = 5。宽度方向：24 ÷ 6 = 4。高度方向：18 ÷ 6 = 3。
Total number = 5 × 4 × 3 = 60 toys.
总数 = 5 × 4 × 3 = 60个玩具。
one toy (6³ = 216 cm³), then divide: 12,960 ÷ 216 = 60. Both methods give the same answer.
你还可以求箱子的体积（30×24×18 = 12,960立方厘米）和一个玩具的体积（6³ = 216立方厘米），然后相除：12,960 ÷ 216 = 60。两种方法结果相同。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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