Year 8 AQA Maths: Unit Test Mock Paper Walkthrough | AQA 8 年级数学单元测试模拟卷解析

📚 Year 8 AQA Maths: Unit Test Mock Paper Walkthrough | AQA 8 年级数学单元测试模拟卷解析

Welcome to this comprehensive walkthrough of a Year 8 AQA Maths unit test mock paper. The paper includes carefully selected questions covering key topics from the Year 8 syllabus: fractions, algebraic manipulation, solving equations, angle properties, perimeter and area, probability, statistics, and speed calculations. Each question is solved step by step with bilingual explanations, helping you understand the logic behind every answer and avoid common mistakes.

欢迎阅读这份 Year 8 AQA 数学单元测试模拟卷的详细解析。试卷精选了涵盖八年级课程核心知识点的题目，包括分数运算、代数化简、解方程、角度性质、周长与面积、概率、统计以及行程问题。每道题都提供逐步解答和中英双语讲解，帮助你理解解题思路，避开常见失分点。

1. Question 1: Fraction Operations | 题目 1：分数运算

Evaluate: 3/5 + 1/4 − 1/10

计算：3/5 + 1/4 − 1/10

To add and subtract fractions, we first find a common denominator. The denominators are 5, 4 and 10. Their lowest common multiple (LCM) is 20.

做分数加减法时，首先要找到公分母。分母分别是 5、4 和 10，它们的最小公倍数（LCM）是 20。

Convert each fraction: 3/5 = (3×4)/(5×4) = 12/20, 1/4 = (1×5)/(4×5) = 5/20, and 1/10 = (1×2)/(10×2) = 2/20.

通分：3/5 = 12/20，1/4 = 5/20，1/10 = 2/20。

Now perform the operations: 12/20 + 5/20 − 2/20 = (12 + 5 − 2)/20 = 15/20.

进行运算：12/20 + 5/20 − 2/20 = (12 + 5 − 2)/20 = 15/20。

Simplify by dividing numerator and denominator by 5: 15/20 = 3/4.

分子分母同时除以 5 进行化简：15/20 = 3/4。

Final Answer: 3/4

最终答案：3/4

Tip: Always check if your final fraction can be simplified further; the answer should be in its simplest form.

提示：一定要检查最终分数能否继续约分，答案应为最简分数。

2. Question 2: Simplifying Algebraic Expressions | 题目 2：代数表达式化简

Simplify: 2(3x − 4) − 5(x + 2)

化简：2(3x − 4) − 5(x + 2)

First, expand the brackets using the distributive law. Multiply each term inside the first bracket by 2: 2 × 3x = 6x, 2 × (−4) = −8. For the second part, distribute the −5: −5 × x = −5x, and −5 × 2 = −10. Be careful with the negative sign.

首先用分配律展开括号。第一组括号每项乘 2：2×3x = 6x，2×(−4) = −8。第二组分配 −5：−5×x = −5x，−5×2 = −10。注意处理负号。

The expression becomes 6x − 8 − 5x − 10.

式子变为 6x − 8 − 5x − 10。

Combine like terms: 6x − 5x = x, and −8 − 10 = −18.

合并同类项：6x − 5x = x，−8 − 10 = −18。

Simplified expression: x − 18

化简结果：x − 18

Tip: When subtracting a bracket, rewrite as adding the negative to avoid sign errors.

提示：减去括号时，可以看作加上括号内各项的相反数，以避免符号错误。

3. Question 3: Solving Linear Equations | 题目 3：解一元一次方程

Solve: 4y + 7 = 3y − 2

解方程：4y + 7 = 3y − 2

We want to isolate y on one side. Subtract 3y from both sides to move the y‑terms together: 4y − 3y + 7 = −2, which simplifies to y + 7 = −2.

我们希望将 y 单独放在一边。两边同时减去 3y，把含 y 的项移到一起：4y − 3y + 7 = −2，化简得 y + 7 = −2。

Now subtract 7 from both sides to keep y by itself: y = −2 − 7.

两边再同时减去 7，得到 y = −2 − 7。

Calculate the right side: −2 − 7 = −9.

右边计算：−2 − 7 = −9。

Solution: y = −9

解：y = −9

You can check by substituting y = −9 back into the original equation: left side 4(−9) + 7 = −36 + 7 = −29, right side 3(−9) − 2 = −27 − 2 = −29. Both sides match.

你可以把 y = −9 代回原方程检验：左边 4(−9) + 7 = −29，右边 3(−9) − 2 = −29，两边相等。

4. Question 4: Angles in a Triangle | 题目 4：三角形内角

A triangle has angles (2x)°, (3x)° and (x + 30)°. Find x and the size of each angle.

一个三角形的三个内角分别是 (2x)°、(3x)° 和 (x + 30)°。求 x 以及每个角的度数。

The three interior angles of any triangle always sum to 180°. This gives the equation: 2x + 3x + (x + 30) = 180.

任何三角形三个内角之和始终为 180°。因此可列出方程：2x + 3x + (x + 30) = 180。

Combine like terms: 2x + 3x + x = 6x, plus 30 gives 6x + 30 = 180.

合并同类项：2x + 3x + x = 6x，再加上 30 得到 6x + 30 = 180。

Subtract 30 from both sides: 6x = 150. Divide by 6: x = 25.

两边减 30：6x = 150。除以 6 得 x = 25。

Now substitute x back: 2x° = 50°, 3x° = 75°, x + 30° = 55°.

代回计算：2x° = 50°，3x° = 75°，x + 30° = 55°。

Check: 50 + 75 + 55 = 180, so the solution is correct.

检验：50 + 75 + 55 = 180，解正确。

Answer: x = 25, angles = 50°, 75°, 55°

答案：x = 25，角度分别为 50°、75°、55°

5. Question 5: Perimeter and Area of a Rectangle | 题目 5：矩形的面积与周长

The area of a rectangle is 50 cm². Its length is twice its width. Find the perimeter of the rectangle.

一个矩形的面积是 50 cm²，它的长是宽的两倍。求该矩形的周长。

Let the width be w cm. Then the length = 2w cm. The area of a rectangle is length × width, so we set up the equation: 2w × w = 2w² = 50.

设宽为 w cm，则长为 2w cm。矩形面积 = 长 × 宽，因此有方程：2w × w = 2w² = 50。

Divide both sides by 2: w² = 25. Since width must be positive, w = √25 = 5.

两边除以 2：w² = 25。因为宽为正数，所以 w = √25 = 5。

Thus length = 2 × 5 =

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Year 8 AQA Maths: Unit Test Mock Paper Walkthrough | AQA 8 年级数学单元测试模拟卷解析