KS3 WJEC Further Mathematics: Unit Test Mock Paper Walkthrough | KS3 WJEC 进阶数学：单元测试模拟卷解析

📚 KS3 WJEC Further Mathematics: Unit Test Mock Paper Walkthrough | KS3 WJEC 进阶数学：单元测试模拟卷解析

This article provides a detailed walkthrough of a mock unit test for the KS3 WJEC Further Mathematics course. Each question is carefully broken down step-by-step in both English and Chinese to help you understand the key concepts and common exam techniques. Use this guide to revise and gain confidence before your assessment.

本文为KS3 WJEC进阶数学课程的单元测试模拟卷提供详细解析。每道题均以中英双语逐步拆解，帮助你掌握核心概念和常见考试技巧。借助本指南进行复习，并在评估前建立信心。

1. Solving Equations with Brackets | 解含有括号的方程

Solve the equation: 2(3x - 1) = 4x + 10

解方程：2(3x - 1) = 4x + 10

Step 1: Expand the bracket on the left-hand side: 2 × 3x - 2 × 1 = 6x - 2.

步骤1：展开左边的括号：2 × 3x − 2 × 1 = 6x − 2。

So the equation becomes 6x - 2 = 4x + 10.

于是方程变为 6x − 2 = 4x + 10。

e and constants to the other. Subtract 4x from both sides: 6x - 4x - 2 = 10 → 2x - 2 = 10.

步骤2：将x项移到一边，常数移到另一边。两边同时减去4x：6x − 4x − 2 = 10 → 2x − 2 = 10。

Step 3: Add 2 to both sides: 2x = 12.

步骤3：两边同时加2：2x = 12。

Step 4: Divide by 2: x = 6.

步骤4：除以2：x = 6。

Answer: x = 6.

答案：x = 6。

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2. Inequalities and Number Lines | 不等式与数轴表示

Solve the inequality: 5 - 2x ≤ 7

解不等式：5 - 2x ≤ 7

Step 1: Subtract 5 from both sides: -2x ≤ 2.

步骤1：两边同时减去5：−2x ≤ 2。

Step 2: Divide both sides by -2, and remember to reverse the inequality sign: x ≥ -1.

步骤2：两边同时除以−2，记住不等号要改变方向：x ≥ −1。

Represent on a number line: draw a number line, mark -1 with a closed circle (since it is '≥'), and shade to the right.

步骤3：在数轴上表示：画出数轴，在 -1 处画实心圆（因为是“≥”），并向右画阴影。

Solution: x ≥ -1.

解集：x ≥ −1。

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3. nth Term of a Linear Sequence | 线性数列的第n项

Find the nth term of the sequence: 7, 11, 15, 19, ...

求数列 7, 11, 15, 19, ... 的第n项公式。

Step 1: Find the common difference. 11 - 7 = 4, 15 - 11 = 4, so the difference d = 4.

步骤1：找出公差。11 − 7 = 4, 15 − 11 = 4，因此公差 d = 4。

a for an arithmetic sequence is: a + (n-1)d, where a is the first term. Here a = 7, d = 4.

步骤2：等差数列的第n项公式为：a + (n−1)d，其中a为首项。这里 a=7，d=4。

Step 3: Substitute: nth term = 7 + (n-1)×4 = 7 + 4n - 4 = 4n + 3.

步骤3：代入：第n项 = 7 + (n−1)×4 = 7 + 4n − 4 = 4n + 3。

Step 4: To find the 20th term, put n = 20: 4×20 + 3 = 80 + 3 = 83.

步骤4：求第20项，令 n=20：4×20 + 3 = 80 + 3 = 83。

Answer: nth term = 4n + 3, 20th term = 83.

答案：第n项 = 4n + 3，第20项 = 83。

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4. Graph of a Linear Function | 线性函数的图像

Draw the graph of y = -½ x + 3 and find the x-intercept and y-intercept.

画出函数 y = −½ x + 3 的图像，并找出x轴截距和y轴截距。

1: Find the y-intercept by setting x = 0: y = -½(0) + 3 = 3. So the y-intercept is (0,3).

步骤1：令 x=0 求y轴截距：y = −½(0) + 3 = 3，因此y轴截距为 (0,3)。

x-intercept by setting y = 0: 0 = -½ x + 3 → ½ x = 3 → x = 6. So the x-intercept is (6,0).

步骤2：令 y=0 求x轴截距：0 = −½ x + 3 → ½ x = 3 → x = 6，x轴截距为 (6,0)。

, 6. Calculate y: when x=-2, y= -½(-2)+3=1+3=4; etc. Plot points and draw a straight line.

步骤3：列出数值表，如 x = −2, 0, 2, 4, 6。计算y：x=−2时，y=−½(−2)+3=1+3=4；以此类推。描点并连成直线。

Graph features: slope is -½, meaning the line goes downwards from left to right.

图像特征：斜率为 −½，意味着直线从左到右下降。

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5. Pythagoras' Theorem | 勾股定理

In a right-angled triangle, the two shorter sides are 5 cm and 12 cm. Calculate the length of the hypotenuse.

在一个直角三角形中，两条较短的边分别为5 cm和12 cm。计算斜边的长度。

Step 1: Use Pythagoras' theorem: c² = a² + b², where c is the hypotenuse.

步骤1：使用勾股定理：c² = a² + b²，其中c为斜边。

Step 2: Substitute a = 5, b = 12: c² = 5² + 12² = 25 + 144 = 169.

步骤2：代入 a=5, b=12：c² = 5² + 12² = 25 + 144 = 169。

Step 3: Take the square root: c = √169 = 13.

步骤3：开平方：c = √169 = 13。

Answer: The hypotenuse is 13 cm.

答案：斜边长为13 cm。

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6. Circumference and Area of a Circle | 圆的周长与面积

culate its circumference and area, giving your answers to one decimal place. Use π = 3.14.

一个圆的半径为7 cm。计算其周长和面积，结果保留一位小数。使用π=3.14。Published by TutorHao | KS3 进阶数学 Revision Series | aleveler.com

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