Year 8 SQA Maths: Unit Test Mock Paper Walkthrough | 八年级SQA数学：单元测试模拟卷解析

📚 Year 8 SQA Maths: Unit Test Mock Paper Walkthrough | 八年级SQA数学：单元测试模拟卷解析

Welcome to this step-by-step walkthrough of a Year 8 SQA Mathematics unit test mock paper. This paper is designed to cover the key topics of the Scottish Curriculum for Excellence at S2 level, including number operations, fractions, decimals, percentages, algebra, geometry, coordinates and statistics. Every question is broken down with a clear solution strategy, common pitfalls and final answers, helping you build confidence for real assessments.

欢迎来到这篇八年级SQA数学单元测试模拟卷的逐步解析。本模拟卷旨在覆盖苏格兰卓越课程S2阶段的核心主题，包括整数运算、分数、小数、百分比、代数、几何、坐标与统计。每一道题都配有清晰的解题策略、常见错误提示和最终答案，帮助你为真实测评树立信心。

1. Question 1: Whole Number Operations | 第1题：整数运算

Question: Calculate 245 + 378 – 129.

题目：计算 245 + 378 – 129。

We solve this by working from left to right, since only addition and subtraction appear. First, add 245 and 378: 245 + 378 = 623.

因为只涉及加法和减法，我们从左到右依次计算。首先，将245与378相加：245 + 378 = 623。

Next, subtract 129 from the sum: 623 – 129 = 494.

接着，从和中减去129：623 – 129 = 494。

Many students mistakenly try to do the subtraction first, but as long as they understand that addition is commutative, they will still arrive at the same answer. However, following the left-to-right convention keeps the working neat.

许多学生容易先做减法，但只要是同级运算，交换顺序结果不变。不过按照从左到右的顺序书写计算过程会更整洁。

Final Answer: 494

最终答案：494

2. Question 2: Adding Fractions | 第2题：分数加法

Question: Work out 3/4 + 1/6, giving your answer in its simplest form.

题目：计算 3/4 + 1/6，结果化为最简分数。

To add fractions, we need a common denominator. The lowest common multiple of 4 and 6 is 12.

要相加分数，需要先找到公分母。4和6的最小公倍数是12。

Convert each fraction: 3/4 = (3 × 3)/(4 × 3) = 9/12, and 1/6 = (1 × 2)/(6 × 2) = 2/12.

通分：3/4 = (3×3)/(4×3) = 9/12，而 1/6 = (1×2)/(6×2) = 2/12。

Now add the numerators: 9/12 + 2/12 = 11/12. The fraction 11/12 is already in its simplest form.

现在将分子相加：9/12 + 2/12 = 11/12。11/12已经是最简分数。

A common mistake is to add numerators and denominators directly, giving 4/10, which is wrong. Always find a common denominator first.

一个常见错误是直接将分子分母分别相加得到4/10，这是错误的。一定要先通分。

Answer: 11/12

答案：11/12

3. Question 3: Decimal Multiplication | 第3题：小数乘法

Question: Calculate 3.2 × 1.5.

题目：计算 3.2 × 1.5。

Ignore the decimal points initially and multiply the numbers as if they were whole numbers: 32 × 15.

先忽略小数点，将两个数看作整数相乘：32 × 15。

32 × 15 can be worked out as 32 × 10 = 320, plus 32 × 5 = 160, giving 480.

32 × 15 可以计算为 32 × 10 = 320，再加 32 × 5 = 160，得到480。

Now count the decimal places: 3.2 has one decimal place, and 1.5 has one, so the product must have 1 + 1 = 2 decimal places. Therefore, 480 becomes 4.80, which is 4.8.

现在数小数位数：3.2有一位小数，1.5有一位小数，所以积应该有1+1=2位小数。因此480变为4.80，即4.8。

3.2 × 1.5 = 4.8

4. Question 4: Finding a Percentage of a Quantity | 第4题：求一个数的百分之几

Question: Find 20% of 150.

题目：求150的20%。

Percent means ‘out of 100’, so 20% can be written as the fraction 20/100 or the decimal 0.2.

百分比表示“每一百份”，所以20%可以写成分数20/100或小数0.2。

Multiply the whole amount by the decimal: 150 × 0.2 = 30.

将总数乘以该小数：150 × 0.2 = 30。

Alternatively, find 10% first (15) and then double it to get 20%.

也可以先求10%（15），再翻倍得到20%。

Always check that your answer is reasonable – 20% is a fifth, and a fifth of 150 is indeed 30.

务必检查答案是否合理——20%就是五分之一，150的五分之一正好是30。

20% of 150 = 30

150的20% = 30

5. Question 5: Simplifying Algebraic Expressions | 第5题：代数式化简

Question: Simplify 5x + 3y – 2x + y.

题目：化简 5x + 3y – 2x + y。

Group like terms together: terms with x and terms with y. The x terms are 5x and -2x, which combine to 3x.

把同类项合并：含x的项和含y的项。x项为5x和-2x，合并得3x。

The y terms are 3y and +y (which is 1y), giving 4y.

y项为3y和+y（即1y），合并得4y。

The simplified expression is 3x + 4y. Remember that you cannot combine x and y terms because they are not like terms.

化简后的表达式为 3x + 4y。记住不能合并x和y项，因为它们不是同类项。

Simplified: 3x + 4y

化简结果：3x + 4y

6. Question 6: Solving a Simple Equation | 第6题：解简单方程

Question: Solve 3y – 7 = 8.

题目：解方程 3y – 7 = 8。

The goal is to get y by itself. First, undo the subtraction by adding 7 to both sides: 3y – 7 + 7 = 8 + 7, which simplifies to 3y = 15.

目标是将y单独放在一边。首先，在等式两边同时加7消去减法：3y – 7 + 7 = 8 + 7，简化得3y = 15。

Next, undo the multiplication by dividing both sides by 3: 3y ÷ 3 = 15 ÷ 3, so y = 5.

然后，两边同时除以3消去乘法：3y ÷ 3 = 15 ÷ 3，因此y = 5。

Always check your solution by plugging it back: 3(5) – 7 = 15 – 7 = 8, which matches the right side.

务必把解代回原方程检验：3(5) – 7 = 15 – 7 = 8，与右侧匹配。

y = 5

7. Question 7: Angles in a Triangle | 第7题：三角形的内角

Question: In a triangle, two angles measure 35° and 75°. Find the third angle.

题目：在一个三角形中，两个角分别为35°和75°，求第三个角。

The sum of the interior angles of any triangle is always 180°. First, add the two given angles: 35° + 75° = 110°.

任何三角形的内角和总是180°。首先，将已知两角相加：35° + 75° = 110°。

Subtract this sum from 180° to find the third angle: 180° – 110° = 70°.

从180°中减去这个和得到第三个角：180° – 110° = 70°。

Check that 35° + 75° + 70° = 180°, confirming the calculation.

验证 35° + 75° + 70° = 180°，确认计算正确。

The third angle is 70°

第三个角为70°

8. Question 8: Area and Perimeter of a Rectangle | 第8题：长方形的面积与周长

Question: A rectangle has length 8 cm and width 3 cm. Calculate its area and perimeter.

题目：一个长方形长8厘米，宽3厘米。计算它的面积和周长。

Area of a rectangle = length × width. So area = 8 cm × 3 cm = 24 cm².

长方形面积 = 长 × 宽。因此面积 = 8 cm × 3 cm = 24 cm²。

Perimeter is the total distance around the shape: P = 2 × (length + width) = 2 × (8 + 3) = 2 × 11 = 22 cm.

周长是图形四周边界的总长度：P = 2 × (长 + 宽) = 2 × (8 + 3) = 2 × 11 = 22 cm。

Don’t confuse the formulas – area uses square units, while perimeter uses linear units.

切勿混淆公式——面积使用平方单位，周长使用长度单位。

Area = 24 cm², Perimeter = 22 cm

面积 = 24 cm²，周长 = 22 cm

9. Question 9: Coordinates and Quadrants | 第9题：坐标与象限

Question: Plot the point (-4, 5) on a coordinate grid and state which quadrant it lies in.

题目：在坐标网格中标出点 (-4, 5)，并说明它位于哪个象限。

The x-coordinate is -4 (move 4 units left from the origin), and the y-coordinate is 5 (move 5 units up). This places the point in the second quadrant, where x is negative and y is positive.

x坐标为-4（从原点左移4个单位），y坐标为5（上移5个单位）。该点位于第二象限，因为x为负，y为正。

The quadrants are counted anticlockwise starting from the top right (Quadrant I: +, +; Quadrant II: -, +; Quadrant III: -, -; Quadrant IV: +, -).

象限从右上角开始逆时针计数（第一象限：+,+；第二象限：-,+；第三象限：-,-；第四象限：+,-）。

So (-4, 5) is clearly in Quadrant II.

因此 (-4, 5) 明显位于第二象限。

Quadrant II

第二象限

10. Question 10: Mean and Median | 第10题：平均数和中位数

Question: Find the mean and median of the data set: 6, 9, 11, 8, 12.

题目：求数据集 6, 9, 11, 8, 12 的平均数和中位数。

To find the mean, add all the numbers: 6 + 9 + 11 + 8 + 12 = 46. There are 5 values, so mean = 46 ÷ 5 = 9.2.

求平均数：将所有数相加：6 + 9 + 11 + 8 + 12 = 46。共有5个值，平均数 = 46 ÷ 5 = 9.2。

For the median, first write the numbers in ascending order: 6, 8, 9, 11, 12. The median is the middle value, which is the 3rd number: 9.

求中位数：先将数据从小到大排列：6, 8, 9, 11, 12。中位数是中间的那个值，即第3个数：9。

If there were an even number of data points, the median would be the average of the two middle numbers, but here the odd count makes it straightforward.

如果数据个数是偶数，中位数是中间两个数的平均数，但这里个数为奇数，计算很简单。

Mean = 9.2, Median = 9

平均数 = 9.2，中位数 = 9

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Year 8 SQA Maths: Unit Test Mock Paper Walkthrough | 八年级SQA数学：单元测试模拟卷解析