Year 9 CCEA Maths Unit Test: Mock Paper Solutions | CCEA 九年级数学单元测试模拟卷解析

📚 Year 9 CCEA Maths Unit Test: Mock Paper Solutions | CCEA 九年级数学单元测试模拟卷解析

This article provides detailed, step-by-step solutions to a mock unit test for Year 9 CCEA Mathematics. Each problem is carefully broken down to reinforce key concepts and boost your confidence for the real assessment. We cover fractions, equations, ratios, percentages, sequences, area, angles, Pythagoras' theorem, statistics and probability.

本文为 CCEA 九年级数学单元测试模拟卷提供详细的分步解析。每道题目都进行了细致的拆解，旨在巩固核心知识点，提升你面对真实考试的信心。内容涵盖分数、方程、比与比例、百分比、数列、面积、角度、勾股定理、统计和概率。

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1. Fractions and Decimals | 分数与小数

Problem: Evaluate 2/3 + 1/4, leaving your answer as a mixed number where appropriate. Then convert the decimal 0.375 into a fraction in its simplest form.

题目：计算 2/3 + 1/4，若结果为假分数请化为带分数。再将小数 0.375 化为最简分数。

Step 1 – Find the common denominator for addition: The denominators are 3 and 4. Their least common multiple (LCM) is 12. This is the smallest number both 3 and 4 divide into without a remainder.

步骤1 – 寻找加法中的公分母：分母是 3 和 4，它们的最小公倍数（LCM）为 12。这是 3 和 4 都能整除的最小数字。

Step 2 – Convert each fraction: Multiply the numerator and denominator of 2/3 by 4 to get 8/12. Multiply the numerator and denominator of 1/4 by 3 to get 3/12.

步骤2 – 转换每个分数：将 2/3 的分子和分母同时乘以 4，得到 8/12；将 1/4 的分子和分母同时乘以 3，得到 3/12。

Step 3 – Add the fractions: 8/12 + 3/12 = 11/12.

步骤3 – 分数相加：8/12 + 3/12 = 11/12。

Step 4 – Express as a mixed number: Since 11 is smaller than 12, the fraction 11/12 is a proper fraction. It cannot be written as a mixed number, so the final answer is simply 11/12.

步骤4 – 化为带分数：因为 11 小于 12，11/12 为真分数，无法化为带分数，因此最终答案就是 11/12。

Step 5 – Convert 0.375 to a fraction: The decimal 0.375 means 375 thousandths, so write it as 375/1000.

步骤5 – 将 0.375 转换为分数：小数 0.375 表示 375 个千分之一，因此写成分数 375/1000。

Step 6 – Simplify the fraction: numbers are divisible by 125. 375 ÷ 125 = 3, 1000 ÷ 125 = 8. So the simplest form is 3/8.

步骤6 – 化简分数：找出 375 和 1000 的最大公因数。两者都能被 125 整除，375 ÷ 125 = 3，1000 ÷ 125 = 8。最简分数为 3/8。

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2. Solving Linear Equations | 解一元一次方程

Problem: Solve the equation 4(x − 3) = 2x + 6.

题目：解方程 4(x − 3) = 2x + 6。

Step 1 – Expand the brackets: inside the brackets: 4 × x = 4x and 4 × (−3) = −12. The equation becomes 4x − 12 = 2x + 6.

步骤1 – 展开括号：将 4 乘以括号内的每一项：4 × x = 4x，4 × (−3) = −12。方程变为 4x − 12 = 2x + 6。

4x − 12 = 2x + 6

Step 2 – Collect x terms on one side: nate the x term on the right: 4x − 12 − 2x = 2x + 6 − 2x, which simplifies to 2x − 12 = 6.

步骤2 – 将含 x 的项移到一边：两边同时减去 2x，消去右边的 x 项：4x − 12 − 2x = 2x + 6 − 2x，化简得 2x − 12 = 6。

Step 3 – Isolate the x term: Add 12 to both sides: 2x − 12 + 12 = 6 + 12, resulting in 2x = 18.

步骤3 – 分离 x 项：两边同时加上 12：2x − 12 + 12 = 6 + 12，得到 2x = 18。

Step 4 – Solve for x: Divide both sides by 2: 2x ÷ 2 = 18 ÷ 2, so x = 9.

步骤4 – 求解 x：两边同时除以 2：2x ÷ 2 = 18 ÷ 2，得出 x = 9。

Step 5 – Check the solution:

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