📚 Year 10 OCR Maths: Unit Test Mock Paper Solutions | 十年级 OCR 数学：单元测试模拟卷解析
This mock paper walks you through key topics covered in the Year 10 OCR Mathematics course, including number operations, algebra, geometry, statistics and probability. Each section provides a worked example to help you revise effectively for your unit test.
本模拟卷带你梳理十年级 OCR 数学课程的重点，涵盖数与运算、代数、几何、统计与概率。每个部分都配有详细例题解析，帮助你高效备考单元测试。
1. Number Skills and BIDMAS | 数字技能与运算顺序
BIDMAS (Brackets, Indices, Division/Multiplication, Addition/Subtraction) sets the order for calculations. Always start with brackets, then powers or roots, then division or multiplication from left to right, and finally addition or subtraction.
BIDMAS（括号、指数、乘除、加减）规定了计算的顺序。先算括号，再算幂或方根，然后从左到右进行乘除，最后进行加减。
Question: Work out 3² + 8 ÷ 2 × (6 − 4)³.
问题：计算 3² + 8 ÷ 2 × (6 − 4)³。
Step 1: Evaluate the bracket first. (6 − 4) = 2.
第一步：先计算括号，(6 − 4) = 2。
Step 2: Apply the indices. 3² = 9 and 2³ = 8.
第二步：计算指数。3² = 9，2³ = 8。
Perform division and multiplication in the order they appear. 8 ÷ 2 = 4, then 4 × 8 = 32.
第三步：按从左到右的顺序进行乘除。8 ÷ 2 = 4，然后 4 × 8 = 32。
Step 4: Finally, carry out the addition. 9 + 32 = 41.
第四步：最后加法。9 + 32 = 41。
The correct answer is 41.
正确答案是 41。
2. Algebraic Simplification | 代数化简
Simplifying an expression means collecting like terms — terms that have exactly the same variable and power. Constants are like terms with each other.
化简表达式就是合并同类项——变量和幂次完全相同的项。常数项之间也是同类项。
Question: Simplify 5x + 3y − 2x + 7y − 4.
问题：化简 5x + 3y − 2x + 7y − 4。
Identify the x terms: 5x and −2x. Combine them: 5x − 2x = 3x.
找出 x 的项：5x 和 −2x。合并：5x − 2x = 3x。
Now the y terms: 3y and +7y give 10y.
然后 y 的项：3y 和 +7y 得到 10y。
The constant term is −4 and it stays as it is.
常数项 −4 保持不变。
Hence the simplified expression is 3x + 10y − 4.
因此化简后的表达式是 3x + 10y − 4。
3. Solving Linear Equations | 解一元一次方程
When an unknown appears on both sides of an equation, first expand any brackets, then collect like terms, and isolate the variable.
当未知数出现在方程两侧时，先展开括号，然后移项合并，最后解出未知数。
Question: Solve 4(x − 3) = 2x + 8.
问题：解方程 4(x − 3) = 2x + 8。
4(x − 3) = 2x + 8
Expand the left-hand side: 4x − 12 = 2x + 8.
展开左边：4x − 12 = 2x + 8。
Subtract 2x from both sides: 2x − 12 = 8.
两边减去 2x：2x − 12 = 8。
Add 12 to both sides: 2x = 20.
两边加 12：2x = 20。
Divide by 2: x = 10.
除以 2：x = 10。
eck: substitute x = 10 into the original equation: 4(10−3)=4×7=28 and 2×10+8=28. It works.
检验：把 x = 10 代回原方程：4(10−3)=4×7=28，2×10+8=28，成立。
4. Angles in Parallel Lines | 平行线中的角
When a transversal crosses parallel lines, corresponding angles are equal, alternate interior angles are equal, and co-interior angles sum to 180°.
当一条横截线与两条平行线相交时，同位角相等，内错角相等，同旁内角互补（和为180°）。
Question: In the diagram, line AB is parallel to CD, and an angle formed by the transversal measures 70°. Find the corresponding angle x and the alternate angle y.
问题：在图中，AB 平行于 CD，横截线构成的一个角为 70°。求同位角 x 和内错角 y。
Angle x is the corresponding angle to the 70° angle, so x = 70°.
角 x 是 70° 的同位角，因此 x = 70°。
Angle y is the alternate interior angle to the 70° angle, so y = 70° as well.
角 y 是 70° 的内错角，因此 y 也是 70°。
If the question asks for the co-interior angle, it would be 180° − 70° = 110°.
如果题目要求同旁内角，则为 180° − 70° = 110°。
5. Area and Perimeter of Compound Shapes | 复合图形的面积与周长
A compound shape can be split into simpler rectangles, or considered as a larger rectangle with a cut-out. Calculate area by adding or subtracting areas of basic shapes, and perimeter by tracing the outer boundary.
复合图形可以分割成简单矩形，或看作大矩形减去一个缺口。面积通过加减基础图形面积计算，周长通过描摹外侧边缘求得。
m × 3 cm rectangle from a corner of a 10 cm × 6 cm rectangle. Find its area and perimeter.
问题：从一个 10 cm × 6 cm 的矩形一角剪掉一个 4 cm × 3 cm 的小矩形，求剩余图形的面积和周长。
Area of large rectangle = 10 × 6 = 60 cm²
Area of cut-out = 4 × 3 = 12 cm².
小矩形面积 = 4 × 3 = 12 cm²。
Area of compound shape = 60 − 12 = 48 cm².
复合图形面积 = 60 − 12 = 48 cm²。
t 4 cm, and up (6−3)=3 cm back to start. Total perimeter = 10 + 6 + 6 + 3 + 4 + 3 = 32 cm.
周长沿外边界走一圈：从左上角开始，向右 10 cm，向下 6 cm，向左 (10−4)=6 cm，向上 3 cm，向左 4 cm，再向上 (6−3)=3 cm 回到起点。总周长 = 10 + 6 + 6 + 3 + 4 + 3 = 32 cm。
6. Fractions, Decimals and Percentages | 分数、小数与百分数
Converting between fractions, decimals and percentages is an essential skill. To change a fraction to a decimal, divide the numerator by the denominator. Multiply by 100 to get the percentage.
分数、小数和百分数之间的转换是必备技能。分数化小数，用分子除以分母；再乘以 100 得到百分数。
Question: Convert 3/8 to a decimal and a percentage. Also, which is larger: 0.35 or 2/5?
问题：将 3/8 转换为小数和百分数。另外，比较 0.35 和 2/5 哪个更大？
3/8 as a decimal: 3 ÷ 8 = 0.375.
3/8 化为小数：3 ÷ 8 = 0.375。
As a percentage: 0.375 × 100 = 37.5%.
化为百分数：0.375 × 100 = 37.5%。
Now compare 0.35 and 2/5. 2/5 = 2 ÷ 5 = 0.4. Since 0.4 > 0.35, therefore 2/5 is larger.
比较 0.35 和 2/5。2/5 = 2 ÷ 5 = 0.4。因为 0.4 > 0.35，所以 2/5 更大。
7. Ratio and Proportion | 比与比例
When a quantity is divided in a given ratio, think of the total number of parts. Each part gets an equal share of the total amount.
当一个量按给定比例分配时，考虑总份数，每一份占据总量的同等份额。
Question: Orange squash and water are mixed in the ratio 2:3. How
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