Year 7 AQA Maths: Unit Test Mock Paper Analysis | 七年级AQA数学：单元测试模拟卷解析

📚 Year 7 AQA Maths: Unit Test Mock Paper Analysis | 七年级AQA数学：单元测试模拟卷解析

This article presents a full mock unit test for Year 7 AQA Mathematics and walks through each question step by step. The mock paper covers core Year 7 topics: number operations, fractions, decimals, algebra, geometry, measurement, statistics and probability. Every solution is explained with clear reasoning and tips to help you avoid common pitfalls.

本文提供一套完整的七年级AQA数学单元测试模拟卷，并逐步解析每一道题目。模拟卷涵盖七年级核心主题：数字运算、分数、小数、代数、几何、测量、统计和概率。每道题的解答都配有清晰的推理和技巧，帮助你避开常见错误。

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1. Number Operations and Word Problems | 数字运算与应用题

Question 1a Calculate 452 × 36.

问题1a 计算 452 × 36。

Break the multiplication into parts: multiply 452 by 30, then by 6, and add the results.

将乘法拆分：先算 452 × 30，再算 452 × 6，最后相加。

452 × 30 = 452 × 3 × 10 = 1356 × 10 = 13 560.

452 × 30 = 452 × 3 × 10 = 1356 × 10 = 13 560。

452 × 6 = 2712. Now add: 13 560 + 2712 = 16 272.

452 × 6 = 2712。相加得 13 560 + 2712 = 16 272。

Always check by estimation: 450 × 36 ≈ 16 200, so 16 272 is reasonable.

用估算检验：450 × 36 ≈ 16 200，因此 16 272 是合理的。

Question 1b Divide 1528 by 8.

问题1b 计算 1528 ÷ 8。

o make 72. 8 goes into 72 nine times exactly. Bring down 8, 8 goes into 8 once. The quotient is 191.

使用短除法。8 除 15 得 1 余 7；把 2 落下来组成 72，8 除 72 得 9 正好；把 8 落下来，8 除 8 得 1。商为 191。

So 1528 ÷ 8 = 191. Verify: 191 × 8 = 1528.

因此 1528 ÷ 8 = 191。检验：191 × 8 = 1528。

Question 1c A theatre has 354 seats. 128 seats are sold for a matinee, and then 215 seats are sold for the evening show. How many seats remain unsold in total across both shows?

问题1c 一家剧院有354个座位。下午场售出128张票，晚场售出215张票。两场总共还有多少座位未售出？

8 + 215 = 343. Then subtract from total seats: 354 − 343 = 11. Eleven seats remain unsold.

先求两场共售出的座位：128 + 215 = 343。再从总座位中减去：354 − 343 = 11。还有11个座位未售出。

Watch out for the wording – it asks for unsold seats overall, not per show.

注意审题——题目问的是总共未售出的座位数，而非单场。

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2. Fractions and Mixed Numbers | 分数与带分数

Question 2a Work out 2/3 + 1/6, giving your answer in its simplest form.

问题2a 计算 2/3 + 1/6，结果化为最简分数。

is 6. Write 2/3 as 4/6. Then add: 4/6 + 1/6 = 5/6. The answer is already in simplest form.

先找公分母。3 和 6 的最小公倍数是 6。将 2/3 化为 4/6。然后相加：4/6 + 1/6 = 5/6。答案已是最简形式。

If you get 3/9 by adding incorrectly, remember you must have the same denominator before adding numerators.

如果错误地得到 3/9，请记住：必须先通分再相加分子。

Question 2b Calculate 2 ½ × 4.

问题2b 计算 2 ½ × 4。

ultiply by 4: (5/2) × 4 = 20/2 = 10. You can also think: two and a half four times is ten.

将带分数化为假分数：2 ½ = 5/2。乘以 4：(5/2) × 4 = 20/2 = 10。也可以想：两个半的四倍是十。

If the answer is left as 20/2, always simplify to a whole number when possible.

如果答案写成 20/2，记得要化简成整数。

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3. Decimals and Percentages | 小数与百分数

Question 3a Write 0.65 as a fraction in its simplest form and as a percentage.

问题3a 将 0.65 写成最简分数和百分数。

iding numerator and denominator by 5: 65 ÷ 5 = 13, 100 ÷ 5 = 20, so the fraction is 13/20.

化为分数：0.65 = 65/100。分子分母除以 5 化简：65 ÷ 5 = 13，100 ÷ 5 = 20，得到 13/20。

As a percentage, multiply by 100: 0.65 × 100% = 65%.

化为百分数：乘以 100，0.65 × 100% = 65%。

Question 3b Which is larger: 0.7 or 3/4?

问题3b 哪个更大：0.7 还是 3/4？

nvert 3/4 to a decimal: 3 ÷ 4 = 0.75. Compare: 0.75 is greater than 0.7. So 3/4 is larger.

把 3/4 化成小数：3 ÷ 4 = 0.75。比较：0.75 大于 0.7，因此 3/4 更大。

Another method is to write 0.7 as 7/10 = 28/40 and 3/4 as 30/40, so 30/40 > 28/40.

另一种方法：0.7 写成 7/10 = 28/40，3/4 写成 30/40，因此 30/40 > 28/40。

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4. Algebraic Expressions | 代数表达式

Question 4 Simplify 5a − 3b + 2a + 7b − a.

问题4 化简 5a − 3b + 2a + 7b − a。

a: 5a + 2a − a = 6a. Terms with b: −3b + 7b = 4b. So the simplified expression is 6a + 4b.

合并同类项：含 a 的项：5a + 2a − a = 6a。含 b 的项：−3b + 7b = 4b。化简得 6a + 4b。

Remember that −a is the same as −1a. Always check that you have combined all like terms correctly.

记住 −a 相当于 −1a。务必检查是否正确地合并了所有同类项。

Extension If a = 3 and b = 2, evaluate the expression.

拓展 若 a = 3，b = 2，求表达式的值。

Substitute: 6(3) + 4(2) = 18 + 8 = 26.

代入：6(3) + 4(2) = 18 + 8 = 26。

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5. Solving One-Step Equations | 解一步方程

Question 5a Solve y + 7 = 15.

问题5a 解方程 y + 7 = 15。

To isolate y, subtract 7 from both sides: y + 7 − 7 = 15 − 7, so y = 8.

为了求出 y，两边同时减去 7：y + 7 − 7 = 15 − 7，得 y = 8。

Question 5b Solve x/4 = 5.

问题5b 解方程 x/4 = 5。

Multiply both sides by 4: (x/4) × 4 = 5 × 4, which gives x = 20.

两边同时乘以 4：(x/4) × 4 = 5 × 4，得 x = 20。

Use inverse operations: addition is undone by subtraction, division by multiplication.

运用逆运算：加法用减法还原，除法用乘法还原。

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6. Angles and Lines | 角与线

Question 6a Two angles are complementary. One angle is 37°. Find the other angle.

问题6a 两个角互为余角，其中一个角是 37°，求另一个角。

Complementary angles sum to 90°. So the missing angle = 90° − 37° = 53°.

互为余角即两角之和为 90°。因此未知角 = 90° − 37° = 53°。

Question 6b In a triangle, two of the angles are 48° and 62°. Find the third angle.

问题6b 三角形中两个角分别为 48° 和 62°，求第三个角。

°. Add the known angles: 48° + 62° = 110°. Then 180° − 110° = 70°. The third angle is 70°.

三角形内角和为 180°。已知角相加：48° + 62° = 110°。180° − 110° = 70°。第三个角是 70°。

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7. Perimeter and Area of Rectangles | 矩形周长与面积

Question 7 A rectangle has length 12 cm and width 7 cm. Calculate its perimeter and area.

问题7 矩形长 12 cm，宽 7 cm。求它的周长和面积。

s the distance around the shape: P = 2 × (length + width) = 2 × (12 + 7) = 2 × 19 = 38 cm.

周长是围绕图形的总长度：P = 2 × (长 + 宽) = 2 × (12 + 7) = 2 × 19 = 38 cm。

Area is the space inside: A = length × width = 12 × 7 = 84 cm².

面积是图形内部的大小：A = 长 × 宽 = 12 × 7 = 84 cm²。

Remember to include units and to use the square unit for area.

记得写上单位，面积使用平方单位。

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8. Statistics – Bar Chart and Mean | 统计——条形图与平均数

Question 8 The table shows the number of books read by a group of students last month.

问题8 表格显示了一组学生上个月阅读的书籍数量。

Books read (x)	Frequency (f)
0	2
1	5
2	4
3	3
4	1

Calculate the mean number of books read.

计算阅读书籍数量的平均数。

umn for f × x: 0×2=0, 1×5=5, 2×4=8, 3×3=9, 4×1=4. Total of f × x = 0 + 5 + 8 + 9 + 4 = 26.

首先添加 f × x 列：0×2=0，1×5=5，2×4=8，3×3=9，4×1=4。f × x 的总和为 0 + 5 + 8 + 9 + 4 = 26。

Total frequency Σf = 2 + 5 + 4 + 3 + 1 = 15.

总频数 Σf = 2 + 5 + 4 + 3 + 1 = 15。

Mean = Σ(f × x) / Σf = 26 / 15 ≈ 1.73 books

The mean number of books read is about 1.73.

平均阅读数量约为 1.73 本。

To draw a bar chart, label the horizontal axis with 'Books read' (0 to 4), and the vertical axis with 'Frequency'. Draw bars with heights equal to the frequencies. Make sure bars are of equal width and separated.

绘制条形图时，横轴标为“阅读本数”(0至4)，纵轴标为“频数”。按频数大小画出等宽且分开的条形。

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9. Introduction to Probability | 概率入门

Question 9 A bag contains 3 red sweets and 2 blue sweets. One sweet is taken at random. What is the probability it is red?

问题9 一个袋子里有 3 颗红色糖果和 2 颗蓝色糖果。随机取出一颗，取出红色糖果的概率是多少？

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