📚 Grade 7 Maths Test Answers | 七年级数学测试答案解析
This revision article works through a typical Grade 7 mathematics test paper and explains the answers step by step. It covers number, algebra, geometry, ratio, and statistics topics commonly assessed at this level.
本文是一篇七年级数学测试答案详解。我们按照常见试卷结构，逐一讲解数与式、代数、几何、比与比例、统计等题型的解题过程与最终答案。
Use the paper as a self-check: attempt each question first, then compare your working with the model answer.
使用时可以先独立作答，再对照答案和解析，找出错误步骤并进行订正。
1. Integers and Order of Operations | 整数与运算顺序
Question 1: Evaluate −5 + 8 × (−3) ÷ 2.
题 1：计算 −5 + 8 × (−3) ÷ 2。
Solution: Follow BIDMAS/BODMAS: multiplication and division before addition. 8 × (−3) = −24, then −24 ÷ 2 = −12. Finally −5 + (−12) = −17.
解析：按照先乘除后加减的顺序。8 × (−3) = −24，再 −24 ÷ 2 = −12，最后 −5 + (−12) = −17。
−5 + 8 × (−3) ÷ 2 = −17
Answer: −17
答案：−17
Question 2: Work out (−2)³ + (−4)².
题 2：计算 (−2)³ + (−4)²。
Solution: (−2)³ = −8 because a negative number raised to an odd power stays negative. (−4)² = 16 because a negative number squared is positive. Add: −8 + 16 = 8.
解析：(−2)³ = −8，因为负数奇次方仍为负；(−4)² = 16，因为负数平方为正。相加得 −8 + 16 = 8。
(−2)³ + (−4)² = 8
Answer: 8
答案：8
- Always complete multiplication and division from left to right before adding or subtracting.
- 计算时先按从左到右完成乘除，再算加减。
- A negative number raised to an even power gives a positive result; an odd power keeps the negative sign.
- 负数偶次方为正，奇次方仍为负。
2. Fractions, Decimals and Percentages | 分数、小数与百分比
Question 1: Convert 7/20 to a decimal and a percentage.
题 1：将 7/20 转换为小数和百分比。
Solution: Divide 7 by 20 to get 0.35. To convert to a percentage, multiply by 100: 0.35 × 100 = 35%.
解析：7 除以 20 得 0.35。转换为百分比时乘以 100：0.35 × 100 = 35%。
| Fraction 分数 | Decimal 小数 | Percentage 百分比 |
| 7/20 | 0.35 | 35% |
Question 2: Find 15% of 240.
题 2：求 240 的 15%。
Solution: Write 15% as 0.15, then multiply: 0.15 × 240 = 36.
解析：将 15% 写作 0.15，再计算 0.15 × 240 = 36。
15% of 240 = 36
Question 3: Work out 2 3/4 + 1 1/3.
题 3：计算 2 3/4 + 1 1/3。
Solution: Convert to improper fractions: 2 3/4 = 11/4 and 1 1/3 = 4/3. The lowest common denominator is 12: 11/4 = 33/12, 4/3 = 16/12. Add: 33/12 + 16/12 = 49/12 = 4 1/12.
解析：化为假分数：2 3/4 = 11/4，1 1/3 = 4/3。最小公分母为 12：11/4 = 33/12，4/3 = 16/12。相加得 33/12 + 16/12 = 49/12 = 4 1/12。
2 3/4 + 1 1/3 = 4 1/12
3. Ratio and Proportion | 比与比例
Question 1: Share $120 between A and B in the ratio 3 : 5.
题 1：按 3 : 5 的比例将 120 美元分给 A 和 B。
Solution: Total parts = 3 + 5 = 8. One part = 120 ÷ 8 = 15. A receives 3 × 15 = 45, and B receives 5 × 15 = 75.
解析：总份数 = 3 + 5 = 8。一份 = 120 ÷ 8 = 15。A 得 3 × 15 = 45，B 得 5 × 15 = 75。
A = 45, B = 75
Question 2: A recipe uses flour and sugar in the ratio 4 : 1. If 600 g of flour is used, how much sugar is needed?
题 2：一个配方中面粉与糖的比例为 4 : 1。如果用了 600 g 面粉，需要多少糖？
Solution: The ratio 4 : 1 means flour is 4 parts and sugar is 1 part. One part = 600 ÷ 4 = 150 g. Therefore sugar = 1 × 150 = 150 g.
解析：4 : 1 表示面粉为 4 份，糖为 1 份。一份 = 600 ÷ 4 = 150 g。因此糖 = 1 × 150 = 150 g。
Answer: 150 g
答案：150 g
4. Algebraic Expressions | 代数式
Question 1: Simplify 3a + 5b − 2a + 7b.
题 1：化简 3a + 5b − 2a + 7b。
Solution: Collect like terms: 3a − 2a = a and 5b + 7b = 12b. The simplified expression is a + 12b.
解析：合并同类项：3a − 2a = a，5b + 7b = 12b。化简结果为 a + 12b。
3a + 5b − 2a + 7b = a + 12b
Question 2: Expand 4(2x − 3).
题 2：展开 4(2x − 3)。
Solution: Multiply each term inside the bracket by 4: 4 × 2x = 8x and 4 × (−3) = −12. The result is 8x − 12.
解析：将括号内每一项都乘以 4：4 × 2x = 8x，4 × (−3) = −12。结果为 8x − 12。
Question 3: Factorise 6x + 9.
题 3：因式分解 6x + 9。
Solution: The highest common factor of 6x and 9 is 3. Write 6x + 9 = 3(2x + 3).
解析：6x 和 9 的最大公因数是 3。因此 6x + 9 = 3(2x + 3)。
Question 4: Substitute x = −2 into 2x² − 4x.
题 4：将 x = −2 代入 2x² − 4x。
Solution: Replace x with −2: 2(−2)² − 4(−2). Since (−2)² = 4, this becomes 2 × 4 + 8 = 8 + 8 = 16.
解析：用 −2 替换 x：2(−2)² − 4(−2)。因为 (−2)² = 4，所以原式 = 2 × 4 + 8 = 8 + 8 = 16。
2(−2)² − 4(−2) = 16
5. Solving Linear Equations | 解一元一次方程
Question 1: Solve 5x − 7 = 18.
题 1：解方程 5x − 7 = 18。
Solution: Add 7 to both sides: 5x = 25. Then divide both sides by 5: x = 5.
解析：两边同时加 7：5x = 25。然后两边同时除以 5：x = 5。
5x − 7 = 18 → x = 5
Question 2: Solve 2(x + 3) = x − 4.
题 2：解方程 2(x + 3) = x − 4。
Solution: Expand the left side: 2x + 6 = x − 4. Subtract x from both sides: x + 6 = −4. Subtract 6: x = −10.
解析：展开左边：2x + 6 = x − 4。两边同时减 x：x + 6 = −4。再减 6：x = −10。
2(x + 3) = x − 4 → x = −10
Question 3: Solve x/4 + 3 = 7.
题 3：解方程 x/4 + 3 = 7。
Solution: Subtract 3 from both sides: x/4 = 4. Multiply both sides by 4: x = 16.
解析：两边同时减 3：x/4 = 4。两边同时乘以 4：x = 16。
6. Inequalities | 不等式
Question 1: Solve 3x − 5 ≤ 10.
题 1：解不等式 3x − 5 ≤ 10。
Solution: Add 5 to both sides: 3x ≤ 15. Divide both sides by 3: x ≤ 5. The solution is all real numbers less than or equal to 5.
解析：两边同时加 5：3x ≤ 15。两边同时除以 3：x ≤ 5。解集为所有小于或等于 5 的实数。
3x − 5 ≤ 10 → x ≤ 5
Question 2: Solve −2x + 4 > 10.
题 2：解不等式 −2x + 4 > 10。
Solution: Subtract 4 from both sides: −2x > 6. Divide both sides by −2 and reverse the inequality sign: x < −3.
解析：两边同时减 4：−2x > 6。两边同时除以 −2，不等号方向要改变：x < −3。
Key rule: When you multiply or divide an inequality by a negative number, you must reverse the direction of the inequality sign.
关键规则：当不等式两边同时乘以或除以一个负数时，必须改变不等号的方向。
7. Angles and Lines | 角与直线
Question 1: Two angles lie on a straight line. One angle is 72°. Find the other angle.
题 1：两个角在一条直线上，其中一个角为 72°。求另一个角。
Solution: Angles on a straight line add up to 180°. So the missing angle is 180° − 72° = 108°.
解析：直线上的相邻角之和为 180°。因此另一个角为 180° − 72° = 108°。
180° − 72° = 108°
Question 2: A triangle has angles of 45° and 60°. Find the third angle.
题 2：一个三角形有两个角分别为 45° 和 60°。求第三个角。
Solution: The three angles of a triangle add up to 180°. Third angle = 180° − 45° − 60° = 75°.
解析：三角形内角和为 180°。第三个角 = 180°
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