AS Mathematics: Calculation Practice Drill | AS 数学：计算题专项训练

📚 AS Mathematics: Calculation Practice Drill | AS 数学：计算题专项训练

Calculation forms the backbone of AS Mathematics, from algebraic manipulation to calculus and applied topics. This drill focuses on essential computational techniques that appear regularly in exam papers. Mastering these methods will not only improve your accuracy but also build the speed required under timed conditions.

计算是AS数学的支柱，从代数运算到微积分和应用专题。本专项训练聚焦于考试中频繁出现的基本计算技巧。掌握这些方法不仅能提高准确性，还能培养在限定时间内解题所需的速度。

1. Expanding and Factorising Algebraic Expressions | 代数表达式的展开与因式分解

Beginner mistakes often arise when expanding brackets, especially with negative signs. Always apply the distributive law systematically: a(b + c) = ab + ac. For factorising, look for common factors first, then recognise patterns like difference of squares a² – b² = (a – b)(a + b).

初学者在去括号时常常因负号而出错。务必系统运用分配律：a(b + c) = ab + ac。因式分解时，先寻找公因子，再识别平方差公式 a² – b² = (a – b)(a + b) 等模式。

Example: Expand and simplify (2x – 3)(x + 5). Multiply each term: 2x×x = 2x², 2x×5 = 10x, –3×x = –3x, –3×5 = –15. Combine like terms: 2x² + 7x – 15. Practice similar problems to avoid sign errors.

例题：展开并化简 (2x – 3)(x + 5)。逐项相乘：2x×x = 2x²，2x×5 = 10x，–3×x = –3x，–3×5 = –15。合并同类项得 2x² + 7x – 15。练习类似题目以避免符号错误。

2. Solving Quadratic Equations | 求解二次方程

Quadratics can be solved by factorising, completing the square, or using the quadratic formula. The formula x = [–b ± √(b² – 4ac)] / (2a) works for any quadratic ax² + bx + c = 0. Always check the discriminant Δ = b² – 4ac first to determine the nature of roots.

二次方程可通过因式分解、配方法或求根公式求解。求根公式 x = [–b ± √(b² – 4ac)] / (2a) 适用于任何二次方程 ax² + bx + c = 0。务必先计算判别式 Δ = b² – 4ac 以判断根的性质。

When factorising, find two numbers that multiply to ac and add to b. For x² + 5x + 6, the numbers are 2 and 3, giving (x + 2)(x + 3) = 0, so x = –2 or –3. If the quadratic is not monic, use grouping or the cross method.

因式分解时，寻找两个数使其乘积为 ac 且和为 b。对于 x² + 5x + 6，这两个数是 2 和 3，得到 (x + 2)(x + 3) = 0，因此 x = –2 或 –3。若二次项系数不为1，可用分组法或十字相乘法。

Example using formula: Solve 2x² – 4x – 1 = 0. Here a=2, b=–4, c=–1. Discriminant = (–4)² – 4×2×(–1) = 16 + 8 = 24. So x = [4 ± √24] / 4 = [4

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