📚 IGCSE Maths G-3 Workbook Practice Collection | IGCSE 数学 G-3 练习册内容合集
This G-3 workbook collection brings together the key mixed-practice tasks found in IGCSE Mathematics papers. Use it as a self-test bank for number, algebra, geometry, trigonometry and statistics.
本 G-3 练习册合集汇集了 IGCSE 数学考试中最常见的混合练习题。可将其作为数字、代数、几何、三角和统计的自测题库。
1. Number Skills | 数字技能
orm and rounding. A common G-3 task is to simplify a calculation such as 3 − (−4) + 6 × 2.
数字技能练习通常考查有向数、幂、根、标准形式和四舍五入。常见的 G-3 任务是化简如 3 − (−4) + 6 × 2 的计算。
a⁰ = 1, a⁻ⁿ = 1 / aⁿ, √a² = |a|
Remember that multiplication and division are carried out before addition and subtraction unless brackets say otherwise.
请记住，除非括号另有说明，乘法和除法优先于加法和减法。
672 in standard form as 6.72 × 10⁻⁴ and round 38.476 to three significant figures as 38.5.
将 0.000672 写成标准形式为 6.72 × 10⁻⁴，将 38.476 舍入到三位有效数字为 38.5。
2. Fractions, Decimals and Percentages | 分数、小数与百分数
Fractions, decimals and percentages are linked in many G-3 questions. You should be able to convert 3/8 to 0.375 and 0.625 to 5/8 quickly.
分数、小数和百分数在 G-3 题目中相互关联。你应能将 3/8 转换为 0.375，将 0.625 快速转换为 5/8。
Percentage change = (new − original) ÷ original × 100%
Repeated percentage change is best handled by decimal multipliers. A 5% increase uses × 1.05 and a 12% decrease uses × 0.88.
重复百分比变化最好用小数乘数处理。增长 5% 使用 × 1.05，下降 12% 使用 × 0.88。
When ordering a mix of fractions, decimals and percentages, convert all values to the same form first.
在对分数、小数和百分数混合排序时，先将所有值转换为同一种形式。
3. Ratio, Proportion and Rates | 比、比例与速率
Ratio questions often ask you to share a quantity in a given ratio or combine two separate ratios. For example, share £240 in the ratio 3 : 5.
比的问题常要求按给定比例分配数量或合并两个独立的比。例如，按 3 : 5 分配 240 英镑。
A : B = 2 : 3 and B : C = 5 : 7 → A : B : C = 10 : 15 : 21
Compound rates such as speed, density and pressure link different units. Always check whether units need converting before substituting into a formula.
速度、密度和压强等复合速率将不同单位联系起来。代入公式前务必检查是否需要转换单位。
Average speed = distance ÷ time
Density = mass ÷ volume
Pressure = force ÷ area
4. Algebraic Manipulation | 代数运算
This section covers expanding brackets, factorising, simplifying algebraic fractions and substituting values into expressions. A typical task is to expand 3x(2x − 5).
本节涵盖去括号、因式分解、化简代数分式和代入数值。典型任务是展开 3x(2x − 5)。
(a + b)(a − b) = a² − b²； (a ± b)² = a² ± 2ab + b²
When expanding two brackets, multiply every term in the first bracket by every term in the second bracket. Then collect like terms.
展开两个括号时，将第一个括号中的每一项分别乘以第二个括号中的每一项。然后合并同类项。
factor is often tested before quadratic factorising, such as x² + 5x + 6 = (x + 2)(x + 3).
在二次因式分解之前，常考提取最高公因式，例如 x² + 5x + 6 = (x + 2)(x + 3)。
5. Linear Equations and Inequalities | 线性方程与不等式
Workbook tasks typically ask you to solve two-step or three-step equations and represent inequalities on a number line. Unknowns may appear on both sides.
练习册任务通常要求解两步或三步方程，并在数轴上表示不等式。未知数可能出现在等号两侧。
2x − 3 = 7 → x = 5； −2x ≤ 6 → x ≥ −3
When multiplying or dividing
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