📚 Review Set 4A: Non-Calculator Focus for IB Maths | IB 数学复习题集 4A：无计算器题型精讲
Mastering non-calculator problems is essential for the IB Mathematics examinations, where Paper 1 sections demand exact answers, algebraic fluency, and deep conceptual understanding. Review Set 4A is designed to strengthen these skills across topics such as surds, exponentials, trigonometry, calculus, vectors, and complex numbers. This article walks you through the key question types and strategies to succeed without relying on a calculator.
掌握无需计算器的解题能力是 IB 数学考试的关键，因为试卷一部分要求精确答案、代数熟练度和深刻的概念理解。复习题集 4A 旨在巩固您在根式、指数对数、三角学、微积分、向量和复数等领域的技能。本文将带您梳理主要的题型与策略，助您在无计算器条件下成功解题。
1. Surds and Rationalization | 根式化简与有理化
c;72 = √(36×2) = 6√2, and 1/(√5 - 2) rationalizes to √5 + 2.
典型的无计算器题目要求化简 √72 或将 5/√3 有理化分母。记住 √(a×b) = √a × √b，对二项式分母乘以共轭根式。例如，√72 = √(36×2) = 6√2，而 1/(√5 - 2) 有理化后为 √5 + 2。
2; to get 3+2√6+2 = 5+2√6. Always express final answers in simplest surd form.
进一步练习包括嵌套根式以及化简类似 (√3+√2)² 的表达式。利用 (a+b)² 展开得 3+2√6+2 = 5+2√6。最终答案务必写成最简根式形式。
2. Exponents and Logarithms | 指数与对数
problems frequently test the laws: a&supm; × a&supn; = a&supm;+&supn; and logₐ(xy) = logₐx + logₐy. You may need to solve 2&# 32 by writing 32 as 2&sup5;, so x=5. For log equations, rewrite in exponential form: log₂(x+1)=3 ⇒ x+1=2³=8 ⇒ x=7.
无计算器题目频繁测试指数律与对数律：a&supm; × a&supn; = a&supm;+&supn; 以及 logₐ(xy) = logₐx + logₐy。解法如 2ˣ = 32，将 32 写为 2&sup5;，得 x=5。对数方程则改写为指数形式：log₂(x+1)=3 ⇒ x+1=2³=8 ⇒ x=7。
Change-of-base and natural logarithms also appear. For instance, evaluate log₄8 without a calculator: since 4¹=4, 4²=16, we need 4ˣ=8 ⇒ x=1.5 because 43/2 = (√4)³ = 2³ = 8. So log₄8 = 3/2.
换底公式和自然对数也会出现。例如，无计算器求 log₄8：因为 4¹=4, 4²=16，需要 4ˣ=8 ⇒ x=1.5，即 43/2 = (√4)³ = 2³ = 8。因此 log₄8 = 3/2。
3. Exact Trigonometric Values | 精确三角函数值
ing θ = π/3, 2π/3. Use the unit circle and CAST diagram to find all solutions.
必须熟记 0°、30°、45°、60°、90° 的正弦、余弦、正切值及其弧度对应值。复习题集 4A 常要求解 sinθ = √3/2 在 0≤θ≤2π 内的解，得 θ=π/3, 2π/3。借助单位圆与 CAST 图求全部解。
heta; and sin²θ+cos²θ=1 are crucial. For example, if cosθ = -1
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