ENGAA 2022 Section 1 Mathematics Answer Key and Analysis | ENGAA 2022 第一部分数学答案解析

📚 ENGAA 2022 Section 1 Mathematics Answer Key and Analysis | ENGAA 2022 第一部分数学答案解析

The ENGAA 2022 Section 1 mathematics questions assess a broad range of A-level and Further Mathematics topics, including algebra, calculus, trigonometry, complex numbers, vectors, and hyperbolic functions. This answer key provides the correct choices and detailed reasoning for each question, helping you identify common pitfalls and master advanced problem‑solving techniques.

ENGAA 2022 第一部分数学试题涵盖了广泛的 A‑level 及进阶数学主题，包括代数、微积分、三角学、复数、向量和双曲函数等。本答案解析给出每道题的正确答案并详解，帮助你识别常见误区，掌握高阶解题技巧。

1. Questions 1–3: Algebraic Techniques | 题1–3：代数技巧

Question 1 involved simplifying a complex rational expression. By factorising denominators such as x² – 1 = (x – 1)(x + 1) and finding a common denominator, the expression collapsed into a much simpler form. Careful cancellation led to option D.

第1题要求化简复杂的有理式。通过将分母 x² – 1 等因式分解为 (x – 1)(x + 1) 并通分，表达式简化为极其简单的形式。仔细约分后得到选项 D。

Question 2 tested the ability to solve an exponential equation of the type a · b^cx+d = k. Taking logarithms (or expressing both sides as powers of the same base) yielded a simple linear equation whose solution matched option C.

第2题考查解形如 a · b^cx+d = k 的指数方程。通过取对数（或写成同底数的幂）得到一个简单的一次方程，其解对应于选项 C。

Question 3 focused on the discriminant of a quadratic equation. For distinct real roots, the condition Δ = b² – 4ac > 0 was applied. Solving the resulting inequality gave the interval in option B.

第3题关注二次方程的判别式。对于两个相异实根，使用条件 Δ = b² – 4ac > 0，解所得不等式得到选项 B 中的区间。

2. Questions 4–6: Graphs and Coordinate Geometry | 题4–6：图形与坐标几何

Question 4 asked for the equation of a circle given its centre (h, k) and a point on the circumference. The radius r was found using r² = (x – h)² + (y – k)². Substituting gave the equation matching option A.

第4题要求已知圆心 (h, k) 及圆周上一点求圆的方程。利用 r² = (x – h)² + (y – k)² 算出半径，代入后得到与选项 A 吻合的方程。

Question 5 dealt with parametric equations x = f(t), y = g(t) and required the gradient of the tangent at a specific t. Using dy/dx = (dy/dt)/(dx/dt) and evaluating the derivatives yielded the slope in option D.

第5题

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