A-Level考试中，微积分和三角函数占有很大比重，如何在这两个部分拿高分需要下一些功夫，下面是重庆新航道A-Level教研组老师给大家解析的P2考点收录，请大家参考。
P2是P1的加深和拓展，微积分和三角函数的部分内容在P1已经学过。其中圆的方程和二项展开式是比较新的内容，需要同学们掌握重点方法和公式。希望通过知识点总结能让同学们事半功倍。
P2考点总结
1.ALGEBRAIC METHODS
(1)分式的约分和通分
因式分解的方法是关键，着重训练提公因式和“十字相乘”法
(2)长除法求余数或证明整除
(3)The factor theorem
The factor theorem states that if f(x) is a
polynomial then:
If f(p) = 0, then (x - p) is a factor of f(x).
If (x - p) is a factor of f(x), then f(p) = 0.
if f(a/b) = 0, then(ax - b) is a factor of f(x).
lf (ax - b) is a factor of f(x) then f(a/b) = 0.
You can use the factor theorem to quickly factorise a cubic function, g(x):
a.Substitute values into the function until you find a value p such that g(p) = 0.
b.Divide the function by (x-p),-----------The remainder will be 0 because(x-p)is a factor of g(x).
c.Write g(x)=(x-p)(ax²+bx+c),-----------The other factor will be quadratic.
d.Factorise the quadratic factor, if possible, to write g(x) as a product of three linear factors.
利用多项式的已知因式可以判断多项式为零的情况。反之，也可以利用令多项式为零的数值快速判断多项式其中的一个因式，再利用长除法分解高次 (三次及以上) 多项式。
(4)Theremainder theorem
You can fnd the remainder when a polynomial is divided by (ax±b) by using the remainder theorem.
lf a polynomial f(x) is divided by (ax - b) then the remainder is f(a/b).
同因式定理，可利用代值快速求余数。
(5)Mathematicalproof
State any information or assumptions you are using
Show every step of your proof clearly
Make sure that every step follows logically from the previous step
Make sure you have covered all possible cases
Write a statement of proof at the end of your working
证明的步骤要写详细，通常是多项式乘法，斜率计算，根的判别的证明。
2.Chapter 2 COORDINATE GEOMETRY
(1) Midpointsandperpendicular bisectors
中点坐标公式是用两点坐标的和除以2即可.
The perpendicular bisector of a line segment A B is the straight line that is perpendicular to A B and passes through the midpoint of AB.
If the gradient of A B is m then the gradient of its perpendicular bisector, 1, will be -1/m.
垂直平分线需要借助线段中点坐标和线段斜率的负倒数综合来求。
(2)Equation ofa circle
圆的标准方程需要圆心坐标和半径大小两个条件。
圆的一般方程化成标准方程，需要熟练使用二次式的配方法。
(3)lntersections ofstraightlines and circles
直线和圆的交点个数和直线与圆的联立方程解的个数保持一致。
(4)Use tangentand chord properties
圆的切线和过切点的半径相互垂直，斜率互为负倒数弦的垂直平分线一定过圆心。
(5)Circlesandtriangles
直径所对的圆周角是直角。
3.CHAPTER 3 EXPONENTIALS AND LOGARITHMS
(1)要掌握对数运算的方法，前提是熟练掌握指数运算，并且能够对二者进行转化，
转化方法:
(2)对数运算法则
(3)对数运算性质
(4)解对数方程要注意检验求出的根是否满足原方程有意义
(5)指对函数基本图像
4.CHAPTER 4 THE BINOMIAL EXPANSION
以上就是关于A-Level微积分考试重点讲解，更多alevel考试培训学习请在线咨询重庆新航道学校官网。
