This note might not cover everything.
（有些很简单的我就没记，最好考前看一眼syllabus: here
Number
数
Real Numbers(ℝ):实数
Integers(Whole Numbers)(ℤ):整数
Natural numbers(ℕ):自然数(不包括0？查一下syllabus)
正整数(N+)(N*)
Rational Numbers(Q):有理数
A factor: 因数
A multiple:倍数
index/order/exponents:指数
reciprocal:倒数
quotient:商
Approximately equal to:约等于
identical to:全等于
bracket:括号
竖式
乘法
除法
集合
{(x, y) : y = 2x + 1}
E:universal set
∅:empty set
n(∅) = 0
upper case: set , lower case: element
a ∈ A means a is an element of A
A ⊆ B means A is a subset of B
A ⊂ B means A is a proper subset of B (A≠B)
A∩B intersection
A∪B union
A' not A
质因数 (与最大公因数最小公倍数)
Prime tree
prime factor decomposition (PFD)
indices are even: square number
indices are multiples of 3: cube number
the highest common factor (HCF)最大公因数
the lowest common multiple (LCM)最小公倍数
指数运算&科学表达式
base number: 底数
index: 指数
square root:平方根
cube root:立方根
A nth root
standard form: 科学表达式
分数
numerator: 分子
denominator: 分母
mixed numbers: 带分数
improper fraction(top heavy fraction): 假分数
比例
A multiplier, p, is the decimal equivalent of a percentage increase or decrease
利息
simple interest: 单利
compound interest: 复利
depreciation: 约等于复利
substitute: 代入
decay: 下降
FDP
terminating decimal: 有限小数
recurring decimal: 无限循环小数
错位相减
Ratio
direct proportion: 正比
inverse proportion: 反比
Compound Measures
没啥好说的
时间 货币 转换
millennium: 千年
midday: 12pm
midnight: 12am
am/pm : 12 1 2 3 4 5 6 7 8 9 10 11
Each column represents a different bus/train – these are often called “services”
The time in each cell usually indicate departure times(when the bus/train leaves that stop/station)
The last location on the list usually shows the arrival time
GBP: 英镑£
汇率类问题单独开一行写A货币比B货币等于几比几，下面一行写x:几几几。再用除法算出scale factor
钱要保留两位小数！！！！
近似 估计 边界
estimate: 一般一个sf
LB <= x < UB
计算：x+-一半精度
计算器
负数：(-)
rounding 不必在计算中进行，用3.1415...省略号表示
Algebra & Graphs
基础
term: 单项式
coefficient: 系数
constants: 常数
expression: 表达式
equation: 方程/等式
formula: 公式(F=ma)
inequality: 不等式
substitution: 代入
v=u+at
v2-u2=2as
s=ut+0.5at2
"like" terms: 同类项
ax=ay
x=y
指数根号
展开括号，因式分解
expanding: 展开
factorisation: 因式分解
quadratic expression: 二次表达式
monic quadratic expression: a=1
non-monic : a!=1
十字相乘
discriminant: 判别式(b2-4ac)
线性方程，不等式
二次方程
completing the square: a(x+p)2+q
quadratic formula: 二次方程求根公式
repeated root: 两个相同的根
重整式子
(rearrange formulae)
(changing the subject)
联立方程
linear simultaneous equations: 线性方程组
Elimination: 加减消元
substitution: 代入
分式
分式: Algebraic Fractions
列方程解方程
5 lots of something: 5x
polygon: 多边形
parallelogram: 平行四边形
rhombus: 菱形
prisms: 柱体
pyramids: 锥体
regular polygon: 正多边形
interpret: 解释
函数
Composite(compound) functions: 复合函数
Inverse Functions: 反函数
数列
Sequences: 数列
term: 项
position: 索引(ish?)
position-to-term rule: 通项公式
term-to-term rule: 由an前面的项得到an
linear(arithmetic)/quadratic(二次序列)/geometric(等比序列) sequences
cubic sequence: the third differences are constant
common ratio: 公比
common difference: 公差
a fibonacci sequence: 泛指an=a(n-1)+a(n-2)的序列，可以改变前两项
the fibonacci sequence: 前两项为1
求quadratic sequence的a: the second difference 除以二
剩下的用原数列减an2,得到一个等差数列
坐标系
steep: 陡峭的
求斜率：rise over run
Pythagoras’ Theorem: 勾股定理
线型图象
ax+by+c=0 -> 斜率: -a/b 截距: -c/b
parallel: 平行(相同的直线不是平行)
the negative reciprocal: 倒数取反
二次图像
parabola: 抛物线
更多图像和切线
解不等式
有等号的用实线，否则用虚线
要shade unwanted的area
生活中的图像
conversion/convert: 转换
deceleration: 减速
微分
the derivative: 导数
the derived function: 导函数
f'(x) -> f-dashed-of-x
Turning points/stationary points: 导数为0的点
peak/trough: 峰/谷
positive cubic: 左边最大值，右边最小值
negative cubic: 左边最小值，右边最大值
d2y/dx2
optimisation/optimal: 优化
Geometry
基本
symmetry: 对称
the order of rotational symmetry: 转一圈有几次和自己一样
(有的时候order是1也会说成没有rotational symmetry)
n lines of symmetry(有n条对称轴)
mirror line
polygon: 多边形
cuboid: 长方体
cylinder: 圆柱
- triangle
- quadrilateral
- pentagon
- hexagon
- heptagon
- octagon
- nonagon
- decagon
cube: 9 planes of symmetry
一般来说，柱体的planes of symmetry是横截面的对称轴数量加1
而锥体的是横截面对称轴数量
equilateral triangle: 等边三角形
isosceles triangle: 等腰三角形
parallelograms: 平行四边形
rhombuses(rhombi): 菱形
trapezium: 梯形（一对边平行）
kite: 两组邻边相等的四边形
bisect: 平分
obtuse angle: 钝角
acute angle: 锐角
dagonal: 对角线
perimeter: 周长
circumference: 圆的周长
prism: 柱体
pyramid: 锥体
square-based pyramid
cone: circular base
tetrahedron: base is an equilateral triangle
face/vertex(vertices)/edge
net: 展开图
1cl = 10 ml
1 hectare (ha) = 10 000 m2
多边形和平行线里的角
basic angle properties:
- Angles that meet at a point add up to 360°
- Angles that meet at a point on a straight line add up to 180°
- Vertically opposite angles are equal(对顶角相等)
regular polygon: 正多边形
sum of interior angles = 180° × (n-2)
外角(exterior angle)和永远为360°
Corresponding angles are equal(同位角相等)
Alternate angles are equal(内错角相等)
Allied (co-interior) angles add to 180°(同旁内角互补)
(on parallel lines)
transverse: 跨过两个平行线的直线
bearings constructions & scale drawings
bearing: 从北方开始顺时针测量，保留三位有效数字，不写degree symbol
(画图记得画north line)
面积用A(Area)
圆
所有的circle theorem在考试中都要写出来
Circle Theorem: The angle subtended by an arc at the centre is twice the angle at the circumference(这个定理必须写出来)
Circle Theorem: The angle in a semicircle is a right angle(俺也一样)
chord(弦)
Any equal chords are equidistant from the centre of the circle
Circle Theorem: The perpendicular bisector of a chord is a radius
Circle Theorem: A radius and a tangent meet at right angles
Two tangents from a circle to the same point outside of a circle are equal
cyclic quadrilaterals(圆内接四边形)
Circle theorem: Opposite angles in a cyclic quadrilateral add up to 180°
Circle Theorem: Angles at the circumference subtended by the same arc are equal(Angles in the same segment are equal)
Circle Theorem: Alternate Segment Theorem(弦切角定理)
面积和周长
compound shapes: 由多个简单图形拼接出来的图形
rectangle: A=lw
triangle: A=1/2 bh
trapezium: A=1/2 (a+b)h
parallelogram: A=bh
圆和扇形和弧
arc:弧
minor arc(劣弧)
major arc(优弧)
sector: 扇形
minor sector
major sector
体积和表面积
volume: 体积
volume of a pyramid: 三分之一底乘高
圆的体积：4/3 πr3
frustum: 圆台
surface area: 表面积
slant height: 斜高
surface area of a sphere = 4πr2
全等和相似(congruence & similarity)
congruent/congruence: 全等
SAS,ASA,AAS,SSS,RHS
similar: 相似
证明任意多边形相似：对应边成比例
三角形：AAA
Equivalent: 对应的
直角三角形
Pythagoras’ Theorem: 勾股定理
hypotenuse: 斜边
opposite: 对边
Adjacent: 邻边
Trigonometry: 三角学
sin: 奇函数
cos: 偶函数
the angles of elevation and depression
sine, cosine rule & 三角形面积
the sine rule: a/sinA = b/sinB = c/sinC
the cosine rule: cosA = (b2+c2-a2) / 2bc
or a2=b2+c2 - 2bc cosA
A = 1/2 ab sinC
表示角的方法: ABC上面加一个^
三维三角函数
d2=a2+b2+c2
三角函数图像和方程
先label出关键点，再连接成线
向量
magnitude direction
translation vector
scalar: 标量
magnitude(modulus): |a|
specific vector: AB->
general vector: a
证明三点共线：找出两个向量平行
变化
original shape: object(A,B,C)
transformed shape: image(A',B',C')
translation
Shape A has been translated using the vector (一个向量)
reflection
Shape A has been reflected in the line x=-1 to create shape B
rotation
Rotation, 90o clockwise with centre (-4, 0)
enlargement
The length scale factor is 2, therefore the area scale factor will be 2^2 = 4, hence, the area of C' is 4 times larger than C
Shape A has been enlarged using a scale factor of 3 and a centre of enlargement (9, 9) to create shape B
C.o.E
objection
Probability & Statistics
基础
An experiment is a repeatable activity that has a result that can be observed or recorded
Trials are what we call the repeats of the experiment
An outcome is a possible result of a trial
An event is an outcome or a collection of outcomes
A sample space is the set of all possible outcomes of an experiment
The probability of event A is denoted as P(A)
The complement of event A is the event where event A does not happen
A'
mutually exclusive events: 发生了A就不可能发生B，A交B为空集
sample space: 所有可能的结果
possibility diagram: combining two things using a grid
Relative frequency(estimate probabilities from experimental data)
expected frequency(the number of times you would expect a particular outcome to occur when repeating a trial numerous times)
概率图像
Two Way Tables
The row/column totals are sometimes called marginal (or sub-) totals
Where the row totals and column totals meet, we have the grand total
Conditional probabilities are sometimes written using the 'straight bar' notation P(A|B)
Venn Diagrams
Tree Diagrams
conditional probability
平均和极差
统计图像
Histogram(直方图)
cumulative frequency & box plots
Correlation is a way of describing the way two quantities are related to each other
positive/negative/no coorelation
correlation doesn't mean causation
scatter graphs & correlation
Some own experience
记得带量角器
多于一分记得写过程
show all your working: 每一步都要写(假分数变带分数的过程也要)
degree 保留一个小数位
有一些题目不需要3sf，直接写出答案
圆切角定理！！！
Arno buys a student ticket for $43.68 .
This is a saving of 16% on the full price of a ticket.
Calculate the full price of a ticket.
43.68是减去16%后的价格，并不是那16%
看清题目要求increase还是自己
Reference: savemyexams