数学IG先行课程大纲
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数学IG先行课程大纲 课程目标 1. 掌握Alevel阶段（包括IGSCE）必备数学词汇； 2. 学习纯数、统计板块基础知识，培养外方数学课程学习的基本逻辑。 3. 衔接IG，Pre-IB，Pre-AP三大数学体系 4. 培养孩子对纯数和统计兴趣 第一节课 linear equation, linear programming and functions Find the gradient of a straight line. Calculate the gradient of a straight line from the co‑ordinates of two points on it. Calculate the length and the co-ordinates of the midpoint of a straight line from the co‑ordinates of its end points. Interpret and obtain the equation of a straight line graph in the form y= mx+ c, and y-y0= m(x-x0). Determine the equation of a straight line parallel or perpendicular to a given lines. Represent inequalities graphically and use this representation in the solution of simple linear programming problems. Use function notation to describe simple functions. Find inverse functions. Explain in words why a given function is a function or why it does not have an inverse. Use sketch graphs to show the relationship between a function and its inverse Form composite functions. 第二节课 indices, exponential function and logarithm Use and interpret positive, negative and zero indices. Use and interpret fractional indices. Use the rules of indices. Use given data to solve problems on personal and small business finance involving earnings, simple interest and compound interest. Use exponential growth and decay in relation to population and finance. Know and use the laws of logarithms (including change of base of logarithms) Solve equations of the form ax = b Know simple properties and graphs of the logarithmic and exponential functions including ln x and ex and graphs of kenx + a and kln(ax+b) where n, k, a and b are integers 第三节课 trigonometry I Interpret and use three-figure bearings. Apply Pythagoras’ theorem and the sine, cosine and tangent ratios for acute angles to the calculation of a side or of an angle of a right-angled triangle. Solve trigonometrical problems in two dimensions involving angles of elevation and depression. Solve problems using the sine and cosine rules for any triangle and the formula area of triangle = 1/2 ab sin C. Solve simple trigonometrical problems in three dimensions including angle between a line and a plane. 第四节课 trigonometry II Extend sine and cosine values to angles between 90° and 180°. Understand amplitude and periodicity and the relationship between graphs of e.g. sin x and sin 2x Draw and use the graphs of y = a sin (bx ) + c y = a cos (bx ) + c y = a tan (bx ) + c where a and b are positive integers and c is an integer Use the relationships and solve simple trigonometric equations involving the six trigonometric functions and the above relationships. Prove simple trigonometric identities. 第五节课 sequence Recognise arithmetic and geometric progressions. Continue a given number sequence, including linear sequences, quadratic and cubic sequences, exponential sequences and simple combinations of these. Use the formulae for the n th term and for the sum of the first n terms to solve problems involving arithmetic or geometric progressions. Fine the n th term of quadratic and cubic sequences. Use the condition for the convergence of a geometric progression, and the formula for the sum to infinity of a convergent geometric progression. Recognise patterns in sequences and relationships between different sequences. 第六节课 vector Describe a translation by using a vector represented by Add and subtract vectors. Multiply a vector by a scalar. Reflect simple plane figures. Rotate simple plane figures through multiples of 90°. Construct given translations and enlargements of simple plane figures. Recognise and describe reflections, rotations, translations and enlargements. Calculate the magnitude of a vector. Represent vectors by directed line segments. Use the sum and difference of two vectors to express given vectors in terms of two coplanar vectors. Know and use position vectors and unit vectors. Compose and resolve velocities. Use relative velocity, including solving problems on interception (but not closest approach). 第七节课 matrix Display information in the form of a matrix of any order. Calculate the sum and product (where appropriate) of two matrices. Calculate the product of a matrix and a scalar quantity. Use the algebra of 2×2 matrices including the zero and identity 2×2 matrices. Calculate the determinant |A| and inverse A–1 of a non‑singular matrix A. Use the following transformations of the plane: reflection (M), rotation (R), translation (T), enlargement (E), and their combinations. Identify and give precise descriptions of transformations connecting given figures. 第八节课 set and probability Use language, notation and Venn diagrams to describe sets and represent relationships between sets. Calculate the probability of a single event as either a fraction, decimal or percentage. Understand and use the probability scale from 0 to 1. Understand that the probability of an event occurring = 1 – the probability of the event not occurring. Understand relative frequency as an estimate of probability. Calculate the probability of simple combined events, using possibility diagrams and tree diagrams where appropriate. Understand the meaning of exclusive and independent events, Calculate and use conditional probabilities in simple cases, 第九节课 permutation and combination Recognise and distinguish between a permutation case and a combination case Know and use the notation n ! (with 0! = 1), and the expressions for permutations and combinations of n items taken r at a time Answer simple problems on arrangement and selection (cases with repetition of objects, or with objects arranged in a circle or involving both permutations and combinations, are excluded) 本文来源：https://www.wddqw.com/doc/203156e9b107e87101f69e3143323968011cf4ec.html