YEAR 12 - Mathematics Pure (C1) Term 1 plan

Transcription

1 Week YEAR 12 - Mathematics Pure (C1) Term 1 plan Algebra Laws of indices for all rational exponents. Use and manipulation of surds. Quadratic functions and their graphs. The discriminant of a quadratic function. Completing the square. Solution of quadratic equations. Solution of simultaneous equations. Analytical solution by substitution. Solution of linear and quadratic inequalities. Algebraic manipulation of polynomials, including expanding brackets and collecting like terms, and factorisation. Graphs of functions; sketching curves defined by simple equations. Geometrical interpretation of algebraic solution of equations. Use of intersection points of graphs of functions to solve equations. Knowledge of the effect of simple transformations on the graph of y = f(x) as represented by y = af(x), y = f(x) + a, y = f(x+a), y = f(ax) 3 Co-ordinate geometry in the (x,y) plane Equation of a straight line in forms y = mx + c, y-y 1 = m(x-x 1) and ax + by + c = 0 Conditions for two straight lines to be parallel or perpendicular to each other. 4-5 Sequences and Series Sequences, including those given by a formula for the nth term and those generated by a simple relation in the form x n+1 = f(x n) Arithmetic series, including the formula for the sum of the first n natural numbers. Understanding of Σ notation. 6-7 Differentiation The derivative of f(x) as the gradient of the tangent to the graph of y = f (x) at a point; the gradient of the tangent as a limit; interpretation as a rate of change. Second order derivatives. Differentiation of x n and related sums and differences. Applications of differentiation to gradients, tangents and normals.

2 8-9 Integration Indefinite integration as the reverse of differentiation. Integration of x n. 10 REVISION AND EXAMINATIONS YEAR 12 - Mathematics Pure (C2) Term 2 plan Week 11 Algebra and functions Simple algebraic division; Use of the Factor Theorem Use of the Remainder Theorem 12 Co-ordinate geometry in the (x,y) plane Coordinate geometry of the circle using the equation of a circle in the form (x-a)² + (y-b)² = r² and including the use of the following circle properties: i) the angle in a semicircle is a right angle; ii) the perpendicular from the centre to a chord bisects the chord; iii) the perpendicularity of the radius and tangent. 13 Sequences and Series The sum of a finite geometric series; the sum to infinity of a convergent geometric series, including the use of lrl<1 Binomial expansion of (1+x) n for a positive integer n. n The notations of n! and ( ) r

3 14,15 Trigonometry The sine and cosine rules; Area of a triangle = ½absinC Radian measure, including use for arc length and area of sector. Sine, cosine and tangent functions. Their graphs, symmetries and periodicity. Knowledge and use of tanx = sinx/cosx and sin²θ +cos²θ=1. Solution of simple trigonometric equations in a given interval.. 16 Exponential and Logarithms y = a x and its graph The laws of logarithms The solution of equations of the form a x = b 17,18 Differentiation Applications of differentiating to maxima and minima and stationary points, increasing and decreasing functions. 19,20 Integration Evaluation of definite integrals. Interpretation of the definite integral as the area under a curve. Approximation of area under a curve using the trapezium rule. Revision and examinations YEAR 12 - Mathematics Pure (C12) Term 3 plan Week 22 to 32 REVISION C1 AND C2 REVISION PRACTICE PAPERS C12

4 YEAR 12 - Mathematics Statistics (S1)- Term 1 plan Week Learning Outcomes 1,2 Mathematical models in probability and statistics. 3-5 Representation and Summary of Data 6-9 Probability Understand what a mathematical model in statistics is. Recognise the 7 different stages of a statistical model as well as the advantages and limitations. Histograms, stem and leaf diagrams, box plots. Measures of location mean, median, mode. Measures of dispersion variance, standard deviation, range and interquartile ranges. Skewness. Concepts of outliers. Note: Use to compare distributions. Back-to-back stem and leaf diagrams may be required. Data may be discrete, continuous, grouped or ungrouped. Understanding and use of coding. Simple interpolation may be required. Interpretation of measure of location and dispersion. Elementary probability. Sample space. Exclusive and complementary events. Conditional probability. Independence of two events. Sum and product laws. Understanding the use of P(A) = 1- P(A), P(AB) = P(A) + P(B) P(AB), P(AB) = P(A)P(BA). P(BA) = P(B), P(AB) = P(A), P(AB) = P(A)P(B) Use of tree diagrams and Venn diagrams. Sampling with and without replacement. 10 REVISION AND EXAMINATION

5 YEAR 12 - Mathematics Statistics (S1)- Term 2 plan Week Scatter diagrams. Linear regression. Explanatory (independent) and response (dependent) variables. Applications and interpretations. The product moment correlation coefficient, its use, interpretation and limitations Correlation and Regression Note: Use to make predictions within the range of values of the explanatory variable and the dangers of extrapolation. Derivations will not be required. Variables other than x and y may be used. Linear change of variable may be required Discrete and random variables Derivations and tests of significance will not be required. The concept of a discrete random variable. The probability function and the cumulative distribution function for a discrete random variable. Mean and variance of a discrete random variable. The discrete uniform distribution The normal distribution The Normal distribution including the mean, variance and use of tables of the cumulative distribution function. 20 REVISION AND EXAMINATION YEAR 12 - Mathematics Statistics (S1)- Term 3 plan REVISION AND EXAMINATION Revision past papers and examination