crashmaths Schemes of Work New A Level Maths (2017)

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1 crashmaths Schemes of Work New A Level Maths (2017) This scheme of work is for a class: with one teacher with 5 contact hours each week sitting the AS exams Textbook references are for our Pure/Applied Textbook (Edexcel version). The scheme of work is applicable for all exam boards, but some modification may be needed in places. This is for the AS/Year 1 content only. It will be updated to include A2/Year 2 content for teaching post-exams after the publication of our A2 textbooks.

2 Week Topic(s) + Length of time Specification references Teaching suggestions Textbook references 1 5 hours on: Proof understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion proof by deduction proof by exhaustion disproof by counter-example 2 2 hours on: Proof understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion proof by deduction proof by exhaustion disproof by counter-example Introduce the idea of proof, including relevant logic symbols,,,, and logic connectives. Introduce the three methods of proof with examples (either one-byone or simultaneously) More examples/recap. Potential for use of end of topic test (45 minutes) 1, Sections , Sections

3 Week 2 3 hours on: Algebra GCSE algebra (expanding/factorising) Take some time to go (cont.) Solution of quadratic equations through the basics to ensure students develop 2, Sections 2.1 fluency. Use mid-topic test Week 3 5 hours on: Algebra Understand and use the laws of indices for all rational exponents Use and manipulate surds including rationalising the denominator Solving quadratics in a function of the unknown (powers of x ) Plenty of examples are important here to build fluency. Use 2, Sections Week 4 5 hours on: Equations and Inequalities Solve simultaneous equations in two variables by elimination and by substitution, including one linear and one quadratic equation Potential to link back to algebra can act as a recap. Encourage Ss to check answers by 3, Sections Solve linear and quadratic inequalities in substitution at the end single variable and interpret such inequalities graphically Express solutions using set notation Brief/informal overview of quadratic graphs is advised.

4 Week 5 2 hours: Equations and inequalities Represent inequalities graphically End of Topic test 3, Section hour: Large Data Set Introduce the large data set and the variables involved Get students to use Excel to look and familiarise themselves with the 1, Section 1.1 variables 2 hours: Sampling Understand and use the terms population and sample Use samples to make informal inferences about the population Understand and use sampling techniques, including simple random sampling Week 6 2 hours: Sampling Understand and use opportunity sampling, stratified sampling, systematic sampling and quota sampling Select and critique sampling techniques in the context of solving a statistical problem, including understanding that different samples can lead to different conclusions Use a real sampling frame of students in a class and use simple random sampling to select students to answer recap questions on prior topics Focus on the difference in systematic and quota sampling 2, Sections , Sections

5 about the population Week 7 5 hours: Functions Work with quadratic functions and their graphs The discriminant of a quadratic function, including the conditions for real and repeated roots Understand and use graphs of functions; sketch curves defined by simple equations, including polynomials and reciprocal graphs Ensure Ss understand what the function notation means For any graph, to find x intersections, set y=0; to find y intersections, set x = 0. Link quadratic graphs and the discriminant Similarity between polynomial curves. Distinction between a root repeated 2n times and (2n+1) times ( n! ) 4, Sections

6 Week 8 5 hours: Functions Interpret algebraic solution of equations graphically; use intersection points of graphs to solve equations Understand and use proportional relationships and their graphs Understand the effect of simple transformations, including y = af ( x), y = f x y = f ax ( ) + a ( ) ( ) y = f x + a Stress the idea that, simultaneous equations tells us where two equations have the same x value and y value, i.e. the same coordinates 4, Sections Week 9 5 hours: The Factor Theorem Simple algebraic long division Use of the factor theorem Even though the remainder theorem is off-spec, it is good to teach it and then teach the factor theorem as a special case 5

7 Week 10&11 10 hours: Coordinate geometry in the (x,y) plane {6 hours on straight lines, 4 hours on circles} Understand and use the equation of a straight line Gradient conditions for two straight lines to be perpendicular Be able to use straight lines to model in a Teach y y 1 = m( x x 1 ) as a special case of y = mx + c, with c = y 1 mx 1. 5 variety of contexts Encourage Ss to make use Understand and use the coordinate of diagrams geometry of a circle Completing the square to find centre and radius on straight lines and circles Circle theorems to assist in geometry problems Week 12 3 hours: the binomial Understand and use the binomial expansion In exams, Ss often make expansion of ( a + bx) n for positive integers n; the notations n! and n C r ; link to binomial probabilities sign errors/struggle to deal with fractions and the algebra. Use plenty of examples of this type (can 6 be found in the book)

8 Week 13 5 hours: measures of central tendency Interpret measures of central tendency: mean, median and mode Make students very clear on the conventions for Select suitable measures of central grouped data (gaps/no 3, Sections tendency depending on context gaps) and that discrete data is treated as cts Excellent opportunity for large data set exploration topic test Week 14 4 hours: measures of dispersion Measures of dispersion: variance, standard deviation, range and interpercentile range *See classroom activities for lesson plan of this LDS 1 hour: measures of central tendency and Use coding centred lesson 1/4, Sections 1.1, dispersion + LDS* Week 15 5 hours: representation of data Cumulative frequency diagrams, frequency polygons and box plots (without outliers) {1 hour} Recap on GCSE diagrams (excl. histograms) in a single lesson. Since Ss 5, Sections Histograms should be familiar with Outliers and data failure, including box plots Bivariate data these already, this is a good chance to explore the

9 LDS again Week 16&17 10 hours: trigonometry Sine, cosine and tangent functions unit circle definitions, graphs and transformations {1 lesson} s 8&9, Sections 8.1- The sine and cosine rule & ambiguous case ½ ab for right-angled 8.6, of the sine rule {2 lessons} triangles as a special case Area of a triangle {1 lesson} of ½ ab sin C Understand use trigonometric identities {2 lessons} Solving simple trigonometric equations in a Proof of trigonometric identities for 0-90 o given interval, including quadratic types {3 lessons} {1 lesson for recap}

10 Week 18 5 hours: exponentials and logarithms Know and use the function a x and its graph, where a is positive Know that the gradient of e kx is k e kx and hence understand why the exponential Difference between a < 1 and a > 1 (link to laws of indices) 10, Sections model is suitable in many applications Know and use the definition of the Link to logic connectives logarithm with x = log a y y = a x Know and use the function lnx and its graph Understand and use the laws of logarithms Solve equations of the form a x = b Proof of laws of logarithms to improve understanding Week 19 5 hours: exponentials Understand and use the laws of logarithms and logarithms Solve equations of the form a x = b Use logarithmic graphs to estimate parameters of the form y = ax n and y = kb x Ss to establish results themselves to recap on straight lines 10, Sections Understand and use exponential growth and decay Week 20 5 hours: probability Understand and use mutually exclusive and independent events when calculating

11 probabilities 6, Sections Venn diagrams and tree diagrams Understand and use simple, discrete probability distributions Link to continuous and discrete distributions Week 21 5 hours: probability The binomial distribution as a model; calculate probabilities using the binomial distribution Probability mass/density functions Link to binomial expansion. Explain reasoning behind the formula, including ncr Use of calculator and tables to find probabilities 6, Sections Week 22 5 hours: hypothesis testing Understand and apply the language of statistical hypothesis testing Distinction between onetailed and two-tailed tests Conduct a statistical hypothesis test 7, Sections

12 Week 23&24: 10 hours: differentiation Understand and use the derivative of f(x) as the gradient of the tangent to the graph of y = f(x) at the general point (x,y); the gradient of the tangent as a limit; interpretation as a rate of change Differentiation from first principles Turning & stationary points Sketching the gradient function for a given curve Tangents and normal Identify where functions are increasing and Make Ss calculate gradient using tangent-method (so they see why we need an alternative). Introduce (informally) what a limit is and practice calculating limits; in particular, limits to 0 Link to straight lines and inequalities 11, sections decreasing Maxima/minima problems Week 25 5 hours: Integration Know and use the Fundamental Theorem of Calculus Integrate x n Evaluate definite integrals Area under curves Use integration as the reverse process of differentiation 12, sections

13 Week 26 5 hours: vectors Use vectors in two dimensions Calculate the magnitude and direction of a vector and convert between component form and magnitude/direction form Vector manipulation and their geometric interpretations Understand and use position vectors; use vectors to calculate the distance between two points Use vectors to solve problems Make sure students know the conventions for the direction of a vector Extension of the formula for length of a line segment 13, sections Week 27 5 hours: models in mechanics and kinematics Understand the modelling assumptions in mechanics Understand and use the language of kinematics: position; displacement; distance travelled; velocity; speed; acceleration. {1 lesson} Simple non-kinematic cases of calculating area under a graph, where the region is a trapezium s 8/9, sections 8.1, Understand, use and interpret graphs in Link to kinematics {1 lesson} differentiation/integration Solve problems involving constant and variable acceleration {3 lessons}

14 Week 28 5 hours: Newton s Newton s laws {1 lesson} Laws Motion in 2D {1 lesson} Connected particles and pulleys {2 lessons} Recap lesson {1 lesson} Link to vectors 10, sections Remaining time is revision time!