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.
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 1.1-1.4 1, Sections 1.1-1.4
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 2.2-2.5 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 3.1-3.5 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.
Week 5 2 hours: Equations and inequalities Represent inequalities graphically End of Topic test 3, Section 3.6 1 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 2.1-2.2 2, Sections 2.3-2.5
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 4.1-4.4
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 4.5-4.8 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
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)
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 3.1-3.5 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, 4.1-4.3 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 5.1-5.5 Histograms should be familiar with Outliers and data failure, including box plots Bivariate data these already, this is a good chance to explore the
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, 9.1-9.3 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}
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 10.1-10.4 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 10.4-10.6 Understand and use exponential growth and decay Week 20 5 hours: probability Understand and use mutually exclusive and independent events when calculating
probabilities 6, Sections 6.1-6.4 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 6.5-6.8 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 7.1-7.4
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 11.1-11.10 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 12.1-12.6
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 13.1-12.5 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, 9.1-9.4 Understand, use and interpret graphs in Link to kinematics {1 lesson} differentiation/integration Solve problems involving constant and variable acceleration {3 lessons}
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 10.1-10.4 Remaining time is revision time!