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1 Indices and surds Laws of indices for all rational exponents. Use and manipulation of surds. WJEC C1/OCR C1/Edexcel C1

 
  
2 Quadratics Quadratic functions and their graphs. The discriminant of a quadratic function. Completing the square. Solution of quadratic equations. WJEC C1/OCR C1/Edexcel C1

 
3 Simultaneous equations Simultaneous equations: analytical solution by substitution, e.g. one linear and one quadratic. WJEC C1/OCR C1/Edexcel C1

 
  
           
4 Inequalities Solution of linear and quadratic inequalities. WJEC C1/OCR C1/Edexcel C1

 
  
5 Graphs/curve sketching Graphs of functions; sketching curves defined by simple equations. Use of intersection points of graphs of curves to solve equations. Transformations. WJEC C1/OCR C1/Edexcel C1

 
  
6 Coordinate geometry Equation of a straight line. Conditions for two straight lines to be parallel or perpendicular to each other. Mid-points. WJEC C1/OCR C1/Edexcel C1

 
  
7 Polynomials Algebraic manipulation of polynomials,including expanding brackets and collecting like terms, factorisation and simple algebraic division; use of the Factor Theorem and the Remainder Theorem. WJEC C1/OCR C1/Edexcel C1

 
  
8 Binomial expansion Binomial expansions of (a+b)n for positive integer n . Factorial notations and nCr. WJEC C1/OCR C2/Edexcel C2

 
  
9 Differentiation of polynomials Differentiation of xn and related sums and differences. Finding from first principles the derivative of a polynomial. WJEC C1/OCR C1/Edexcel C1

 
  
10 Applications of Differentiation Application of differentiation to gradients,tangents and normals, maxima and minima, points of inflection, increasing and decreasing functions. Optimisation problems and simple curve sketching. WJEC C1/OCR C1/Edexcel C1

 
  
11 Arithmetic series Arithmetic series. The sum of a finite arithmetic series. The sum of the first n natural numbers. Proof of summation formula. WJEC C2/OCR C2/Edexcel C1

 
  
12 Geometric series Geometric series. The sum of a finite geometric series. The sum to infinity of a convergent geometric series. Proof of summation formula.Use and proof of WJEC C2/OCR C2/Edexcel C2

 
  
13 Sequences Sequences, including those given by a formula for the nth term and those generated by a simple relation of the form xn+1 = f(xn). The S notation. WJEC C2/OCR C2/Edexcel C2

 
  
14 Logarithms Laws of logarithms. Graphs. The solution of equations. Proof of the laws of logarithms. Use of the laws of logarithms. The use of a calculator to solve equations. WJEC C2/OCR C2/Edexcel C2

 
  
15 Coordinate geometry of the circle Two forms of the equation of a circle. Angle in a semicircle, perpendicular from the centre to a chord , perpendicularity of radius & tangent. Equations of tangents. Condition for two circles to touch, points of intersection or the point of contact of a line and a circle. WJEC C2/OCR C1/Edexcel C2

 
  
16 Sine and cosine rules The sine and cosine rules, and the area of a triangle in the form 1/2 absinC. WJEC C2/OCR C2/Edexcel C2

 
  
17 Radian measure Radian measure. Arc length, area of sector and area of segment. Ambiguous case. WJEC C2/OCR C2/Edexcel C2

 
  
18 Trig Functions Sine, cosine and tangent functions. Their graphs, symmetries and periodicity. WJEC C2/OCR C2/Edexcel C2

 
  
19 Trig Identities Knowledge and use of tan x = sin x/cos x and cos2x + sin2x = 1. WJEC C2/OCR C2/Edexcel C2

 
  
20 Trig Equations Solution of simple trigonometric equations in a given interval. Use of the exact values of the sine, cosine and tangent of 30°, 45° and 60°. WJEC C2/OCR C2/Edexcel C2

 
  
21 Integration Indefinite integration as the reverse of differentiation. Integration of xn. Including sums, differences and polynomials. WJEC C2/OCR C2/Edexcel C2

 
  
22 Trapezium rule Approximation of area under a curve using the trapezium rule. WJEC C2/OCR C2/Edexcel C2

 
  
23 Indefinite untegrals Interpretation of the definite integral as the area under a curve. Evaluation of definite integrals. Finding the area of a region between a straight line and a curve. WJEC C2/OCR C2/Edexcel C2

 
  
24 Sec, cosec etc Secant, cosecant and cotangent. Relationships to sine, cosine and tangent. Sin-1, cos-1 and tan-1.Knowledge and use of sec2 ? = 1 + tan2 ? and cosec2 ? = 1 + cot2 ?. WJEC C3/OCR C3/Edexcel C3

 
  
25 Functions Definition of a function. Domain and range of functions. Composition of functions. Inverse functions and their graphs. The modulus function. Combinations of transformations. WJEC C3/OCR C3/Edexcel C3

 
  
26 Exponential & Log functions The function ex and its graph. The function lnx and its graph; lnx as the inverse function of ex. WJEC C3/OCR C3/Edexcel C3

 
  
27 Differentialtion of functions Differentiation of ex, lnx, sinx, cosx, tanx and their sums and differences. Differentiation using the product rule, the quotient rule and the chain rule. Differentiation of simple functions defined implicitly or parametrically. Derivatives of Sin-1x, cos-1x and tan-1x. WJEC C3/OCR C3/Edexcel C3

 
  
28 Integration of functions Integration of ex, sinx, cosx. WJEC C3/OCR C3/Edexcel C4

 
  
29 Iterative solutions Location of roots of f(x) = 0. Approximate solutions of equations using simple iterative methods. Sequences generated by a simple recurrence relation of the form xn+1 = f(xn). WJEC C3/OCR C3/Edexcel C3

 
  
30 Numerical integration Numerical integration of functions. Simpson’s Rule. WJEC C3/OCR C3/Edexcel C4

 
  
31 Further Binomial Binomial series for any rational n including the condition for convergence. WJEC C4/OCR C4/Edexcel C4

 
  
32 Rational expressions Simplification of rational expressions including factorising and cancelling, and algebraic division. WJEC C4/OCR C4/Edexcel C4

 
  
33 Partial fractions Partial fractions with denominators of the form (ax + b)(cx + d), and (ax + b)(cx + d)2. Integration using partial fractions. Integration using partial fractions. WJEC C4/OCR C4/Edexcel C4

 
  
34 Double angle formulae Knowledge and use of formulae for sin(A ± B), cos(A ± B) and tan(A ± B); of double angle formulae; and of expressions for a cos ? + bsin ? in the equivalent forms r cos( ? ± a) or r sin ( ? ± a). Use of these formulae to solve and find greatest and least values, WJEC C4/OCR C3/Edexcel C3

 
  
35 Parametric points Cartesian and parametric equations of curves and conversion between the two forms. Including finding the equations of tangents and normals to curves defined parametrically or implicitly. WJEC C4/OCR C4/Edexcel C4

 
  
36 Differential equations Formation of simple differential equations. Exponential growth and decay. Analytical solution of first order differential equations with separable variables. WJEC C4/OCR C4/Edexcel C4

 
  
37 Volume of revolution Evaluation of volume of revolution. WJEC C4/OCR C3/Edexcel C4

 
  
38 Integration by parts/substitution Simple cases of integration by substitution and integration by parts. WJEC C4/OCR C4/Edexcel C4

 
  
40 Vectors Vectors in two and three dimensions. Magnitude of a vector. Vector addition and multiplication by scalars. Position vectors. The distance between two points. Vector equations of lines. The scalar product. Its use for calculating the angle between two lines. Unit vectors. Condition for two vectors to be parallel. Use and derivation of the position vector of a point dividing a line in a given ratio. Intersection of two lines. Condition for two vectors to be perpendicular. WJEC C4/OCR C4/Edexcel C4

 
  
41 Random experiments & sample space Random experiments, sample space as the set of all possible outcomes. Events described verbally and as subsets of the sample space. Complementary events. WJEC S1/OCR S1/Edexcel S1

 
  
42 Probability 1 The addition law for mutually exclusive events. The generalised addition law. Conditional probability. Multiplication law for independent events. Multiplication law for dependent events. Venn diagrams. WJEC S1/OCR S1/Edexcel S1

 
  
43 Probability 2 Exhaustive events, the Law of Total Probability and Bayes’ Theorem. Probabilities for samples drawn with replacement and without replacement. Tree diagrams. WJEC S1/OCR S1/Edexcel S1

 
  
44 Discrete probability distributions Discrete probability distributions. Mean, variance and standard deviation of a discrete random variable. Use of the results: E(aX + b) = aE(X) + b, Var(aX + b) = a2Var(X). E[g(X)] = Sg(x)P(X = x). WJEC S1/OCR S1/Edexcel S1

 
  
45 Binomial distribution Bernoulli trials and the binomial distribution. Mean and variance of the binomial distribution. Use of the binomial formula and tables. WJEC S1/OCR S2/Edexcel S2

 
  
46 Poisson distribution The Poisson distribution. Mean and variance of the Poisson distribution. Poisson approximation to a binomial. Use of the Poisson formula and tables. WJEC S1/OCR S2/Edexcel S2

 
  
47 Continuous probability distributions Continuous probability distributions. Probability density and cumulative distribution functions and their relationships. Median, quartiles and percentiles. Mean, variance and standard deviation. Use of the results: E(aX + b) = aE(X) + b, Var(aX + b) = a2 WJEC S1/OCR S2/Edexcel S2

 
  
48 Uniform distribution The uniform (rectangular) distribution. WJEC S2/OCR S1/Edexcel S1

 
  
49 Normal Distribution Description and use of the normal distribution. WJEC S2/OCR S2/Edexcel S1

 
  
50 Normal approximation The normal distribution as an approximation to the binomial and Poisson distributions. WJEC S2/OCR S2/Edexcel S2

 
  
51 Expectation of products Use of the result E(aX + bY) = aE(X) + bE(Y). For independent X and Y, use of the results E(XY) = E(X)E(Y), Var(aX + bY) = a2Var(X) + b2Var(Y). Generalisation to n random variables. WJEC S2/OCR n/a/Edexcel n/a

 
  
52 Sum of Poisson Application of the result that the sum of independent Poisson random variables has a Poisson distribution. Include the use of continuity correction. WJEC S2/OCR S2/Edexcel S2

 
  
53 Linear combs ind. Normal Application of the result that a linear combination of independent normally distributed random variables has a normal distribution. WJEC S2/OCR S3/Edexcel S3

 
  
54 Distn of sample means Definition of a random sample of observations of a random variable. Distribution of the mean of a random sample from a normal distribution with known mean and variance. The Central Limit WJEC S2/OCR S2/Edexcel S3

 
  
55 Hypothesis testing 1 Hypothesis testing, null hypothesis and alternative hypothesis. Test statistic, significance level and critical region. p-value. One-sided and two-sided tests. Test for the mean of a normal distribution of known variance; a specified difference between the means of two normal distributions. WJEC S2/OCR S2/Edexcel S2

 
  
56 Hypothesis testing 2 Test for a population proportion or binomial probability parameter, the mean of a Poisson distribution, WJEC S2/OCR S3/Edexcel S3

 
  
57 Confidence limits Confidence limits for the mean of a normal distribution with known variance, the difference between the means of two normal distributions whose variances are known. WJEC S2/OCR S3/Edexcel S3

 
  
58 Samples and populations Samples and populations. General discussion of statistics and their sampling distributions. A statistic as an estimator of a population parameter. Unbiased estimators. The variance criterion for choosing between unbiased estimators. Unbiased estimators of a probability and of a population mean and their standard errors. Unbiased estimator of a population variance. WJEC S3/OCR S3/Edexcel S3

 
  
59 Further hypothesis testing Further hypothesis testing. Tests for (a) a specified mean of any distribution whose variance is estimated from large samples, (c) a specified mean of a normal distribution with unknown variance. Use of Student’s t-distribution. WJEC S3/OCR S3/Edexcel S3

 
  
60 Confidence limits for mean Confidence limits for the mean of a normal distribution with unknown variance. Approximate confidence limits, given large samples, for (a) a probability or a proportion, (b) the mean of any distribution whose variance is unknown, (c) the difference between the means of two populations whose variances are unknown. Student’s t-distribution. WJEC S3/OCR S3/Edexcel S3

 
  
61 Least squares regression The principle of least squares, with particular reference to its use for estimating a linear relationship y = a + ßx. Confidence limits and hypothesis tests for a, ß and the true value of y. WJEC S3/OCR S1/Edexcel S1

 
  
62 Correlation Correlation coefficient. Calculation, interpretation and significance testing. WJEC n/a/OCR S1/Edexcel S1

 
  
63 Rank Correlation Rank Correlation coefficient. Calculation, interpretation and significance testing. WJEC n/a/OCR S1/Edexcel S1

 
  
64 Chi-squared Chi-squared test and contingency tables. WJEC n/a/OCR S3/Edexcel S3

 
  
65 Summarizing data Mean, median, mode, box plots, stem and leaf. Variand standard deviation. Interpercentile ranges. WJEC n/a/OCR S1/Edexcel S1

 
  
66 Type I and Type II errors Type I and Type II errors in relation to hypothesis testing. WJEC n/a/OCR S2/Edexcel n/a

 
  
   

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 Dr Colin Davies C.Stat, MSc, PhD