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Checklist Topic Algebra Simple algebraic division; use of the Factor Theorem and the Remainder Theorem. Module : Core 2 Board : Edexcel Amplification Confidence with this topic Only division by (x + a) or (x – a) will be required. Candidates should know that if f(x) = 0 when x = a, then (x – a) is a factor of f(x). factor theorem Candidates may be required to factorise cubic expressions such as x3 + 3x2 – 4 and 6x3 + 11x2 – x – 6. Candidates should be familiar with the terms ‘quotient’ and ‘remainder’ and be able to determine the remainder when the polynomial f(x) is divided by (ax + b) using the remainder theorem. 2. Coordinate geometry in the (x, y) plane Candidates should be able to find the radius and the Coordinate geometry of the circle using the equation of a circle in the form coordinates of the centre of the circle given the (x – a)2 + (y – b)2 = r2 and including use of the following circle properties: equation of the circle, and vice versa. (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 radius and tangent. Sequences and Series Recurrence Relation Definition of Recurrence Relation: un = f(un-1) Binomial Expansion Definition of an exponential function ax Graph sketching (such as y = 2x) Definition of a logarithmic function: The inverse function of an exponential function of the same base. a = bc logba = c Binomial expansion: using Pascal’s triangle to obtain coefficients of powers of x such as: (1 + x)n and (a + bx)n where n is a positive integers and n is small (n < 7). Extension of the Pascal’s triangle to obtain the Binomial Expansion formula : n(n 1) 2 1 nx x ... n (1 + x) = 2! n(n 1)(n 2)...(n r 1) r x ... x n r! Factorial Notation The sum of a finite geometric series; the sum to The general term, the sum to n terms and sum to infinity are required. infinity of a convergent geometric series, including The proof of the sum formula should be known. the use of r 1 . Exponentials & Logarithms Exponentials Logarithms 840987193 Page 1 5/7/2017 Checklist Laws of logarithms Changing Base Equations Trigonometry Solve trig problems involving nonright-angled triangles Radian measure, including use for arc length and area of sector. Sine, cosine and tangent functions. Their graphs, symmetries and periodicity. Know and use Trig identities Solution of simple trigonometric equations in a given interval. Differentiation Applications of differentiation to maxima and minima and stationary points, increasing and decreasing functions. Integration Evaluation of definite integrals. Interpretation of the definite integral as the area under a curve. Numerical Methods Numerical Integration Module : Core 2 Board : Edexcel Notation and log laws: log10x = log x 1. logax + logay = logaxy 2. logax - logay = loga(x/y) 3. logaxn = n logax Important results: logaa = 1 and loga1 = 0 logba = logca/ logcb (change of base) Solving exponential and logarithmic equations in linear and quadratic forms (incl simultaneous equations). Knowledge of graphs of curves with equations such as y = 3 sin x, y = sin(x + π/6), y = sin 2x is expected. sin , and sin2 + cos2 = 1. cos Finding all solutions within the interval The notation f(x) may be used for the second order derivative. To include applications to curve sketching. Maxima and minima problems may be set in the context of a practical problem. The sine and cosine rules, and the area of a triangle in the form Use of the formulae s = rθ and A = Knowledge and use of tan = 1 2 1 2 ab sin C. r2θ for a circle. Candidates will be expected to be able to evaluate the area of a region bounded by a curve and given straight lines. E.g. find the finite area bounded by the curve y = 6x – x2 and the line y = 2x. The use of the Trapezium Rule: b , ydx 12 h{(y 0 yn ) 2(y1 y2 ... yn 1 )} a where h b a . n 840987193 Page 2 5/7/2017