AQA A/AS LEVEL AQA Level 2 Certificate in Further Mathematics 27

AQA A/AS LEVEL AQA Level 2 Certificate in Further Mathematics 27 2.6 Manipulation of rational expressions: Use of + – × ÷ for algebraic fractions with denominators being numeric, linear or quadratic Simplify Simplify x2 + 3x – 10 x2 –9 x3 + 2x2 + x x2 + x ÷ x + 5 x2 + 3x Simplify 5x2 – 14x –3 ÷ 4x2 – 25 x –3 4x2 + 10x 2.7 Use and manipulation of formulae and Rearrange 1 = 1 + 1 to make v the subject expressions f u v 2.8 Use of the factor theorem for integer values of Factorise x3 – 2x2 – 5x + 6 the variable, including cubics Show that x – 1 is a factor of x3 – 3x2 – 4x + 6 Solve x3 + x2 – 10x + 8 = 0 2.9 Completing the square Work out the values of a, b and c such that 2x2 + 6x + 7 Ξ a(x + b)2 + c Ref Content Notes 2.10 Sketching of functions Graphs could be linear, quadratic or restricted to no Sketch graphs of linear and quadratic functions more than 3 domains eg y = x2 – 5x + 6 Label clearly any points of the intersection with the axes eg A function f(x) is defined as f(x) = x2 0 “ x 1 = 1 1 “ x 2 = 3 – x 2 “ x 3 Draw the graph of f(x) on the grid below for values of x from 0 to 3 2.11 Solution of linear and quadratic equations Solutions of quadratics to include solution by factorisation, by graph, by completing the square or by formula 3 Problems will be set in a variety of contexts, which result in the solution of linear or quadratic equations 2.12 Algebraic and graphical solution of simultaneous Solve 4x – 3y = 0 and 6x + 15y = 13 equations in two unknowns where the equations Solve y = x + 2 and y2 = 4x + 5 could both be linear or one linear and one second order Solve y = x2 and y – 5x = 6 2.13 Solution of linear and quadratic inequalities Solve 5(x – 7) 2(x + 1) Solve x2 9 Solve 2x2 + 5x “ 3 2.14 Index laws, including fractional and negative indices Express as a single power of x Express as a single power of x – 1 1 7 x 2  x 2 3 7 x 2  x 2 x2 Solve x 2 = 3 2.15 Algebraic proof Prove (n + 5)2 – (n + 3)2 is divisible by 4 for any integer value of n 2.16 nth terms of linear and quadratic sequences Write down the 10th term of the sequence Limiting value of a sequence as n ∞ 2n n + 4 Write down the limiting value of 2n as n ∞ n + 4 Ref Content Notes 3.1 Know and use the definition of a gradient 3.2 Know the relationship between the gradients of Show that A (0, 2), B (4, 6) and C (10, 0) form a parallel and perpendicular lines right angled triangle 3.3 Use Pythagoras’ theorem to calculate the distance between two points 3.4 Use ratio to find the coordinates of a point on a Including midpoint line given the coordinates of two other points. 3.5 The equation of a straight line in the forms Including interpretation of the gradient and y = mx + c and y – y1 = m (x – x1) y-intercept from the equation 3.6 Draw a straight line from given information 3 3.7 Understand that the equation of a circle, centre Including writing down the equation of a circle given (0, 0), radius r is x2 + y2 = r2 centre (0, 0) and radius The application of circle geometry facts where appropriate: eg the angle in a semi-circle is 90°, the perpendicular from the centre to a chord bisects the chord, the angle between tangent and radius is 90° 3.8 Understand that (x – a)2 + (y – b)2 = r2 is the Including writing down the equation of any circle equation of a circle with centre (a, b) and given centre and radius radius r 4.1 Know that the gradient function dy gives the x gradient of the curve and measures the rate of change of y with respect to x 4.2 Know that the gradient of a function is the gradient of the tangent at that point 4.3 Differentiation of kxn where n is a positive Including expressions which need to be integer or 0, and the sum of such functions simplified first Given y = (3x + 2)(x – 3) work out dy 4.4 The equation of a tangent and normal at any point on a curve 4.5 Use of differentiation to find stationary points on Understand the terms ‘increasing function’ and a curve: maxima, minima and points of inflection ‘decreasing function’ and applying them to determine the nature of stationary points 4.6 Sketch a curve with known stationary points 3