AQA Core 1
Use and manipulation of surds To include simplification and rationalization of the denominator of a fraction √12 + 2√27 = 8√3 1 = √2 + 1 √2 1 
Algebraic manipulation of polynomials, including expanding brackets and collecting like terms 
Quadratic functions and their graphs Reference to the vertex and line of symmetry of the graph 
Completing the square 
The discriminant Conditions for real roots, distinct real roots and for no real roots 
Factorization of quadratic poynomials Eg 2x^{2} + x – 6 
Solution of quadratic equations Any method

Solution of linear & quadratic inequalities 2x^{2} + x ³ 6 
Simple algebraic division Quadratic or cubic polynomial divided by a linear term of the form (x+ a) ( x – a) where a is a small whole number 
Use of the remainder theorem When a quadratic or cubic polynomial f(x) is divided by ( x – a) the remainder is f(a) and, that when f(a) = 0, then ( x – a) is a factor and vice versa 
Use of the factor theorem Greatest level of difficulty x^{3} – 5x^{2} + 7x – 3 ie always a factor ( x + a) ( x – a ) including cases of three distinct linear factors, repeated linear factors or a quadratic factor which cannot be factorised

Graphs of functions: sketching, f(x) notation, but only a general idea of the concept of a function is required. Domain and range are not included linear, quadratic, cubic graphs of circles are included 
Knowledge of the effect of translations on graphs and their equations Applied to quadratic graphs and circles ie y = ( x – a )^{2} + b as a translation of y = x^{2} and (x – a)^{2} + ( y –b)^{2} = r^{2} as a translation of x^{2} + y^{2} = r^{2} 
Solving simultaneous equations Two linear A linear and a quadratic Analytical solution by substitution

Equation of a straight line, including the forms y – y1 = m( x – x1 ) , ax + by c = 0 and y = mx + c Problems using gradients, midpoints and the distance between two points 
Conditions for two straight lines to be parallel or perpendicular to each other Product of two perpendicular lines is 1 
The equation of a circle in the form ( x – a) ^{2} + ( y – b ) ^{2} = r^{2} Completing the square to ind the centre and radius of a circle Eg x^{2} + 4x + y^{2} 6y – 12 = 0 
Coordinate geometry of the circle Use of the following circle properties is required i) the angle in a semicircle is a right angle ii) the perpendicular from the centre to a chord bisects the chord iii) the tangent to a circle is perpendicular to the radius at its point of contact

Intersection of a straight line and a curve Solutions from intersection points Applications will be to either circles or graphs of quadratic functions Interpretation of geometrical implication of equal roots, distinct real toots or no real rots 
The equation of the tangent and normal at a given point to the circle Implicit differentiation is not required. Candidates will be expected to use the coordinates of the centre and a point on the circle or of other appropriate points to find relevant gradients 
Construction and presentation of rigorous mathematical arguments through appropriate use of precise statements and logical deduction. Not counter examples 
Correct understanding and use of mathematical language and grammar in respect of terms such as ‘equals’, ‘identically equals’, ‘therefore’, ‘because’, implies’, ‘is implied by’, ‘necessary’, ‘sufficient’, and notation for Û, Ü, or Þ therefore X+3<3X * X>3 Replace * by Û, Ü, or Þ 
The derivative of f(x) as the gradient of the tangent to the graph y = f(x) at a point The notations f’(x) or dy will be used dx By first principles is not required but the gradient of the tangent as a limit

Interpretation as rate of change 
Differentiation of polynomials A general appreciation only of the derivative when interpreting it is required. Differentiation from first principles will not be tested 
Applications of differentiation to gradients, tangents and normals 
Applications of differentiation to: maxima and minima stationary points increasing and decreasing functions Questions will not be set requiring the determination of or knowledge of points of inflection Questions may be set in the form of a practical problems where a function of a single variable has to be optimised 
Second order derivatives Application to determining maxima and minima 
Indefinite integration as the reverse of differentiation
Integration of polynomials 
Evaluation of definite integrals Interpretation of the definite integral as the area under the curve Area between a curve and the x axis Areas wholly below the x axis, knowledge that the integral will give a negative value. Areas partially above and below the x axis will not be set 