Maths — Pure 1 — AS

1.1.1 · carry out the process of completing the square for a quadratic polynomial ax + bx + c and use y a completed square form

8 resources

1.1.2 · find the discriminant of a quadratic polynomial ax + bx + c and use the discriminant ‘repeated root’ is included.

12 resources

1.1.3 · solve quadratic equations, and quadratic By factorising, completing the square and using the inequalities, in one unknown formula.

20 resources

1.1.4 · solve by substitution a pair of simultaneous e.g. equations of which one is linear and one is 2 quadratic

10 resources

1.1.5 · recognise and solve equations in x which are quadratic in some function of x . tan

11 resources

1.2.1 · understand the terms function, domain, range, one-one function, inverse function and composition of functions

11 resources

1.2.2 · identify the range of a given function in simple cases, and find the composition of two given functions condition that a composite function

17 resources

1.2.3 · determine whether or not a given function is one-one, and find the inverse of a one-one function in simple cases

10 resources

1.2.4 · illustrate in graphical terms the relation between Sketches should include an indication of the mirror a one-one function and its inverse line

3 resources

1.2.5 · understand and use the transformations of the Including use of the terms ‘translation’, ‘reflection’ graph of y = f( x ) given by and ‘stretch’ in describing transformations. Questions y = f( x ) + a , y = f( x + a ) , may involve algebraic or trigonometric functions, or other graphs with given features. y = a f( x ) , y = f( ax ) and simple combinations of these.

9 resources

1.3.1 · find the equation of a straight line given e.g. given two points, or one point and the gradient. sufficient information

17 resources

1.3.2 · interpret and use any of the forms y = mx + c , y – y = m ( x – x ) , ax + by + c = 0 in solving

60 resources

1.4.1 · understand the definition of a radian, and use the relationship between radians and degrees

17 resources

1.5.1 · sketch and use graphs of the sine, cosine and Including e.g. tangent functions (for angles of any size, and using either degrees or radians)

23 resources

1.5.2 · use the exact values of the sine, cosine and tangent of 30 °, 45 °, 60 °, and related angles

6 resources

1.5.3 · use the notations sin⁻¹x, cos⁻¹x, tan⁻¹x to denote the principal values of the inverse trigonometric relations: • No specialised knowledge of these functions is required, but understanding of them as examples of inverse functions is expected.

3 resources

1.5.4 · use the identities θ≡tanθ and sin²θ+cos²θ ≡ 1: • e.g. in proving identities, simplifying expressions and solving equations.

14 resources

1.5.5 · find all the solutions of simple trigonometrical equations lying in a specified interval (general forms of solution are not included).

11 resources

1.6.1 · use the expansion of ( a + b ) , where n is a positive integer

13 resources

1.6.2 · recognise arithmetic and geometric progressions

3 resources

1.6.3 · use the formulae for the n th term and for the Including knowledge that numbers sum of the first n terms to solve problems involving arithmetic or geometric progressions equivalent).

28 resources

1.6.4 · Questions may involve more than one progression. geometric progression, and the formula for the sum to infinity of a convergent geometric progression.: • use the condition for the convergence of a

14 resources

1.7.1 · understand the gradient of a curve at a point as the limit of the gradients of a suitable sequence of chords, and use the notations d y , and d y f ′ ( x ) , f ″( x ) , 2 for first and second derivatives

5 resources

1.7.2 · use the derivative of x (for any rational n ), together with constant multiples, sums and differences of functions, and of composite functions using the chain rule

39 resources

1.7.3 · apply differentiation to gradients, tangents and normals, increasing and decreasing functions and rates of change

29 resources

1.7.4 · locate stationary points and determine their nature, and use information about stationary points in sketching graphs.

38 resources

1.8.1 · understand integration as the reverse process of differentiation, and integrate ( ax + b ) (for any rational n except –1), together with constant multiples, sums and differences

2 resources

1.8.2 · solve problems involving the evaluation of a constant of integration

4 resources

1.8.3 · evaluate definite integrals

10 resources

1.8.4 · use definite integration to find lines parallel to the axes, or between a curve and a line or between two curves: • the area of a region bounded by a curve and • a volume of revolution about one of the axes.

12 resources