Core Mathematics Worksheet (Page 2 of 2) in pdf

Coordinate Geometry and Graphs

(a) find the length, gradient and mid-point of a line-segment, given the coordinates of its endpoints

(b) find the equation of a straight line given sufficient information (e.g. the coordinates of two

points on it, or one point on it and its gradient)

=m(x−x

(d) interpret and use linear equations, particularly the forms y=mx+c , y−y

) and

ax+by+c=0

+(y−b)

(e) understand that the equation (x−a)

represents the circle with centre (a , b) and

radius r

(f) use algebraic methods to solve problems involving lines and circles, including the use of the

+2gx+2fy+c=0 (knowledge of the following

equation of a circle in expanded form x

circle properties is included: the angle in a semicircle is a right angle; the perpendicular from

the centre to a chord bisects the chord; tangent and line from tangent to centre (radius) are perpendicular );

(g) understand the relationship between a graph and its associated algebraic equation, use points of

intersection of graphs to solve equations, and interpret geometrically the algebraic solution of

equations (to include, in simple cases, understanding of the correspondence between a line

being tangent to a curve and a repeated root of an equation);

(h) sketch curves with equations of the form

(i) y = kx

, where n is a positive or negative integer and k is a constant,

(ii) y =k√ x, where k is a constant,

+bx+c , where a, b and c are constants,

(iii) y=ax

(iv) y = f(x) , where f(x) is the product of at most 3 linear factors, not necessarily all distinct

(i) understand and use the relationships between the graphs of y = f(x) , y =af(x) , y=f(x)+a,

y=f(x+a) , y = f(ax) , where a is a constant, and express the transformations involved in

terms of translations, reflections and stretches.

Differentiation

(a) understand the gradient of a curve at a point as the limit of the gradients of a suitable sequence

of chords (an informal understanding only is required, and the technique of differentiation from

first principles is not included)

(b) understand the ideas of a derived function and second order derivative, and use the notations

f ′

f ′ ′

)

and

(for any rational n), together with constant multiples, sums and

Differences

(d) apply differentiation (including applications to practical problems) to gradients, tangents and

normals, rates of change, increasing and decreasing functions, and the location of stationary

points (the ability to distinguish between maximum points and minimum points is required, but

identification of points of inflexion is not included).

Core Mathematics Worksheet Page 2

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