A-Level Maths OCR A H240

Understand and be able to use the equation of a straight line, including the forms $y = mx + c$, $y - y_1 = m(x - x_1)$ and $ax + by + c = 0$.

*Learners should be able to draw a straight line given its equation and to form the equation given a graph of the line, the gradient and one point on the line, or at least two points on the line.

Learners should be able to use straight lines to find:[ol]lithe coordinates of the midpoint of a line segment joining two points,[/li]lithe distance between two points and[/li]lithe point of intersection of two lines.[/li]/ol*

Be able to use the gradient conditions for two straight lines to be parallel or perpendicular.

i.e. For parallel lines $m_1 = m_2$ and for perpendicular lines $m_1m_2 =-1$.

Be able to use straight line models in a variety of contexts.

These problems may be presented within realistic contexts including average rates of change.

Understand and be able to use the coordinate geometry of a circle including using the equation of a circle in the form $(x - a)^2 + (y - b)^2 = r^2$.

Learners should be able to draw a circle given its equation or to form the equation given its centre and radius.

Be able to complete the square to find the centre and radius of a circle.

Be able to use the following circle properties in the context of problems in coordinate geometry: [ol]lithe angle in a semicircle is a right angle,[/li]lithe perpendicular from the centre of a circle to a chord bisects the chord,[/li]lithe radius of a circle at a given point on its circumference is perpendicular to the tangent to the circle at that point.[/li]/olLearners should also be able to investigate whether or not a line and a circle or two circles intersect.

Understand and be able to use the parametric equations of curves and be able to convert between cartesian and parametric forms.

*Learners should understand the meaning of the terms parameter and parametric equation.

Includes sketching simple parametric curves.

See also Section 1.07s.*

Be able to use parametric equations in modelling in a variety of contexts.

The contexts may be within pure mathematics or in realistic contexts, for example those involving related rates of change.