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:

• the coordinates of the midpoint of a line segment joining two points,
• the distance between two points and
• the point of intersection of two lines.

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:

• the angle in a semicircle is a right angle,
• the perpendicular from the centre of a circle to a chord bisects the chord,
• the radius of a circle at a given point on its circumference is perpendicular to the tangent to the circle at that point.

Learners 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.