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:

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

Straight 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 \(m_1m_2 =-1\).

Straight lines

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.

Straight lines

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.

Circles

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

Circles

Be able to use the following circle properties in the context of problems in coordinate geometry:

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

Circles

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.

Parametric equations

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.

Parametric modelling