A-Level Maths OCR B (MEI) H640

Understand and use the equation $y = mx + c$.

Know and be able to use the relationship between the gradients of parallel lines and perpendicular lines.

For parallel lines $m_1 = m_2$. For perpendicular lines $m_1m_2 = -1$.

Be able to calculate the distance between two points.

Be able to find the coordinates of the midpoint of a line segment joining two points.

Be able to form the equation of a straight line.

Including $y - y_1 = m(x - x_1)$ and $ax + by + c = 0$

Be able to draw a line given its equation.

By using gradient and intercept or intercepts with axes as well as by plotting points.

Be able to find the point of intersection of two lines.

By solution of simultaneous equations.

Be able to use straight line models.

In a variety of contexts; includes considering the assumptions that lead to a straight line model.

Be able to find the point(s) of intersection of a line and a curve or of two curves.

Be able to find the point(s) of intersection of a line and a circle.

Understand and use the equation of a circle in the form $(x - a)^2 + (y - b)^2 = r^2$.

Includes completing the square to find the centre and radius.

Know and be able to use the following properties:

• 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.

These results may be used in the context of coordinate geometry.

Understand the meaning of the terms parameter and parametric equations.

Be able to convert between cartesian and parametric forms of equations.

When converting from cartesian to parametric form, guidance will be given as to the choice of parameter.

Understand and use the equation of a circle written in parametric form.

Be able to find the gradient of a curve defined in terms of a parameter by differentiation.

$\dfrac{dy}{dx} = \dfrac{\Bigg(\dfrac{dy}{dt}\Bigg)}{\Bigg(\dfrac{dx}{dt}\Bigg)}$

Excludes: Second and higher derivatives.

Be able to use parametric equations in modelling.

Contexts include kinematics and projectiles in mechanics. Including modelling with a parameter with a restricted domain.