A sequence of activities in this guide takes you from familiar ideas about lines, then emphasises the ‘across’ and ‘up’ aspect of gradient to explain why the product of gradients of perpendicular lines is -1, then uses Pythagoras Theorem to produce the equations of circles and recaps on properties of perpendicular lines […]
Explain your findings about the four lines in this diagram and their gradients.
Match each sketch graph from column A below with a description and a fact about gradients from the other two columns.
The line LP with equation y + x – 2 = 0 is a tangent at L to the circle with centre M(-4 , 4).
LN is a diameter of the circle.
LP is parallel to NQ where P is on the x-axis and Q is on the y-axis.
What equations […]
DO NOT USE CALCULATORS FOR THIS WHOLE CLASS ACTIVITY.
YOU NEED TO KNOW: that the cosine and sine functions for ALL ANGLES are given by the coordinates of points on the UNIT CIRCLE. The x-coordinates of points on the unit circle give the cosine of the angle between the x-axis and the radius measured anti-clockwise […]
(i) Write down the coordinates (0; c) of the point of intersection of the line with the y-axis (the y intercept).
(ii) Choose two points on the line . […]
How do you find the coordinates of the centre of square 1 if you know that (0, 3), (3, 4), (4, 1) and (1, 0) are vertices?
What are the coordinates of the centre of the 20th square?
Imagine the sequence of […]
Will the route pass through the point (18,17)?
If so, which point will be visited next? Explain how you found out.
How many points does the route pass through […]