**"Gradient"**

## UPPER SECONDARY FC2 LINES, CIRCLES AND TANGENTS

*By toni On 12 August, 2018 · Leave a Comment*

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 […]

## Grades 10 to 12 Line Match

*By toni On 1 July, 2018 · Leave a Comment*

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.

Click here for the Notes for Teachers.

## Grade 12 D’riving

*By toni On 17 July, 2017 · Leave a Comment*

Imagine this graph is a road and you are driving from the bottom left hand (South West) corner to the top right hand (North East) corner. Describe how you would steer the car.

When would you be turning the steering wheel to the right?

When would you be turning the steering wheel […]

## Grades 7 and 8 Dotty Relations

*By toni On 15 February, 2017 · Leave a Comment*

On the grid join the two red dots, A and B, together with a straight line.

Now join the blue dots, C and D, with a straight line.

At what angle do the two lines cross?

Investigate the number of squares “along” and “down” from A to B compared with the number […]

## Grade 12 GP Geometrically

*By toni On 12 January, 2017 · Leave a Comment*

The squares in the diagram are to help us visualise an infinite geometric sum and we are not summing the areas of the squares, simply the lengths along the x-axis. The squares have side lengths given by powers of r: where 0 < r < 1 .

## Grades 7 to 10 Paper Weight

*By toni On 13 November, 2016 · Leave a Comment*

The graph shows how the weight of a letter (including the envelope) varies with the number of sheets of paper used.

What is the weight of a single sheet of paper?

What is the weight of the envelope?

If w is the weight of the letter (including the envelope) and s is […]

## Grades 7 to 9 Lattice Points

*By toni On 6 November, 2016 · Leave a Comment*

A point whose x- and y-coordinates are both whole numbers is called a lattice point.

How many lattice points are there in the first quadrant (where both x and y coordinates are positive) that lie on the line 3x + 4y = 59?

Find these points. How many different methods can you think of to […]

## Grades 7 to 9 Steps

*By toni On 5 November, 2016 · Leave a Comment*

Continue these sequences for the next three terms and continue the sequences backwards to the previous 3 terms:

7, 10, 13, 16, 19, …

15, 18, 21, 24, 27, …

1, -2, -5, -8, -11, …

What do you notice?

The first two sequences come from a multiplication table shifted up. Which […]

1. For each line fill in your answers to the following questions in the table below: (Line E has been done for you.)

(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 . […]

## Grades 6 – 10 How Many Squares?

*By toni On 18 January, 2012 · Leave a Comment*

How many squares can you make by joining four points on this grid?

Look for squares of different sizes and also tilted squares

Start with a 3 by 3 grid of nine dots. Can you find six squares?

Then go on to the 4 by 4 grid of sixteen dots.

What can you say […]

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