Posts by: toni
Multiply out these expressions:
What do you notice?
Does this pattern continue?
Can you prove it?
What does this tell you about the sum to n terms of the geometric series with first term 1 and common ratio r?
Why do we get a formula for all values of r except r = 1?
Explain […]
Angles A, B and C are the angles of a triangle. Decide whether each of the following is an identity, always true for all triangles, or an equation, sometimes true. If you decide it is an equation find the solution or solutions and describe the corresponding triangle.
The angle of elevation from a point C on the ground, at the centre of the goalpost is 64.75 degrees to the highest point A of the arc, directly above the centre of the Moses Madhiba Soccer Stadium in Durban. The soccer pitch is 100 metres long (PQ in the diagram) and […]
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 […]
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 .
Insert signs and symbols to make each line a true equation.
Hint: You can use square roots and cube roots.
As an extension you could investigate the factorial sign on your calculator and use factorials to answer the same questions for 0 0 0 = 6 and 1 1 1 = […]
Story 1 A generous little monkey had some peaches.
On the first day he gave half his peaches away and ate one.
On the second day he gave away half of the rest and ate one.
On the third day he gave away half of the rest and […]
The diagram shows a tally chart and bar graph done by Adam and Mary for their class. Adam’s name had the most common initial letter and Mary’s the least common.
Make a list of the first names of all the learners in your class. What do you notice about […]
The graph shows the distance along a race track for two racing cars as they approach a bend in a race. Copy the table below, take readings from the graph and fill in the table for the first 10 seconds.
How far does each car go in the 3rd second? How far […]
If you know the sizes of the angles marked with coloured dots in the diagram which angles can you find by calculation? Explain your reasoning.
If you also know that AB and CD are parallel which angles can you find?
What extra information do you need to find all the numbered angles?
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