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## Grades 11 and 12 Always or sometimes

*By toni On 20 May, 2017 · Leave a Comment*

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.

Click here for Notes for Teachers

## GRADE 12 IN A SOCCER STADIUM

*By toni On 30 April, 2017 · Leave a Comment*

The angle of elevation from a point C on the ground, at the centre of the goalpost, to the highest point A of the arc, directly above the centre of the Moses Madhiba Soccer Stadium in Cape Town, is 64.75 degrees. The soccer pitch is 100 metres long (PQ […]

## Grades 10 to 12 Trig Lengths

*By toni On 23 July, 2016 · Leave a Comment*

In the diagram the line OS is perpendicular to the lines OR and PQ.

The line RS is a tangent at P to the circle centre O and radius 1 unit.

Find the lengths OQ, PQ, PS, OS, OR and RP.

If OS and OR lie on the coordinate axes, what are the coordinates […]

## Grades 10 to 12 Three By One

*By toni On 1 June, 2016 · 2 Comments*

This rectangle measures three units by one unit. The diagram shows three angles a, b and c.

How many ways can you prove that a + b = c?

What other interesting properties can you find?

## Grades 10 to 12 Flagpoles

*By toni On 9 March, 2013 · 2 Comments*

Two flagpoles are 30 metres apart. One has height 10 m and the other has height 15 m. Two tight ropes connect the top of each pole to the foot of the other.

How high do the two ropes intersect above the ground?

How many different methods can you find to solve this problem?

What […]

## Grade 7 or 8 – Seven Squares

*By toni On 5 January, 2013 · 3 Comments*

Seven squares are drawn inside each other. The centre points of each side of the outer square are joined to make a smaller square inside it and so on.

The centre square has the area of 1 (one) square unit.

Draw the diagram. You can download square dotty paper here.

What is […]

## Grades 11 to 12 – Geometric Trig

*By toni On 21 May, 2012 · 8 Comments*

This is a unit circle with a tangent at A.

The angle marked in the diagram is angle a.

Copy the diagram and find all the angles in terms of the angle a.

Find the six line segments in the diagram corresponding to sina, cosa, tana, 1/sina, 1/cosa and 1/tana.

Find the areas of […]

## Grade 9 and 10 – Making Sixty

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

Why does this fold create an angle of sixty degrees?

Make a centre crease down the length of the paper then open it up.

Next fold one corner over and onto the centre crease so that the fold line passes through the corner next to it (on the short side of the paper).

You […]

## Grade 9 and 10 – Tet Trouble

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

Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units.

Is it possible for a tetrahedron to have edges of lengths 10, 20, 25, 45, 50 and 60 units?

Can you write general rules for someone else to use to check whether […]

## Grades 9 to 12 – Is it possible?

*By toni On 17 January, 2012 · Leave a Comment*

Imagine you have a pencil, ruler, protractor and compass and you try to draw this triangle. Is it possible? Try to do the construction. What do you notice?

Can you give reasons for your answer to the question “Is it possible?”

Click here for The Notes for Teachers. This problem is adapted from […]

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