Circle and Angle Essay examples

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|Level 1 Mathematics and Statistics |
|91031 (1.6): Apply geometric reasoning in solving problems |

Credits: Four

You should answer ALL parts of ALL questions in this booklet.

You should show ALL your working.

If you need more space for any answer, use the page(s) provided at the back of this booklet and clearly number the question.

Check that this booklet has pages 2–11 in the correct order and that none of these pages is blank.


|For Assessor’s |Achievement Criteria | |
|use only | | |
|Achievement |Achievement |Achievement |
| |with Merit |with Excellence |
|Apply geometric reasoning in solving problems. |Apply geometric reasoning, using relational |Apply geometric reasoning, using extended abstract|
| |thinking, in solving problems. |thinking, in solving problems. |
|Overall Level of Performance |
You are advised to spend 60 minutes answering the questions in this booklet.

Question one

a) The triangle FGH is part of the frame for a climbing net.

HF=4.4m and the distance along the ground, HG=6.2m


i) Calculate the length of the side of the frame FG.

FG = _________________________________

ii) Calculate the angle the frame makes with the ground at FGH.

Angle FGH = b) A balloon, A, is tied to the ground by the rope labelled TA.


The wind is strong and causes the rope, TA, to make a straight line. The balloon is 40 m above the ground. The rope TA makes an angle of 26° with the ground.

Calculate the length of the rope, TA.

Length of rope TA = m

c) An orienteering course is planned from point O. The first leg to a point marked A is 120 m on a bearing of 030°. The second leg begins at A and ends at point B. B is on a bearing of 120° and 110 m from A.


i) Calculate the distance from O to B giving reasons for each step.

ii) Calculate the bearing of the starting point O from the finish B.

d) A shed in the playground has a roof that is 3.6 m long. 0.4 m of the roof overhangs the wall. The roof is at an angle of 40° to the horizontal. If the walls of the shed are 3.8 m high how far above the ground is the highest point on the roof and the width of the shed.


i) Calculate the height of the shed.

= m

ii) Calculate the width of the shed.

= m
Question twO

a) ABCD is an isosceles trapezium. Angle CBA = 78°. AD = BC.


Calculate the size of angle EDA giving reasons for each step of your answer.

b) ABCDE is a regular pentagon.


i) Calculate the size of angle ABC giving reasons for each step.

Angle ABC = ii) If many objects of the same shape fit together to form a pattern,