Download Y10 Geometry practice test B

Form 4
GEOMETRY ASSESSMENT
Name ____________________
Form___________
Answer on the test sheet.
SHOW ALL YOUR WORKING,
and explain answers where required.
Read all questions carefully.
I
A
Part A
B
E
F
G
H
Betty builds her dog a kennel to live in. Her idea is like this diagram.
Help her draw some plans by constructing the front view of the kennel.
The line CD, the points A, B, and F have been drawn for you below.
C
D
1) Construct the perpendicular bisector of line CD in the diagram below.
Label the midpoint G. Show all construction lines.
(2 marks)
2) Construct a line perpendicular to the line CD, that goes through point F
Show all construction lines.
Hint: You should extend line CD.
(2 marks)
3) In the diagram below construct the triangle ABI such that line AI is 7.5 cm, and line BI is 5 cm.
Show all construction lines.
(3 marks)
4) In the diagram below measure the angle BCD
(1 mark)
.
A
B
E
.
C
.
F
.
.
.
D
Part B
Saw cut
Betty starts building the dog kennel.
She plans to cut a piece of timber on an
angle.
A
740
Timber
B
C
Calculate the unknown angles in the diagram, and give mathematical reasons for each angle.
(Give two reasons for angle A) Do NOT measure the angles.
5) Angle A = ______ Reason 1) ______________________________________________________________
6) Angle B = ______ Reason 1) ______________________________________________________________
7) Angle C = ______ Reason 1) ______________________________________________________________
Reason 2) ______________________________________________________________
(7 marks)
As Betty was building the kennel she noticed an offcut of timber that looked like a regular hexagon. She
measures an interior angle and gets 130 o Help her decide if this is true by answering the following questions.
8) a) Calculate the exterior angle of a regular hexagon. Explain what you calculate and why.
Exterior angle of a hexagon = _________ degrees.
Reason and explanation.
(1 mark)
_______________________________________________________________________________________
_______________________________________________________________________________________
____________________________________________________________________________
(2 marks)
b) Calculate the interior angle of a regular hexagon. Give two mathematical reasons for how you could
calculate the angle. (Hint: refer back to part 8a)
Interior angle of a hexagon = _________ degrees.
(1 mark)
Reason 1) ______________________________________________________________________________
Reason 2) ______________________________________________________________________________
____________________________________________________________________________
(2marks)
c) Is Betty correct? Is the offcut a regular hexagon? Circle the correct answer.
( 1 mark)
YES / NO
Part C
Betty decides to change the roof design to a
right angled triangle ABC with the dimensions
shown in the diagram.
(note that the diagram is not drawn to scale)
A
x cm
40 cm
D degrees
9) Use Pythagoras to calculate the length x.
Show all working and leave your
answer to 2 decimal places
C
85 cm
B
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
___________________________________________
x = ________________________ cm
(3 marks)
10) Use Trigonometry to calculate the angle D, using the 40 cm and 85 cm sides. Show all working .
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
___________________________________________
Angle D = _________________degrees (3 marks)
Betty finds she doesn’t have enough timber for the roof
in this design, so she decides to change the height of
the roof. She only has 90 cm of timber for the
sloping part of the roof.
A
90 cm
H cm
o
Estimate of 22
C
B
85 cm
11) Use Pythagoras to find the new height H of the roof.
Show all working
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
___________________________________________
H = _______________________ cm
(3 marks)
12) Betty Estimates that the angle of the roof is 22 o Use Trigonometry to calculate the length H, using this
angle estimate of 22 o and one of the 90 cm or 85 cm sides, to see if Betty’s Estimate is correct.
Show all working. Answer to 2 decimal places.
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
Height H = _________________ cm
PART A __________
8
Was Betty’s Angle Estimate Correct?
PART B ___________
14
PART C ___________
13
Yes / No
(4 marks)
TOTAL ___________
35