Download 12_Practice_test

TRIGONOMETRY
Conditions: PRACTICE test. Closed book.
Calculators may be used.
THE SKATEBOARD RAMP
1.
Sally the skateboarder built a ramp with a metal sloping top
28cm
140 cm
The ramp is 140cm wide and 28cm high.
How long is the metal sloping top?
2.
On another ramp, the metal top is set at an angle of 34º to the ground. If
the ramp is 110cm wide, how high (x) is the ramp?
x
34°
110 cm
1
There are 2 grind rails in the skate park:
3.
One of the grind rails is 2.4m long and is placed
0.2m up a wall.
How far sideways does the rail reach?
0.2 m
2.4 m
?
4
0.3 m
The other rail is 2.1 metres long. It is rested against a wall and reaches
0.3 metres up the wall. What angle  does this rail make with the
ground?
2.1 m

The world’s biggest skateboard is 4.1 metres long
5.
The skateboard at an angle of 19º to the
ground. If the skateboard is 4.1metres long,
calculate the height front of the board.
4.1m
?
19º
2
6.
Another skateboard is 65cm long. The shadow is 50cm along the ground.
At what angle (θ) to the ground is the board?
65cm
θ
50cm
Some planks of timber are leaning against a wall
7.
If a plank is leaning 1600mm up the wall and resting 700mm away from
the wall, how long is the plank (p)?
p
1600mm
700mm
8.
Another plank is leaning 1550mm up the wall and is resting 600mm away
from the wall. What angle (θ) does the plank make with the wall?
1550mm
θ
600mm
3
9.
A piece of wood is shaped as in the diagram. How long is the base?
130 mm
33°
base
10. The skate boarder’s yard is a rectangular shape and is 6.12 metres long.
The width is not easy to measure because of the ramps in the way, but the
yard measures 8.45 metres from one corner to the opposite corner.
Calculate the width (w) of the yard.
8.45 metres
w
6.12 metres
4
Name:
Mathematics Assessment Activity
Unit Standard Number: 5236
TRIGONOMETRY
Element 1:
Level: 1
Version: 4
Credits: 2
Use Pythagoras’ Theorem and trigonometry to
Find unknowns in right angled triangles.
Unit Standard Completed
For markers use only
Situation
Questions
Element 1
1
1, 3, 7,10
Sufficiency all 3 situations
2
4, 6, 8
3
2, 5, 9
Sufficiency
3 out of 4
2 of 3
2 of 3
Situation met
5
Unit: 5236: TRIGONOMETRY Version
Assessment Schedule-
4
D2
Unit Standard 5236 Trigonometry Use Pythagoras’ Theorem and trigonometry to find unknowns in right angled triangles.
Element
Description
Use Pythagoras’
Theorem to find
lengths in right
angled triangles.
Use trigonometry
ratios to find
angles in right
angled triangles.
Situation
Refer
ence
Evidence
Judgment decision.

Finding length of hypotenuse
1
142.77cm
Accept any correct answer to any sensible rounding.

Finding length of another side
3
2.39m
Units not necessary

Finding length of hypotenuse
7
1746mm
Require 3 out of 4

Finding length of another side
10
5.83 m

Finding angles using sin
4
8.2º

Finding angles using cos
6
39.7º

Finding angles using tan
8
68.8º

Finding length using tan
2
74.2cm
Require 2 out of 3 correct
5
1.33m
Accept any correct answer to any sensible rounding.
9
109mm
Accept any correct answer to any rounding
Require 2 out of 3 correct
Use trigonometry
ratios to find sides
in right angled
triangles.


Finding length using sin
Finding length using cos
Sufficiency: To achieve unit 5236 requirements for element 1. All 3 situations to be met. Both angles and lengths need to be found using 2 of sin, cos, tan.
Both the hypotenuse and another side need to be found using Pythagoras theorem.
7