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Work Place and Apprenticeship 10
Final Review Part Two
Units 4-7 January 2016
Chapter 4 Mass, Temperature, and Volume
WORKING WITH TEMPERATURE
1. Firefighters can estimate the temperature of a burning fire by the colour of its flame.
A clear orange flame has a temperature of about 2190°F. How hot is this in degrees
Celsius?
The flame is 1198.9°C.
2. The normal temperature for a dog is from 99°F to 102°F. Ashley’s dog has a
temperature of 40°C. Convert the temperature to Fahrenheit to calculate if it falls
within the normal range.
Ashley’s dog has a temperature of 104°F. This is outside (higher than) the normal range.
WORKING WITH WEIGHT
3. Rochelle gave birth to twin boys weighing 6 lb 5 oz and 5 lb 14 oz. What was their
total weight?
The babies’ combined weight was 12 lb 3 oz
4. The weight of water is approximately 2 pounds 3 ounces per litre. How much will 8
litres of water weigh?
8 litres of water weigh 17 lb 8 oz.
5. An elevator has a maximum load restriction of 1.5 tons. Is it safe for two tile layers
weighing 195 lb and 210 lb to load it with 65 boxes of tile weighing 42 lb each?
The weight of the load is about 1.6 tons, so it is unsafe and over the acceptable limit of 1.5 tons.
6. 6. Kurt is planting wheat at the rate of 90 pounds per acre. If he plans to plant 320
acres of wheat, how many tons of wheat will he use?
Kurt will use 14.4 tons of wheat.
7. An 18-oz jar of peanut butter costs $3.29, a 28-oz jar costs $4.79, and a 2.5-lb jar
costs $5.99. Which is the best buy?
$5.99 for a 2.5-lb jar is the best buy.
8. You buy 4 loaves of bread for $3.99 each that are 500 grams per loaf. One of the
loaves of bread is moldy, so you have to throw it out. What was your true cost per
kg for the bread?
Figure out how much you paid in total and how many kg you got in total and divide.
$10.64/kg
9. Mark bought 8 bags of sand, each weighing 25 lb, for $1.68/bag. One bag ripped
and he lost all the sand. What was his true price per pound of sand?
The true cost of the sand is $0.08/lb.
WORKING WITH SI UNITS OF MASS
10. What is the total weight of a loaded truck if the truck weighs 2.6 tonnes and it is
loaded with 15 skids of boxes that weigh 210 kilograms each? Give your answer in
tonnes.
The total weight of the loaded truck is 5.75 tonnes.
WORKING WITH MASS/WEIGHT CONVERSION BETWEEN IMPERIAL AND SI
11.A recipe calls for 180 g of flour. How much is this in ounces?
180 g equals about 6.3 oz.
12. A baby weighed 7 pounds 12 ounces at birth. How much did it weigh in grams?
The baby weighed about 3522.4 g.
13. The weight of a car is listed as 1250 kg. How many tons is this?
1.375 tons
14.Karen is making a batch of potato soup. She needs 8 potatoes, and each potato
weighs about 375 g. How many pounds of potatoes does she need?
Karen will need 6.6 pounds of potatoes.
WORKING WITH CONVERSIONS BETWEEN MEASURES OF VOLUME AND WEIGHT
15. If Jore gets $195.76 per metric ton for wheat, how much does he earn per bushel
(conversion factor 36.744 bu/t)?
Jore earns $5.33/bu.
16. How many tonnes of rye are there is 900 bushels if there are 39.368 bushels/tonne?
The weight of rye is about 22.9 tonnes.
WORKING WITH CONVERSION BETWEEN SI AND IMPERIAL UNITS OF WEIGHT
1 lb ≈ 0.45 kg
1 oz ≈ 28.3 g
1 tn ≈ 0.9 t
17. A crane can lift a maximum of 5 t. Sandstone weighs about 150 lb per cubic foot, and
a container contains 70 cubic feet of sandstone. Can the crane be used to load the
container onto a train?
The sandstone weighs about 4.8 t, which is less than the 5 t lifting limit of the crane. Yes, the
crane can be used to load the container onto the train.
Chapter 5 Angles and Parallel Lines
1. Given each of the following angles, determine the size of the complement and/or
the size of the supplement (if they exist).
a) 75°
b) 43°
c) 103°
d) 87°
e) 300°
2. The complement of an angle is 0°.
Comp
Sup
a)
5°
95°
b)
37°
127°
c)
n/a
77°
d)
3°
93°
e)
n/a
n/a
a) What is the size of the angle?
90°
b) What is the size of the supplement of the angle?
90°
WORKING WITH ANGLE BISECTORS
3. An angle is bisected. Each resulting angle is 42°. What is the complement of the
original angle?
Original angle is 84o so the complement is 6o
4. Calculate the size of the indicated angles. Name as many pairs of complementary
and supplementary angles as possible.
Angle Size
Complementary Supplementary
Size after Original
Angle is Bisected
o
o
o
15
75
165
7.5o
75o
15o
105o
37.5o
60o
30o
120o
30o
140o
N/A
40o
70o
WORKING WITH ANGLES FORMED BY INTERSECTING LINES
5. In the following diagram, identify each of the following:
a) an interior angle on the same side of the transversal as ∠6
<4
b) an angle corresponding to ∠2
<6
c) an angle corresponding to ∠4
<8
d) an alternate interior angle to ∠4
<5
6. In the diagram below, identify the relationship between each pair of angles.
(Vertically Opposite, Corresponding, Alternate Interior, Alternate Exterior, Interior
on the same side of the transversal, Exterior on the same side of the transversal,
Supplementary)
a) ∠7 and ∠6 – Vertically Opposite
b) ∠2 and ∠7 – Alternate Exterior
c) ∠1 and ∠3 - Supplementary
d) ∠6 and ∠3 – Alternate Interior
WORKING WITH ANGLES FORMED BY PARALLEL LINES INTERSECTED BY A
TRANSVERSAL
7. Consider the diagram below, in which ℓ1 is parallel to ℓ2. If ,<1 is 1350, what are
the rest of the angles?
<2, <3, <6, <7 = 45o
<4, <5, <8 = 135o
8. If ℓ1 and ℓ2 are parallel and are intersected by transversals t1 and t2, what are
the measures of the indicated angles? Solve for the measures in the given order,
stating your reasoning.
Chapter 6 Similarity of Figures
WORKING WITH SIMILAR FIGURES
1. If ΔRST is similar to ΔLMN and angle measures of ΔLMN are as follows, what are
the angle measures of ΔRST?
∠L = 85°=∠R
∠M = 78°=∠S
∠N = 17°=∠T
2. If ΔABC is similar to ΔXYZ and the following angle measures are known, what are
the values of the remaining angles?
∠A = 32°=∠X
∠C = 48°=∠Z
∠Y = 100°=∠B
3. Two triangles are similar. One has sides of 10 m, 7 m, and 8 m. If the longest side
of the second triangle is 5 m, what are the lengths of the other two sides?
3.5 m and 4 m
WORKING WITH SIMILAR POLYGONS
4. One cylinder has a radius of 25 cm and a height of 35 cm. Another cylinder has a
radius of 30 cm and a height of 40 cm. Are the cylinders similar? Show your
calculations.
Calculate the proportions of the dimensions of the smaller cylinder to the larger.
Since the proportions are not the same, the two cylinders are not similar.
5. The scale on a map is 3.5 cm:800 m.
a) What distance is represented by a 14 -cm segment on the map?
Set up a proportion to solve for the distance represented by 14 cm on the map. Let x represent the
actual distance. A 14 cm segment on the map represents 3200 m.
b) How long would a segment on the map be if it represented 2.4 km?
Let y be the length of the line on the map. Set up a proportion to solve for y, the
segment
on the map. In the proportion, convert 2.4 km to 2400 m. 2.4 km would be represented by a line 10.5
cm long on the map.
WORKING WITH SIMILAR TRIANGLES
6. What is the height of X?
3.0 m. Find scale factor or set up a proportion to solve.
7. Given that ΔABC in similar to ΔRST, AB is 11 cm long, BC is 7 cm long, and RS is 8
cm long, find the length of a second side in ΔRST. Can you find the length of the third
side? Explain your answer.
Set up a proportion to solve for side ST to be 5.1 cm. You are not given enough information to
find the length of the third side, TR.
Chapter 7 Trigonometry of Right Triangles
1. A 3 m ladder is leaned up against the side of a house so that it is 2.5 m high up
the side of the house. How far away from the house is the ladder placed?
Use Pythagorean Theorem to find that the ladder is 1.7 m away from the side of the house.
2. A rope is tied to a tree 9 ft up the trunk. The rope reaches 7 ft out from the
base of the tree. What is the length of the rope?
Use Pythagorean Theorem to find that the rope is 11.4 ft away from the base of the tree.
3. A plane travels 12 km along its flight path while climbing at a constant rate of
8°. What is the vertical change in height during this time?
Use the Sine Ratio. The plane travelled about 1.67km
4. A chute from an open window to the ground makes an angle of 52° with the
side of a building. If the window is 18 metres from the ground, how long is the
chute?
Use the Cosine ratio. The chute is about 29.2 m long.
5. A tree casts a shadow that is 10 metres long. If the angle of elevation to the
top of the tree from the ground at the end of the shadow is 60°, how high is
the tree?
Use the Tangent ratio. The tree is about 17.3 m tall.
6. A tree casts a shadow that is 3.5 m long on the ground. The tree is 5.0 m tall.
What is the angle of elevation from the shadow on the ground to the top of
the tree?
55o. Use the tan ratio and then second function tan.
7. What is the angle of elevation of a ramp if the ramp is 15 feet long and the
vertical height of the ramp is 3.0 ft?
11.5o use the sine ratio and then second function sin.
8. What is the angle of elevation of a ramp that is 13 m long if it covers a
horizontal distance of 10 m?
40o use cosine ratio and then second function cos.
9. Solve each triangle Completely (all sides and all angles):
a. Bottom is 13.4 m, Hypotenuse is 15.9 m and the other angle is 48o
b. Bottom is 10.7 in, Side is 22.9 in, Angle is 65o
c.
Hypotenuse is 23.6 m, side is 17.8 m,
angle is 41o