Work Place and Apprenticeship 10
Final Review
Part Two
Units 4-6
Name:_____________
January 2011
That is why we review!!!
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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.
About 200 cocoa beans are used to make 1 lb of chocolate. Beans are shipped in 200lb sacks, which contain about 88 000 beans. How many 1.5-oz chocolate bars can be made from one sack of beans?
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Approximately 4693 bars can be made from one bag of cocoa beans
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 dosage of a certain medicine is 0.05 mg/kg of weight. Tom weighs 185 lbs. a) How many milligrams of the medicine should he take?
Tom should receive 4.2 mg of medicine. b) If the medicine costs $1.95/mg, what will his dosage cost?
The medicine will cost $8.19
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.
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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.
1.
Given each of the following angles, determine the size of the complement and/or the size of the supplement (if they exist).
Comp Sup a) 75° a)
5
°
95
° b) 43° b)
127
° c) 103°
37
° c) n/a d) 87°
77
° d) e) 300°
3
°
93
°
2. The complement of an angle is 0°. 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?
180°
WORKING WITH ANGLE BISECTORS
3. An angle is bisected. Each resulting angle is 78°. How big was the original angle?
156°
4. Calculate the size of the indicated angles. Name as many pairs of complementary and supplementary angles as possible.
4

X=70 °
Y=110°
X= 72 °
X=99 ° X=245 °
WORKING WITH ANGLES FORMED BY INTERSECTING LINES
5. In the following diagram, identify each of the following, and specify which lines and transversals you are using. a) an interior angle on the same side of the transversal as ∠ 6
∠ 8 using lines 3and 4 and transversal line 1 b) an angle corresponding to ∠ 2
∠ 4 using lines 3 and 4 and tranversal line 2 c) an angle corresponding to ∠ 4
∠ 7 using lines 1 and 2 and transversal line 4 d) an alternate interior angle to ∠ 4
∠ 9 lines 3 and 4 and transversal line 2
6.
In the diagram below, identify the relationship between each pair of angles.
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a) ∠ 7 and ∠ 8 alternate interior b) ∠ 2 and ∠ 7 corresponding c) ∠ 1 and ∠ 6 same side exterior d) ∠ 5 and ∠ 7 same side interior
WORKING WITH ANGLES FORMED BY PARALLEL LINES INTERSECTED BY A
TRANSVERSAL
7.
Consider the diagram below, in which ℓ1 is parallel to ℓ2. What are the measures of the three indicated angles? Explain how you reached your answers.
∠ 1 is 122 ْ –corresponding to ∠ 4
∠ 2 is 58 ْ - supplementary to ∠ 4
∠ 3 is 58 ْ - vertically opposite to
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.
∠ 2
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9.
Examine the following diagram. By how many degrees do the studs need to be moved in order to be parallel to each other? What direction do they need to move in? (The studs are indicated by the capital letters.)
The top of stud A must be moved 1° to the right, to change the 89° angle to 90°.
The top of stud B must be moved 1° to the left, to change the 91° angle to 90°.
The top of stud D must be moved 1° to the left, to change the 134° angle to 135°.
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
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∠ 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 8 m, 5 m, and 6 m. If the longest side of the second triangle is 5 m, what are the lengths of the other two sides?
The lengths of the other two sides of the smaller triangle are about 3.1 m and 3.75 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 2.5 cm:500 m. a) What distance is represented by a 12.5-cm segment on the map?
Set up a proportion to solve for the distance represented by 12.5 cm on the map. Let x represent the actual distance. A 12.5 cm segment on the map represents 2500 m.
b) How long would a segment on the map be if it represented 1.5 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 1.5 km to 1500 m. 1.5 km would be represented by a line 7.5 cm long on the map.
WORKING WITH SIMILAR TRIANGLES
6. In each of the diagrams below, ΔABC is similar to ΔXYZ. Find the length of the indicated side (to one decimal place).
8

Set up proportions to solve for the unknown sides x ≈ 3.9 cm
7. Given that ΔABC in similar to ΔRST, AB is 6 cm long, BC is 5 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. You are not given enough information to find the length of the third side, TR.
8. Assuming that the slope of a hill is constant, and that a point 100 metres along the surface of the hill is 4.2 metres higher than the starting point, how high will you be if you walk 250 metres along the slope of the hill?
Let h be the height of the hill. Set up a proportion to solve for h.
If you walk 250 m up the hill along the slope, you will be 10.5 m higher.
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