WorkPlace Math 10 Final Review (Solutions) Chapter 1

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1 WorkPlace Math 10 Final Review (Solutions) Chapter 1 1) If the price of an item is $50.00, what is the final price including GST and PST (5% each in Sask)? 50 x.10 = = $ ) If the price of an item is $150.00, what is the selling price (not with taxes) if the item is marked up 30%? 150 x.30 = = $ ) If a package of 12 pens cost $38.98, what is the cost of 1 pen (unit cost)? = $3.25 / pen 12 4) Loretta works as a surveyor near Burwash Landing, YT. Her map uses a scale of 2.5 cm:100 km. On her map, two sites she must visit are 7.4 cm apart. What is the actual distance between the two sites? 2.5cm 7. 4cm = 100x = y y = 296 km 100km y 5) The bakery in Regina is selling day-old buns at a 40% reduction. If the regular price is $4.79/doz, what is the reduced price including a 5% GST tax? 4.79 x.40 = = x.05 = = $3.01 6) James works for an industrial lighting company. He travels to Hong Kong to attend a trade show. James sees a fluorescent track lighting unit priced at Hong Kong dollars. What is the cost in Canadian dollars if $1.00 CAD is worth Hong Kong dollars? 1CAD y = x = y y = $ CAD HK HK Chapter 2 1) Write a short definition for any 5 of these terms: Wage, Salary, Overtime, CPP, EI, deductions, Federal Income Tax, Provincial Income Tax, Gross Pay, Net Pay, Commission, Contract, Piecework, Semi-Monthly, Bi-Weekly, Bonus, Shift Premium, Union Dues, Taxable Income, RRSP s, Pension Plan Contributions Wage = what you earn per hour Salary = what you earn per year Overtime = hours worked (usually over 40), you are paid at least time and a half (1.5) CPP = Canada Pension Plan (money put away for retirement) EI = Employment Insurance (money put away in case you can find a job) deductions = money taken off your pay cheque Federal Income Tax = money that goes to the Canadian government Provincial Income Tax = money that goes to the Provincial government Gross Pay = money you make before deductions Net Pay = money you make after deductions (money you get to spend) Commission = money earned based on how much product you sell Contract = money paid for an entire job Piecework = money paid for each item produced/fixed/etc. Semi-Monthly = twice a month (24 pay periods per year)

2 Bi-Weekly = every 2 weeks (26 pay periods per year) Bonus = extra pay Shift Premium = extra pay for special hours worked Union Dues = money paid to your union Taxable Income = Gross Pay - Union Dues - Pension Contributions RRSP'S = Registered Retirement Savings Plan (money put away by you for retirement) Pension Contributions = money put away by you and your employer for retirement 2) Normally, John works a 40 hr work week from Monday to Friday. However, this week he works an extra 3 hours on Monday and an extra 4 hours on Friday. John s regular wage is $15.00 per hour. If he receives time and a half for working overtime, what are his total wages for the week? 40 x 15 = 600 reg pay 7 x 15 x 1.5 = overtime pay = $ ) How much will you earn in a year as an apprentice metalworker if you are paid $ biweekly? 750 x 26 = $19, ) What is your annual salary if your weekly paycheck is $ ? 1200 x 52 = $62, ) If you make $250 weekly, how much does that convert to monthly? (Hint: The answer is not $1000) 250 x = $ ) Calculate the EI Premiums (at a rate of 1.78%) and the CPP payments (at a rate of 4.95% with $3500 exempt per year) for each of the following: CPP formula: 3500 numberofpayperiodsperyear = Exempt CPP = (GrossPay Exempt) x 4.95% a) John makes $500 biweekly. EI = 500 x.0178 = $ = ( )x.0495 = CPP CPP = $18.09 b) Jackie makes $1470 monthly. EI = 1470 x.0178 = $ = ( )x.0495 = CPP CPP = $ ) As a medical technician, Stephanie has been offered a job that pays $ per year and another job that pays $25.50 per hour. Assuming a 40-hour work week and all other conditions being the same, at which job will she earn more? x 40 x 52 = The $25.50 per hour job is better. Chapter 3 1) Convert the following to the nearest tenth. a) 240 inches = 20 feet (240 12=20) b) 5 feet 3 inches = centimeters (5 ft = 60 in, 63x2.54=160.02) c) 50 US gallons = litres (50x3.785 = ) d) 60 litres = 13.2 Imperial gallons ( =13.198) e) 20 fl oz (US) = ml (20x =591.47) f) 25 yards = 75 feet (25x3=75) g) 250 km = miles (250x.621=155.25)

3 2) If the radius of a cylinder is 5 metres and the height is 10 metres, what is the surface area? SA = 2πr 2 + 2πrh SA = 2(3.14)(5)(5) + 2(3.14)(5)(10) = 471 m 2 3) What is volume of the cylinder in question #2 above? V = πr 2 h V = (3.14)(5)(5)(10) = 785 m 3 4) If a rectangular box is 1.5 feet by 10 inches by 4 inches, what is the surface area in square feet? 10 in 12 = ft 4 in 12 =.3333 ft SA = 2(lw + lh + wh) SA = 2[(1.5)(.83333) + (1.5)(.3333) + (.83333)(.3333)] = 4.1 ft 2 5) What is the surface area of the box in question #4 in square inches? 1.5 ft = 18 in SA = 2[(18)(10) + (18)(4) + (10)(4)] = 584 in 2 6) What is the volume of the box in question #4 in cubic inches? V = lwh V = (18)(10)(4) = 720 in 3 7) 9'2" Add all the feet: = 35 ft + 9 for missing right side parts = 44 ft Add all the inches: = 138 in + 2 for right side = 140 in 140 in = 11 ft 8 in 44 ft + 11 ft 8 in = 55 ft 8 in 8) Hershy uses coloured wire to make a model of the Olympic symbol (5 interlocking circles). If each circle has a radius of 35 cm, how much wire does he need for the rings? Perimeter of Circle = 2πr = 2(3.14)(35) = x = 1099 cm 9) Mr. Kerbrat wants to cover an area of his backyard with gravel. If the dimensions of the area are 25 ft by 10 ft and he wants to spread the gravel 3 inches think, how many cubic yards of gravel will he need to order? V = lwh 25 ft 3= yds 10 ft 3= yds 3 in 36 = yds V = (8.3333)(3.3333)( ) = 2.3 yd 3

4 Chapter 4 1) Convert the following to the nearest tenth. a) 240 oz = 15 lb (240 16=15) b) 200 lb = 90.9 kg ( =90.9) c) 50 kg = 110 lb (50x2.2 = 110) d) 10.5 tons = 21,000 lbs (10.5x2000=21000) e) 20 tonnes = 20,000 kg (20x1000=20000) 2) Convert the following temperatures. a) 15 F = -9.4 C C=(15-32)x = b) -2 F = C C=(-2-32)x = c) 15 C = 59 F F=1.8(15)+32=59 3) A cake recipe says to bake at 350 F. Your oven only shows temperatures in degrees Celsius. At what temperature should you set your oven? C = (350-32)x = C 4) Rochelle gave birth to twin boys weighing 6 lb 5 oz and 5 lb 14 oz. What was their total weight in pounds and ounces? 6lb 5oz + 5lb 14oz = 11lb 19oz = 11lb + 1lb 3oz = 12lb 3oz 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? 65x42=2730lb = 3135lb 1.5tons = 3000lb No, it is not safe. 6) Irene needs 1.6 kg of tomatoes to make her grandmother s recipe for ratatouille. She has baskets of tomatoes that weigh 256 g, 452 g, 158 g, and 320 g. How many more grams of tomatoes does she need? =1186g 1.6kg = 1600g =414g 7) A truck weight 5.5 tonnes. If the truck is carrying 500 bushels of barley, what is the weight of the loaded truck? 45.9bu/t =10.89 t = 16.4 tonnes 8) How many bushels of canola can a cylindrical grain bin with a radius of 10 feet and a height of 20 feet hold? (Hint: You must find the Volume in cubic inches!) 10 ft = 120 in 20 ft = 240 in V=πr 2 h V=(3.14)(120) 2 (240) = 10,851,840 cu inches 10,851, = 4888 bushels (2220 cu in = 1 bushel)

5 Chapter 5 1) Determine the size of the following angles. 2) none 68 none 20 none none 3) An angle is bisected. Each resulting angle is 78. How big was the original angle? 78x2 = 156 4) A carpenter is inlaying different types of wood on a tabletop. What must be the size of angles a, b, c, and d? (Do not measure the angles with a protractor!) a=45 ( ) b=50 ( ) c=55 (alt int to 55 ) d=30 ( ) 75 here alt int to 75

6 5) 3 and or 1 5 and 7 6) In the diagram below, where t is the transversal, identify two pairs of each of the following angles. a) alternate interior angles 2 8 and 3 5 b) corresponding angles 1 5 and and 3 7 c) interior angles on the same side of the transversal 2 5 and 3 8 7) Calculate the sizes of the six angles indicated in the figure. 1 = 60 ( ) 2 = 120 (Vertical to 120) 3 = 60 ( ) 4 = 110 (180-70) 5 = 70 (Vertical to 70) 6 = 110 (180-70)

7 8) Find the true bearing from North from point A to point B and from point A to point C. N N B C A A Chapter 6 1) If ΔABC is similar to ΔXYZ and the following angle measures are known, what are the values of the remaining angles? A = 32 X = 32 C = 48 Z = 48 Y = 100 B = 100 2) 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 = =.875 Not the same ratios, so they are not similar ) Below are two rectangles with the measurements included. Are the rectangles similar? Why or why not? Yes, they are similar. All angles are 90. and the sides are in proportion. (1:2 ratio) 4) What is the scale factor of question #3 if the larger rectangle was the original drawing and the smaller rectangle was the newly created one? S.F.= new original 1 = 2 =.5

8 5) Show whether a rectangular prism that is 6 m by 10 m by 8 m is similar to one that is 4 m by 7 m by 5 m = 1.5 = 1.43 Not similar. Not the same ratios ) Calculate the value of side length x in the diagram if: a = 10 cm b = 6 cm E 10 x 10 x = = c = 5 cm C 15x = =x b x x = 4 A a B c D 7) Create a figure that is twice as big as the diagram below using any method you wish. The figures must be similar.

9 Imperial Conversions 1 foot = 12 inches 1 yard = 3 feet 1 mile = 1760 yards 1 mile = 5280 feet Imperial/SI Conversions 1 inch = 2.54 centimetres 1 centimetre =.394 inches 1 foot =.305 metres 1 metre = feet 1 yard =.914 metres 1 metre = yards 1 mile = kilometres 1 kilometre =.621 miles Perimeter of a Circle = πd or Perimeter of a Circle = 2πr Surface Area Formulas Rectangular Prism Cylinder SA = 2(lw + lh + wh) where l = length, w = width, h= height SA = 2πr 2 + 2πrh where r = radius, h = height Volume Formulas Rectangular Prism Cylinder V = lwh where l = length, w = width, h = height V = πr 2 h where r = radius, h = height

10 US Metric (SI) ml L 1 fl oz ml 1 pint (16 fl oz) ml.473 L 1 quart (2 pints) ml.946 L 1 gallon (4 quarts) ml L Imperial (British) Metric (SI) ml L 1 teaspoon 5 ml 1 tablespoon (3 teaspoons) 15 ml 1 cup 250 ml 1 fl oz ml 1 pint (20 fl oz) ml 1 quart (2 pints) L 1 gallon (4 quarts) L Trig Formulas a 2 + b 2 = c 2 OR a 2 = c 2 b 2 SIN of an angle = side opposite the angle hypotenuse side adjacent the angle COS of an angle = OR SOHCAHTOA hypotenuse TAN of an angle = side opposite the angle side adjacent the angle

11 Other Formulas Temperature 9 F C C = OR F = 1.8C (F 32) 9 = OR C =.5555(F 32) Mass/Weight 1 pound (lb) = 16 ounces (oz) 1 ton (tn) = 2000 pounds (lb) 1 metric tonne (t) = 1000 kilograms (kg) 1 kilogram (kg) = 1000 grams (g) 1 gram (g) = 1000 milligrams (mg) 1 kilogram (kg) = 2.2 pounds (lb) 1 pound (lb) =.4545 kilograms (kg) Mass and Volumes 1 bushel = 2220 cubic inches 1 tonne of barley = 45.9 bushels OR 45.9 bu/t (bushels per tonne) 1 tonne of wheat = 36.7 bushels OR 36.7 bu/t 1 tonne of oats = 64.8 bushels OR 64.8 bu/t 1 tonne of canola = 44.1 bushels OR 44.1 bu/t