Essay

Review Practice ALGONQUIN COLLEGE Problems MATH FOUNDATIONS 1. Evaluate: a) 24 ( 23 - (8 - 7) + 12 X 7 b) 221 - (√64-2)3 + 64 ( 8 2. Round: a) 75.1472 to the nearest hundreds b) 41.412 to 1 decimal places 3. a) Change to an improper fraction: 24[pic] b) Change to a mixed number: [pic] 4. Simplify (leave your solution in fraction form): [pic] X [pic] ( [pic] 5. Simplify (leave your solution in fraction form): ([pic] + [pic] + [pic]) ( ([pic] ( 5) 6. Complete the table: |Fraction form |Decimal form |Percent form | |[pic] | | | | | | | | | |172.52 | | | | | | |78.91 | | 7. A statue weighing 150 kg is made of 55% gold. The rest of the statue is wood. How many kg of wood are contained in the statue' 8. A car’s weight including four passengers is 3,100 kg. If the passengers weigh 285 kg, what percent of the total weight was due to the weight of the car itself' 9. If [pic]of a pole is 80 m long, how long is the entire pole' 10. 320 tvs are to be delivered to 3 stores in the ratio of 4:5:7. How many tvs should each store get' 11. Calculate the lateral surface area and volume of the following cylinder: r = 2 m 121 6 m 12. Calculate the lateral surface area and volume of the following pyramid: H = 24 cm (slant height) A = 16 cm (altitude) 8 cm equilateral triangle with h = 15 cm 13. Convert the following: a) 8.5 m = km b) 1456 feet = inches c) 500 acres = square miles 14. Simplify: a) (3x + 4y) + x + (x - y) + 2x b) [pic]xy3(3x2 + 9yx2) 15. Solve the following equations: a) 3x3 + 4x3 = 448 b) 16 = 5w + 8w + 4 – 7w 16. Solve for the variable T: STR + R - Z = Q Measuring Units Conversion Tables The tables below provide for conversion from/to metric and imperial and US measurement systems. Length metric -> imperial 1 kilometre km = 1,000m = 0.6214 mile 1 metre m = 1m = 100 cm = 1.0936 yd = 39.37 inches 1 centimetre cm = 0.01m = 10 mm = 0.3937 inch imperial -> metric 1 inch [in] = 2.54 cm 1 foot [ft] = 12 inches [in] = 0.3048 m 1 yard [yd] = 3 feet = 0.9144 m 1 mile = 1760 yd = 5280 feet = 1.6093 km Area metric -> imperial 1 square kilometre = 1,000,000m = 100 ha = 0.3861 square miles 1 hectare ha = 10,000 square metres = 2.4711 acres imperial -> metric 1 square inch [in2] = 6.4516 cm2 1 square foot [ft2] = 144 in2 = 0.0929 m2 1 square yd [yd2] = 9 ft2 = 0.8361 m2 Capacity / Volume metric -> imperial 1 litre = 61.02 cubic inches = 0.9081 dry quart = 0.2642 gallons 1 cubic metre = 1,000 dm3 = 1.3079 cubic yards 1 cubic centimetre = 0.061 cubic inch imperial -> metric 1 fluid ounce [fl oz] = 28.413 ml 1 gallon [gal] = 8 pt = 4.5461 l 1 cubic foot [ft3] = 1,728 in3 = 0.0283 m3 USA measure -> metric 1 fluid ounce = 1.0408 UK fl oz = 29.574 ml 1 gallon = 0.8327 UK gal = 3.7854 l Mass metric -> imperial 1 metric ton t = 1,000 kg = 0.9842 long ton [UK] = 1.102 short tons 1 kilogram kg = 1,000 g = 2.2046 pounds 1 gram g = 1,000 mg = 0.0353 ounce imperial -> metric 1 ounce [oz] = 437.5 grain = 28.35 g 1 pound [lb] = 16 oz = 0.4536 kg The Metric System Equivalent Values Length 1 kilometre km = 1,000m 1 metre m = 100 cm = 10 decimetres 1 centimetre cm = 0.01m = 10 millimetres mm Area 1 square kilometre = 1,000,000m = 100 ha 1 hectare ha = 10,000 square metres Capacity / Volume 1 litre = 1000 millilitres [ml] 1 cubic metre = 1,000 dm3 1 cubic decimetre = 1,000 cm3 Mass 1 metric ton t = 1,000 kg 1 kilogram kg = 1000 grams g The U.S. System Equivalent Values Length 1 foot [ft] = 12 inches [in] 1 yard [yd] = 3 feet 1 mile = 1760 yd = 5280 feet Area 1 square foot [ft2] = 144 in2 1 square yd [yd2] = 9 ft2 1 acre = 4840 yd2 1 square mile [mile2] = 640 acres Capacity / Volume 1 cubic foot [ft3] = 1,728 in3 Mass 1 short ton [US] = 2,000 lb Lateral Surface Area and Volume Formulas Lateral Surface Area (SA): Cylinder SA = Circumference X height = 2(r X height Pyramid SA = 1.5 X slant height X length of base (equilateral triangle base) Volume (V): Cylinder V = Area of base X height = (r2 X height Pyramid V = [Area of base X altitude] / 3 (triangle base) = [(0.5bXh) X altitude] / 3 Solutions: 1. a) 86 b) 13 2. a) 75.15 b) 41.4 3. a) 171/7 b) 5 4/7 4. 22869/840 = 7623/280 5. 21800/252 = 10900/126 = 5450/63 6. 0.3061 30.61%; 17252/10000 = 8626/5000 = 4313/2500, 1.7252; 7891/100, 7891% 7. 67.5 kg 8. 90.8% 9. 320m 10. 80, 100, 140 11. lateral SA = 75.4 m sq V = 75.4 m cu 12. lateral SA = 288 cm sq V = 320 cm cu 13. a) 8500 km b) 17472 inches c) 0.78125 sq miles 14. a) 7x + 3y b) 6x6y3 + 18 x6y4 15. a) x = 4 b) w = 2 16. T = (Q – R + Z) / SR