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Multiple Choice: Choose the best answer and write it on your ANSWER SHEET (in second booklet) 1. Which of the following expressions is not equal to 36 36 a. 36 2 b. 2. The completely simplified form of a. 2 5 a. 23 5 9 8 c. d. 6 2 80 is: b. 2 10 3. The completely simplified form of 72 ? 3 c. 4 5 d. 8 10 c. 43 5 d. 83 5 40 is: b. 2 5 3 4. Express 5 2 in radical form. a. b. 5 3 5 c. 53 d. 1000 d. 3 52 5. Which of the following is equivalent to 2.53 4 ? a. 3 6. Express 62.5 x 4 7 b. 62.5 3 1000 as an exponent. 4 7 a. x 7 b. x 4 7. Express c. c. x4 7 d. 4x 7 6480 as an equivalent mixed radical in simplest form. a. 6 80 b. 9 80 c. 12 45 d. 36 5 c. whole d. irrational c. rational d. real 8. Which number set does belong to? a. natural b. rational 9. Which number set does -5 not belong to? a. natural b. integer Intro to Applied and Pre-Calculus Mathematics Page 1 10. Which of the following numbers is not both a perfect square and a perfect cube? a. 64 b. 729 11. What is y 3 2 b. 12. Express 8 a. 8 d. 4096 expressed in radical form? a. y 3 c. 1000 y 3 2 1 c. 3 d. y2 1 y3 as a power with a single exponent. 8 5 40 b. 8 13 c. 8 d. 64 3 5 13. What is the next number in the sequence 33 , 32 , 31 , 30 , ... ? a. 1 b. 3 2 1 3 d. 1 c. 0 d. 1 c. 14. Determine the value of 1 7 0 . 0 a. –8 b. –2 15. Which expression is not equal to 4? 27 a. 5 2 1 b. 2 2 1 16. Which value of x satisfies the equation x 2 a. 18 b. 9 c. 2 2 0 1 d. 4 1 1 ? 9 c. 4.5 d. 3 17. The root of a number can be represented by a. an integral exponent c. a rational exponent b. a negative exponent d. all exponents 18. Jean invests $800 in a fund. The investment doubles in value each year. The formula n A 8002 models the total value of the investment, A, in dollars, after n years. What is the value of her investment after 4 years? a. $12 800 b. $6400 Intro to Applied and Pre-Calculus Mathematics c. $3200 d. $800 Page 2 19. Which of the following referents is not appropriate to estimate the specified measurement unit? a. b. c. d. one rotation of a mountain bike wheel, foot height at waist level, metre width of paper clip, millimetre width of pinky finger, half an inch Use the figure to the right to answer questions 20 and 21. 20. What is the most appropriate SI measurement unit to use when estimating the perimeter of this figure? a. centimetre b. kilometre c. metre d. millimetre 21. Estimate the imperial measurement of the perimeter of the figure shown. a. 7 ft b. 7 in c. 7 mi d. 7 yd 22. Brenda states that her bedroom is 4.5 _____ wide. What unit is most appropriate for this measurement? a. centimeter b. meter c. kilometer d. millimeter 23. Ben measures the length of the street he lives on to be 90,000 cm. Which of the following measurements is the same length? a. 0.9 km b. 0.9 m c. 90 km d. 90 m 24. Find the volume of the figure at the right. a. 18 un3 b. 32 un3 c. 48 un3 d. 72 un3 e. 144 un3 f. 1728 un3 4 25. Find the surface area of the figure at the right. a. 48 un2 b. 51 un2 c. 60 un2 d. 66 un2 e. 84 un2 f. 96 un2 Intro to Applied and Pre-Calculus Mathematics 6 6 6 6 Page 3 26. Find the volume of this sphere with height 10 units. a. 79 un3 b. 314 un3 c. 524 un3 d. 628 un3 e. 1257 un3 f. 4189 un3 10 27. Find the surface area of this sphere with height 10 units. a. 79 un2 b. 314 un2 c. 524 un2 d. 628 un2 e. 1257 un2 f. 4189 un2 28. A cylinder and a cone each have a radius of 3 in. and a height of 8 in. What is the ratio of the volume of the cone to the volume of the cylinder? a. Vcone : Vcylinder = 1 : 2 b. Vcone : Vcylinder = 1 : 3 c. Vcone : Vcylinder = 1 : c. Vcone : Vcylinder = 1 : 1 29. If the base is a square with a side length of 10 and the slant height is 15, find the surface area of the pyramid. a. 85 b. 220 c. 310 d. 400 30. Find the volume, to the nearest cubic inch, of a cone whose radius is 12 inches and whose height is 15 inches. a. 2827 in 3 b. 2262 in 3 c. 565 in 3 d. 188 in 3 31. Find the volume of a hemisphere whose radius is 10 feet. Round answer to the nearest cubic foot. a. 419 ft 3 b. 1047 ft 3 c. 2094 ft 3 d. 4189 ft 3 32. Find the volume of the figure at the right. a. 300 ft 3 b. 110 ft 3 c. 80 ft 3 d. 100 ft 3 Intro to Applied and Pre-Calculus Mathematics Page 4 33. Find the volume of each solid. Round to the nearest tenth if necessary. cone: radius 5.1 km; height 8.5 km a. 45.4 km3 b. 231.5 km3 c. 289.4 km3 d. 57.9 km3 34. Find the volume of each solid. Round to the nearest tenth if necessary. triangular pyramid: triangle base, 8.6 km; triangle height, 7.5 km; pyramid height, 13.7 km a. 441.8 km3 b. 294.6 km3 c. 110.5 km3 d. 147.3 km3 35. Find the surface area of the figure at the right. Round to the nearest tenth if necessary. a. 500.7 km2 b. 479 km2 c. 638.6 km2 d. 1161.1 km2 36. Trigonometry is the study of ________. a. triangles b. angles c. trigonometric functions d. all of these 37. Which trigonometric function can be used to determine the length of the hypotenuse if the angle theta and the length of the opposite side are known? a. tangent b. cosine c. sine d. cosine inverse 38. Which trigonometric function can be used to determine the angle theta when the length of the opposite and adjacent sides are known? a. tangent b. sine inverse c. sine d. tangent inverse 39. Which trigonometric function can be used to determine the length of the adjacent side when the angle theta and the length of the hypotenuse are known? a. cosine b. cosine inverse Intro to Applied and Pre-Calculus Mathematics c. sine d. sine inverse Page 5 40. Solve for x in the right triangle pictured. a. 4.8 b. 5.2 c. 6.03 d. 10.02 e. 10.6 f. 13.3 Use for questions 40 and 41 y 8 37º 41. Solve for y in the right triangle pictured. x a. 4.8 b. 5.2 c. 6.03 d. 10.02 e. 10.6 f. 13.3 42. Solve for in the right triangle pictured. a. 53º b. 51 º c. 39º d. 37º e. 22º f. 14º Use for questions 42 and 43 5 43. Solve for in the right triangle pictured. a. 53º b. 51 º c. 39º d. 37º e. 22º f. 14º 44. Determine the length of x in the figure below, to nearest tenth of a metre. a. 5.7 m b. 7.0 m c. 6.3 m d. 8.2 m 4 Use for questions 44 and 45 45. Determine the length of y in the figure, to the nearest tenth of a metre. a. 5.7 m b. 7.0 m c. 6.3 m d. 8.2 m Intro to Applied and Pre-Calculus Mathematics Page 6 For questions 46-50 use the right triangle pictured. 46. Which of the following is equivalent to sin B ? a. 20 12 b. 20 16 c. 16 12 d. 12 20 e. 16 20 f. 12 16 47. Which of the following is equivalent to tan C ? a. 20 12 b. 20 16 c. 16 12 d. 12 20 e. 16 20 f. 12 16 C 20 48. Which of the following is equivalent to cos B ? a. 20 12 b. 20 16 c. 16 12 d. 12 20 e. 16 20 f. 12 16 A B 12 49. Which of the following is equivalent to cos C ? a. 20 12 b. 20 16 c. 16 12 d. 12 20 e. 16 20 f. 12 16 50. Which of the following is equivalent to sin C ? a. 20 12 b. 20 16 c. 16 12 d. 12 20 e. 16 20 f. 12 16 Intro to Applied and Pre-Calculus Mathematics Page 7 Match each statement to its corresponding term. A term may be used more than once or not at all. Please place your answers on the corresponding ANSWER SHEET! 1. all linear SI units are derived from this 2. based on British units of measure a. angle of elevation 3. a personal item used to approximate a measurement b. angle of depression 4. a system of measurement in which all units are based on multiples of ten c. base 5. the angle between the horizontal and the line of sight looking down to an object e. cosine ratio d. caliper f. cube root g. entire radical 6. h. exponent i. hypotenuse 7. j. imperial system k. inch 8. the side opposite the right angle in a right triangle l. index 9. the angle between the horizontal and the line of sight up to an object m. irrational number 10. a number that can be expressed as the product of two equal factors o. mixed radical 11. a number that can be expressed as the product of three equal factors q. perfect square 12. one of two equal factors of a number s. Pythagorean theorem 13. one of three equal factors of a number n. metre p. perfect cube r. prime factorization t. radical u. radicand 14. a number that cannot be expressed as a terminating or repeating decimal v. referent w. sine ratio 15. the number 3 in the expression 16. the number 25 in the expression 17. the product of 1 and a radical x. square root y. Système International d’Unités z. tangent ratio 18. the product of a rational number and a radical 19. consists of a root symbol, an index, and a radicand Intro to Applied and Pre-Calculus Mathematics Page 8 Answer Sheet Multiple Choice Matching 1. _____ 20. _____ 39. _____ 1. _____ 2. _____ 21. _____ 40. _____ 2. _____ 3. _____ 22. _____ 41. _____ 3. _____ 4. _____ 23. _____ 42. _____ 4. _____ 5. _____ 24. _____ 43. _____ 5. _____ 6. _____ 25. _____ 44. _____ 6. _____ 7. _____ 26. _____ 45. _____ 7. _____ 8. _____ 27. _____ 46. _____ 8. _____ 9. _____ 28. _____ 47. _____ 9. _____ 10. _____ 29. _____ 48. _____ 10. _____ 11. _____ 30. _____ 49. _____ 11. _____ 12. _____ 31. _____ 50. _____ 12. _____ 13. _____ 32. _____ 13. _____ 14. _____ 33. _____ 14. _____ 15. _____ 34. _____ 15. _____ 16. _____ 35. _____ 16. _____ 17. _____ 36. _____ 17. _____ 18. _____ 37. _____ 18. _____ 19. _____ 38. _____ 19. _____ Intro to Applied and Pre-Calculus Mathematics Page 9 Written Response: Show all of your work for full marks. Round answers to the nearest tenth unless otherwise specified. 1. Write equivalent expressions using rational exponents. Negative exponents ARE allowed. (4 marks) a. 9 114 b. c. x 1 7 w3 2. Write equivalent expressions in radical form. (2 marks) x 3 2 a. c. 8 3 1 3. Write each of the following terms in simplest mixed radical form. (4 marks) a. 75 b. c. 96 c. Intro to Applied and Pre-Calculus Mathematics 27 3 54 Page 10 4. Without using a calculator, arrange the following in order from least to greatest. Must show your work for full marks. (3 marks) 4 3, 6 2 , 5 6, 3 7, 5 5. Simplify each expression. Express answer using positive exponents. (10 marks) 3 c. 9 x y 4 4 2 9 2 0 a. 12 x y 6 x y 2 b. 4x y 3 4 Intro to Applied and Pre-Calculus Mathematics 9 4 93 1 12a 3 b 2 d. 2 5 4a b 3 Page 11 6. Simplify each expression. Express answer using positive exponents. (5 marks) 2 3 1 a. 5 2 5 3 23 y b. 4 12 y 6 7. Without using a calculator, solve: (3 marks) 4 19 36 8. A radioactive element has a half-life of one month. The formula for the amount of the n 1 element remaining is A m , where m is the mass of the element, in grams, and n is the 2 number of months. How much of a 740-g sample of the element a. remains after 6 months? Express your answer to two decimal places. (1 mark) b. was there 4 months ago? Express your answer to the nearest gram. (1 mark) Intro to Applied and Pre-Calculus Mathematics Page 12 9. Convert each of the following measurements. Show the conversions factors as a part of your work. Round to the nearest tenth when necessary. (15 marks) Imperial 1 in. 1 ft 1 yd 1 mi Metric 2.54 cm (0.0254 m) 0.3048 m (30.48 cm) 0.9144 m 1.609 km Metric 1 mm 1 cm 1m 1 km Imperial 0.0394 in. 0.3937 in. 3.281 ft (39.37 in. or 1.094 yd) 0.6214 mi (3 280.84 ft) a. 5 yd to ft b. 3 yd to inches c. 574 in to yd, ft, in d. 19 m to ft e. 6 ft 2 in to cm f. 5 km to mi and yd Intro to Applied and Pre-Calculus Mathematics Page 13 10. Find the surface area AND volume for each solid. a. (8 marks) b. radius of 3 in. (4 marks) Intro to Applied and Pre-Calculus Mathematics Page 14 c. (6 marks) 6 12 11. Solve for x in each of the following triangles. (4 marks) a. b. 12 11 x 24 x 7 Intro to Applied and Pre-Calculus Mathematics Page 15 12. Solve the triangle using only the given information. (5 marks) c x 7 y 4.5 13. A pilot starts his takeoff and climbs steadily at an angle of 12.2 . Determine the horizontal distance the plane has travelled when it has climbed 5.4 km along its flight path. (3 marks) 14. A ladder is leaning against a building. It makes a 65 angle with the ground when placed 6 feet away from the base of the building. How long is the ladder? (3 marks) Intro to Applied and Pre-Calculus Mathematics Page 16 15. You are in a lighthouse that is 50 m above sea level. You can see a ship in the bay at an angle of depression of 20 . Further out into the bay you can see a yacht, which is directly in line with the ship. The yacht has an angle of depression of 17 . (6 marks) a. Draw a diagram of the situation b. How far off shore is the ship? c. How far off shore is the yacht? d. How far apart are the ship and the yacht? Intro to Applied and Pre-Calculus Mathematics Page 17