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Basic Algebra No calculator unless specified otherwise. 1. What numbers sum to 10? 2. 2 ex. 1 9, 2 8 10 3. 5 36 4. What coin combinations make a dollar? 31 ex. 4 quarters 5. 800/40 6. 14 7. 5 7 8 20 20 . Find . 6 . Find . 12 8. What time is it? 7:40 9. Draw the hour and minute hand of a clock at time 23 : 30 10. 4500 2500 7000 11. 12.34 0.27 12.61 12. 789 3945 5 13. How many zeros do the following large number have? a. Million 6 b. Billion 9 c. Trillion 12 d. Quadrillion 15 e. Googol 100 10googol 14. What is Googolplex? 15. Approximately how many stars are there in our universe? 16. 5 x 3 . Find x. 2 17. Mentally multiply to up to 15 15 18. True or False: 5 19. True or False: 20. True or False: 0 21. 0/1 22. 1 23. 1 sextillion 3 0 156 true 2 2 ex. 12 13 false true 0 0 0 0 24. Evaluate 32 27 undefined undefined 864 25. 2.3 0.8 26. Mentally evaluate 1200 30 27. Use long division to evaluate 168 7 28. Use long division to evaluate 200 3 a. Identify the quotient, remainder, and divisor. b. Express 200 c. True or False: 2 29. 2 ( 3) 31. 2 ( 3) 32. 2 2 33. 34. 35. 2 3 3 5 36. 2 37. 2 39. 4 3 5 2 3 2 38. 2 2 3 1 5 2 3 1 2/3 2 2 1 42. 2 3 43. 10 01 44. 210 45. 00 46. 4 47. 100 48. 1 49. 196 50. 0 1 5 40. ( 3 / 4) 41. ( 2)(5) 3 2 3 ( 1) 1 1 2 2 means 2 2 ( 2) ( 3)( 2) 7 1 5 30. 5 34 2 5 1/ 5 b 2 in the form a (( 1 / 3) ( 5 / 2)) c 1 2 but 2 1 2 means 2 1 2 1 51. 52. 4 9 16 169 53. List the first 5 perfect squares. 54. List the first 5 perfect cubes. 55. Is 64 a perfect cube? 56. Is 80 a perfect cube? 57. Estimate the square root of 30. 58. List the first 5 prime numbers (hint: 1 is not considered to be a prime number). 59. What is the prime factorization of 180? 60. What are the prime factors of 180? 61. What is the greatest common factor of 4 and 6? 62. What is the least common multiple of 4 and 6? 63. What is the greatest common factor of 4, 10, and 12? 64. What is the least common multiple of 4, 10, and 12? 65. Convert to a decimal number: a. 1/10 b. 1/3 c. 2/3 d. 5/3 e. 3/1000 66. Rewrite 1/2 as: a. A decimal number b. As a percent c. As a ratio 67. Express 0.2% as a: a. Decimal b. Fraction in lowest terms 68. Express 3:12 as a fraction in lowest terms. 69. Draw a jar of jelly beans where three is a ratio of 2:3 white to black jelly beans. 70. A string is cut into three pieces whose lengths form a ratio of 2:3:5. If the string was 200 cm long, how long are the pieces? 71. Which of the following is the best buy? Deal A: 500 mL of juice for $2.49. Deal B: 250 mL of juice for $1.89. Deal C: 4L of juice for $11. 72. You decide to build your own computer desktop. Click here to see how fast a new video card is. Which video card would you choose if you want a strong video card at the best value? Justify your answer by calculating the unit cost per PassMark performance unit P. 73. Suppose you earn a salary of $50,000 and are taxed at a rate of 20%. a. How much take home case do you make each day? (assume 365 days in a year). b. Suppose you have the following monthly bills: rent ($1,000), car bills ($500), student loans ($500). How much take home cash do you have left over each day? You still haven’t paid for other things including: food, clothes, utilities, travel, investments, etc. 74. There is a “buy one and get one free – equal to or less than in value” sale happening at your favorite clothing store. You buy three items at the following prices: shirt ($20), pants ($30), and a belt ($10). You qualify to get one of these items for free. With a tax rate of 12%, how much do you end up paying in total? 75. Suppose you have two Starbucks drinks a day at $6 for each drink. If you were to invest this money at a rate of 8% interest, how much money would you have by the time you retire? Try this compound interest calculator. 76. Simplify a. 1x 3x b. x c. 2 12 . Solve x. 77. 3x 78. Distance Speed Time formula: d s t a. You travel at the rate of 10 m/s for 50 seconds. How far do you travel? Specify units. b. You travel 40 km in 8 hours. What is your average speed? 79. Solve the following basic equations a. 3a a 10 b. 3x 2 7 c. z 5z 3z 2 80. Expand: a. 2(x b. 3) x) 2(3 c. 5(1 d. (t 4w ) 3) 81. Do you have to use cross multiplying to solve the following? a. x 3 2 5 b. c. d. e. f. g. h. i. p 5 2 t 3 4 5 3 5 x 7 1 3 2 x 1 5 w 2x 7 3 2 3 7 3x 5 x 2 2x 3 2 1 3 82. Draw a right triangle with square boxes on each side to show that c 2 a2 b 2 is a plausible equation. 83. Challenge: Prove the Pythagorean Theorem. 84. Solve x in the triangle below: 85. Solve x in the triangle below: 86. Use the Pythagorean Theorem twice to find the diagonal distance across a 3 4 12 m box. 87. 1 2 88. 1 2x (4 / 5)2 3 2 / 3(x 6) 89. Simplify a. (x 2 2x 4) (2x 2 b. (5x 7) (2x 3) c. 2n (n d. (15k 2 90. Represent (2x 3x 4) 7) 10k ) (5k ) 1) (x 2) using algebra tiles.