Algebra 1 Honors 1st Semester Exam Review PDF

# Algebra 1 Honors - 1st Semester Exam Review ## Part 1 **1. Evaluate a - b for a = -3 and b = 4.** (-3) - 4 = -7 **2. 6(y + 8) - 5(8y - 10)** 6y + 48 - 40y + 50 = -34y + 98 **3. Simplify 9x^3 + 7x^2 + 4x^2 - x + 4x^3 - 3x^2** 13x^3 - 6x^2 - x **4. Write an algebraic expression for each stateme...

# Algebra 1 Honors - 1st Semester Exam Review ## Part 1 **1. Evaluate a - b for a = -3 and b = 4.** (-3) - 4 = -7 **2. 6(y + 8) - 5(8y - 10)** 6y + 48 - 40y + 50 = -34y + 98 **3. Simplify 9x^3 + 7x^2 + 4x^2 - x + 4x^3 - 3x^2** 13x^3 - 6x^2 - x **4. Write an algebraic expression for each statement below:** * The quotient of 2 and p, plus 7: 2/p + 7 * The difference of 2 times q and 3: 2q - 3 * 3 more than the product of 2 and q: 2q + 3 * 3 less than the quotient of 2 and q: 2/q - 3 **5. It costs $20 per hour to bowl and $3 for shoe rental. Write an algebraic expression to represent the cost for *n* hours of bowling.** 20*n + 3 **6. Lola spends one-third of her allowance on movies. She spends $8 per week at the movies. Write and solve an equation to determine Lola's weekly allowance *w*.** w/3 = 8 w = 24 **7. Use order of operations to simplify this expression: 10 - 2 - [3 - (3^2 + 2)]** 10 - 2 - [3 - (9 + 2)] 10 - 2 - [3 - 11] 10 - 2 - (-8) = 10 + 16 = 26 **8. Order the numbers below from least to greatest. -9; -7.4; -1; √6; 4; 8** -9; -7.4; -1; √6; 4; 8 **9. Evaluate the expression for w = 5 and x = 6. -3[(w - 6)^2 / x]^2** -3[(5-6)^2 / 6]^2 = -3[1/6]^2 = -3/36 = -1/12 **10. Classify each number using all that apply:** * -8: Integer, Rational * 2π: Irrational * √11: Irrational * -3[(5 - 6)^2 / 6]^2: Integer, Rational ## Part 2 **11. Simplify the expression: 4(10x + 6) - 10(9x + 9)** 40x + 24 - 90x - 90 = -50x - 66 **Solve Each Equation** **12. a/3 = 18** a = 54 **13. (p/5) = 10** p = 50 **14. -10 - h = 4** h = -14 **15. -3.2k = 16** k = -5 **16. (15g - 50) - 5g = 15** 10g - 50 = 15 10g = 65 g = 6.5 **17. 7n + 12 = 23** 7n = 11 n = 11/7 **18. -18 = 3(-z + 6) + 2z** -18 = -3z + 18 + 2z -18 = -z + 18 -36 = -z z = 36 **19. -8m - 4 = 4m - 2(6m + 2)** -8m - 4 = 4m - 12m - 4 -8m - 4 = -8m - 4 Identity **20. -32 + 18m + 4 = 4m - 2(6m + 2)** -32 + 18m + 4 = 4m - 12m - 4 -8m + 4 = -8m - 4 Identity **21. 2n + 4(n - 2) = 8 + 6n** 2n + 4n - 8 = 8 + 6n -8 = 8 No solution **22. 4(-3x + 4) = -2(6x - 8)** -12x + 16 = -12x + 16 Identity **23. Solve for y: 3z = x + y** 3z - x = y **24. Solve for y then find the value of y for each value of x. -5y + 10x = 5** -5y = 5 - 10x y = -1 + 2x When x = -2, then y = -5 When x = 0, then y = -1 When x = 2, then y = 3 ## Part 3 **26. What is the radius of a circle with a circumference of 5 cm? (Use 3.14 for pi)** C = 2πr 5 = 2 * 3.14 * r r = 5/6.28 **Solve Each Proportion Below:** **27. 4v - 2/8 = 2v - 6/4** 8v - 4 = 4v - 12 4v = -8 v = -2 **28. 4d + 1/3 = -3d - 27/-2** -8d - 2 = -9d - 81 d = -79 **29. Emmanuel was speaking with a friend from another country who told him that the speed limit on most highways is 100 kilometers per hour. Approximately what speed is this in miles per hour? (1 mile = 1.61 kilometers)** 100km / 1.61km/mi = 62mph **30. A healthy, adult cheetah can run 110 feet per second. How fast can a cheetah run in miles per hour? (1 mi = 5,280 ft)** 110 ft/sec / 5280 ft/mi = 0.0208 mi/sec 0.0208 mi/sec * 3600 sec/hr = 75mph **31. The triangles are similar. Find the missing side length x.** 9/x = 6/26 x = 39 **32. In the diagram of the park shown below, AADF ~ ABCF. The crosswalk at point A is about 20 yd long. A bridge across the pond will be built, from point B to point C. What will the length of the bridge be?** 20/x = 50/125 x = 50 yd **33. What percent of 92 is 23?** 23/92 = 25% **34. 68% of what number is 64.6?** 64.6/0.68 = 95 **35. A pair of pants that regularly costs $55 are on sale for 35% off the regular price. What is the sale price of the pants?** $55 * 0.35 = $19.25 $55 - $19.25 = $35.75 ## Part 4 **36. Five years ago you deposited a sum of money into a savings account which has earned $150 in interest. The interest rate for the account is 3% simple interest per year. How much money was originally deposited in the account?** I = PRT $150 = P * 0.03 * 5 P = $1000 **37. The Ragnier's purchased a house for $357,000. They sold their home for $475,000. What was the percent increase to the nearest percent?** ($475000 - $357000) / $357000 = 0.3285 0.3285 * 100 = 32.85% The percent increase is approximately 33% **38. A carpenter estimates the roof to be 375 square feet. The rectangular roof measures 18 feet wide by 22 feet long. What is the percent error? (Area = L*W)** Area = 18 ft * 22 ft = 396 sq ft (396 sq ft - 375 sq ft)/ 375 sq ft = 0.056 0.056 * 100 = 5.6% **39. Graph the inequality: 2 < c** On a number line, draw an open circle at 2 and shade the entire number line to the right of the circle. **40. Write the inequality for the given graph. (A number line is shaded to the left of an open circle on -3)** x < -3 **Solve and graph the inequalities below:** **41. ½c - 2 ≤ 1** 1/2c ≤ 3 c ≤ 6 On a number line, draw a closed circle at 6 and shade the entire number line to the left of the circle. **42. -½z + 9 ≥ 12** -1/2z ≥ 3 z ≤ -6 On a number line, draw a closed circle at -6 and shade the entire number line to the left of the circle. **43. 2(x - 4) - 3x ≤ -3** 2x - 8 - 3x ≤ -3 -x ≤ 5 x ≥ -5 On a number line, draw a closed circle at -5 and shade the entire number line to the right of the circle. **44. 8x - 8 ≤ 8(x - 1)** 8x - 8 ≤ 8x - 8 0 ≤ 0 All real numbers **45. 3r + 25 > 7r - 10 > 60** 3r > 7r - 35 -4r > -35 r < 35/4 r < 8.75 7r - 10 > 60 7r > 70 r > 10 The solution is: 10 < r < 8.75, which is an empty set. **46. 5x + 5 ≤ -10 and 2x ≤ 0** 5x ≤ -15 x ≤ -3 2x ≤ 0 x ≤ 0 The solution is: x ≤ -3 ## Part 5 **47. Ho Ho Ho** **48. -4 (x - 1) < 1** -4x + 4 < 1 -4x < -3 x > 3/4 **49. 9 (x - 1) - 3x ≤ 18 or x + 2 ≥ 13** 9x - 9 - 3x ≤ 18 6x ≤ 27 x ≤ 27/6 = 9/2 = 4.5 x + 2 ≥ 13 x ≥ 11 The solution is x ≤ 4.5 or x ≥ 11. **50. (7/3) y - 4 - 8 = 48** (7/3) y - 12 = 48 (7/3) y = 60 y = 60 * (3/7) y = 180/7 **51. Janelle has 29 coins in her collection. Her goal is to have at least 45 coins by the end of the year. Write and solve an inequality to find out how many more coins Janelle must add to her collection to meet or exceed her goal.** 29 + x ≥ 45 x ≥ 16 **52. Complete the following frequency table:** |Ages|Frequency| |---|---| |41-50|3| |51-60|10| |61-70|4| **53. Find the mean, median, and mode of the data.** * Mean = (42 + 51 + 56 + 55 + 51 + 54 + 51 + 60 + 62 + 43 + 55 + 56 + 61 + 52 + 69 + 64 + 46 + 42 + 43 + 46 + 51 + 51 + 52 + 54 + 55 + 55 + 56 + 56 + 60 + 61 + 62 + 64 + 69) / 37 ≈ 54.6 * Median = 55 * Mode = 51 ## Part 6 **54. Make a box-and-whisker plot using this data:** (This would require a plot which cannot be created in markdown. You can use a drawing tool to create the plot based on the given data set.) **55. Tony brings 10 movies to a movie club. The group is going to select 6 out of the 10 movies to watch. How many different groups of movies could the group select?** 10C6 = 10! / (6! * 4!) = 210 **56. A website requires a 3-digit password consisting of letters which cannot be repeated. How many passwords are possible?** 26 * 25 * 24 = 15600 **You spin a spinner that has 8 equally-sized sections numbered 1 to 8. Find each probability.** **57. P(7)** 1/8 **58. P(odd number)** 4/8 = 1/2 **59. P(multiple of 2)** 4/8 = 1/2 **60. P(less than 6)** 5/8 **61. P(multiple of 3 or multiple of 2)** 3/8 + 4/8 - 1/8 = 6/8 = 3/4 **You choose a marble at random from a bag containing 3 blue marbles, 5 red marbles, and 2 green marbles. You replace the marble and then choose again. Find each probability.** **62. P(both blue)** 3/10 * 3/10 = 9/100 **63. P(blue then green)** 3/10 * 2/10 = 6/100 **64. P(both green)** 2/10 * 2/10 = 4/100 **You choose a marble at random from a bag containing 5 orange marbles, 3 green marbles, and 2 blue marbles. You pick a second marble without replacing the first. Find each probability.** **65. P(orange then green)** 5/10 * 3/9 = 15/90 **66. P(both green)** 3/10 * 2/9 = 6/90 **67. P(green then blue)** 3/10 * 2/9 = 6/90