Geometry Honors Summer Packet 2024 - GBHS PDF

Summer Packet 2024 Geometry Honors GBHS Name: _____________________________________ Duffy Completion of this review packet will be the first required grade for all Geometry Honors’ students. Simplify, leave answers exact....

Summer Packet 2024 Geometry Honors GBHS Name: _____________________________________ Duffy Completion of this review packet will be the first required grade for all Geometry Honors’ students. Simplify, leave answers exact. 10000 1. 12 ÷ 2(1 + 2) 2. 2[3 – (8)23 + 4(6 – 2)] 3. (5−6)3 _____ ______ ______ 4. 2 - 31 5. 2 ÷ 11 6. √(10 − 4)2 + (−7 − 1)2 3 5 3 30 _______ ________ ________ Solve each equation. Show all work. 7. 5g + 8 = 3 + 2(3g – 4) g = ______ 8. - 5(2b – 3) = 7(3 – b) b = ______ ℎ 8 9. = h = ______ 12 5 𝑠−3 𝑠 10. = s = _______ 𝑠+3 𝑠+5 Working with linear equations. Show all necessary work. 11. Write the equation of the line in slope-intercept form that passes through (10, 21) and (15, 36) _________________ 12. Write in point-slope form, slope-intercept form, and standard form an equation that passes through (- 1, 2) with slope 4. ________________ __________________ ________________  1 13. Determine whether y = 4x + 5 and y = 4 𝑥 − 2 are perpendicular. _______ 14. Write the equation of the line in slope-intercept form that is parallel to the line y = - 4x + 2 and passes through (2, -4) _______________ 15. Where do the lines y = 5 and x = -7 intersect? ____________ Solve each word problem. 16. The number 312.8 is 34% of x. What is the value of x rounded to the nearest whole number? ______ 17. Five times one number added to another number is 32. Three times the first number minus the other number is 8. Find the numbers. _____ _____ 18. Sean bought a pen and received change of $4.75 in 25 coins, all dimes and quarters. How many of each kind did he receive? dimes ______ quarters ______ Graph each. 19. Graph each, then find the slope and y-intercept: a. y = x – 4 b. 5x + 10y = 20 c. y = -21 d. x + 5 = 0 ____________ _____________ _____________ slope __________ slope __________ slope _________ slope __________ y-int ________ y-int _______ y-int ________ y-int ______  20. Graph each quadratic, find the axis of symmetry, vertex and zeros. a. y = x2 + 2x – 15 b. y = x2 – 9 c. y = -3x2 – 12x - 12 axis ________ axis _______ axis _______ vertex ________ vertex ________ vertex _________ zeros _________ zeros __________ zeros __________ 21. Solve the system: x = 2y – 1 3x + y = 11 _______ 22. Solve the system: 5x – y = 17 3x – y = 13 _______ 23. The graphs of 2x + 3y = 5 and 3x + y = 18 contain two sides of a triangle. A vertex of the triangle is at the intersection of the graphs. What are the coordinates of the vertex? ________ 24. The measures of two sides of a triangle are given. If P is the perimeter, find the measure of the third side. P = 8x2 + 4x – 1 5x2 + x – 4 ______________ 3x + 2 Simplify each 25. (5x)o ______________ 26. (3a2b5)(-2ab3) ______________ 27. (-3x4yz5)3 ______________ 28. 4a4b8 + 2(ab2)4 + 4(a2b4)2 ______________ 29. 4a-3d2 8a2d-5 ______________ 30. (3r3t5)3 (-3r2t7)2 ______________ Find each product. 31. 3x2y(2x2y – 5xy2 + 8y3x2) ______________ 32. (2n + 3)(3n2 – 4n + 1) _______________ 33. (5y + 6)2 _______________ 34. (y + 2)3 _______________ Factor each polynomial. If it cannot be factored, write prime. 35. 10x2yz – 22x3y2z _______________ 36. 2xy – 4x + 3y – 6 _______________ 37. m2 + 12m – 28 _______________ 38. 5t2 + 17t – 12 _______________ 39. 6p2 – 20p + 16 _______________  40. 49a2 – 169 _______________ 41. x4 – 81 _______________ 42. 3x5 – 75x3 _______________ 43. 81c2 + 72c + 16 _______________ 44. 25x2 + 70x – 49 _______________ Simplify each, factor when necessary. 45. 8(x + 3)(x – 7)(x – 8) 46. x2 – 4 2(x – 7)(x + 3)(8 – x) x2 + 4x + 4 47. 5x2 – 80 48. 15x + 30 ÷ x2 + 5x + 6 10x2 – 20x – 80 5x2 – 5x – 10 x2 + x – 6 Solve each equation, check your solutions. 49. 12b2 – 8b = 0 _______________ 50. y2 + 4y = 45 _______________ 51. 9n2 + 6n = 3 _______________  −𝒃±√𝒃𝟐 −𝟒𝒂𝒄 Solve each equation by using the Quadratic Formula x =. Simplify any radical. 𝟐𝒂 Do not round. 52. 12x2 + x – 6 = 0 ______________ 53. x2 – 14x = 22 ______________ 54. 15n2 – 3 = 4n ______________ Simplify each expression. 55. √81 56. √80 57. √50𝑥 3 𝑦 2 ______________ √2 58. ______________ √5 59. 2√24 +√54 + 3√150 ______________ 60. (√11 − √6)(√2 + √33) ______________ 61. (6 - √3)2 ______________ 62. (2 - √7)(2 + √7) ______________ 3 63. √125 ____________ This packet is due as a grade the first day of geometry honors. Be prepared to test your knowledge on ALL of this material the first week of school.