2016 Geometry Honors Summer Packet
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1 Name: 2016 Geometry Honors Summer Packet This packet is due the first day of school. It will be graded for completion and effort shown. There will be an assessment on these concepts the first week of school. Please take the time to answer each question thoughtfully and carefully. Include all work that is necessary and circle your final answer. If you are unsure how to answer a question, use your resources; your notebook from Algebra I, Google, Khan Academy, etc. The topics that are covered in this packet are essential to your success in Geometry. They come directly from the Pre-Algebra and Algebra I curriculum and should be familiar. Part I: Points, Slopes, and Equations of Lines 1. Write an equation in Slope-Intercept Form (y = mx + b) for a line that goes through the points (1, -2) and (5, 6). 2. Write an equation in Slope-Intercept Form that has a slope of 3 and goes 2 through the point (-4, 5). 3. Write an equation in Slope- Intercept Form that is parallel to the equation y = 3x 4 and goes through the point (7, 6). 4. Write an equation in Slope-Intercept Form that is perpendicular to the equation y = 3x + 1 and goes through the point (6, -8).
2 5. Rewrite the equation y = 1 x + 5 in Standard Form (Ax + By= C) where A, B, 2 and C are integers. 6. Rewrite the the equation y = 1 2 x + 5in Point-Slope Form (y y 1 = m(x x 1 )). 7. Solve the following equations algebraically. Show all work in order to receive any credit. Check your final answer. a. 3(y 5) = 12 b. 6(x 4) + 5 = 11 c. 1 2n 9 (28x 8) = 7x 2 d. = n The length of a rectangle is 11 cm more than its width. The perimeter is 90 cm. Find the length and width of the rectangle. Show all work algebraically in order to receive any credit.
3 9. Solve and graph the following inequalities on a number line. Show all work in order to receive any credit. a. 2x b. 3x + 2 5x Graph a line that goes through the points (5,-2) and (-6, 10) and give the equation in Standard Form of that line. Equation: Part 2: Algebraic Skills Perform the operations below without a calculator. Write your final answer in simplest form.
4 (3x 3-5x) + 20x 16. Evaluate -6s 3-4t 2, for s = 2 and t = -3. Simplify. Show all work. 17. (a + 5)(a + 3) 18. (3x - 8)(x - 6) 19. (5x + 4)(5x - 4)
5 20. (x + 6) (y - 2) (3 - g)(2g + 3) 23. 5x(x + 6) 24. 2y(y 2 + 3y - 4) 25. (3 - g)(g - 3) Factor the expression. If the expression cannot be factored, say so. 26. x 2 + 6x x 2 + 3x x 2-13x x 2-4x x 2 + 2x x 2-11x + 28 Part 3: Basic Geometry Knowledge (Show all work in order to receive any credit.) 32. A rectangle has length of 10 and width of 4. Find its: area perimeter
6 33. A circle has diameter of 8. LEAVING YOUR ANSWERS IN TERMS OF π, find its: area circumference 34. A right triangle has legs 9 and 12. Sketch this figure: Find the hypotenuse. (Hint: Use the Pythagorean Theorem.) Find its perimeter. Find its area. 35. A square has an area of 169 square centimeters. How long is one of its sides? Find its perimeter 36. A regular polygon is a figure in which all of the sides have the same length and all of the angles have the same measure. Find the perimeter of a regular pentagon in which one side has a length of 5x. 37. Using this figure: Find its perimeter. Find its area.
7 38. Find the area of ΔABC. 39. Find the area of ΔABC. Given: AD = 10, DC = 4, DB = A triangle has vertices (-3,3), (2,7), and (5,3) Draw the triangle on the coordinate plane on the right. Find the area of the triangle.
8 41. One side of an equilateral triangle has length 15 inches. What is its perimeter? 42. The length of one side of a square is ⅗ of a foot. Find its area. Find its perimeter.
9 The sketch below shows three circular disks cut from a rectangular sheet of metal. EXPLAIN IN A SENTENCE how you can tell that the sketch is labeled INCORRECTLY. 45. A geometry classroom is square-shaped and has a perimeter of 88 feet. What is its area?
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