Math Summer Work for Students entering Honors Geometry
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1 Math Summer Work for Students entering Honors Geometry Complete the problems in this packet. SHOW ALL WORK and complete all work on separate sheets of paper. The work will be collected within the first two week upon returning to school. You will also be assessed on the material in the packet so be sure that you have reviewed the material. This is a review of various topics from Algebra I that are important to your success in Honors Geometry. Khan Academy is a great tutorial website that may assist you if you get stuck. You can use it for video tutorials or additional practice. In Khan Academy, click on Learn, and then Knowledge Map. Type topics into the text box to find them. You may also visit Mrs. Riesen s webpage of tutorials for assistance at: Have a great summer and see you in August!
2 . Solve each equation. Check your answer. a. 67 = 8n + 5 b. 2x + 23 = 49 c. 6 3(2x + 4) = 8 d. 5(t 3) 2t = Write an equation to model each situation. Then solve. a. The perimeter of a pool table is 30 ft. The table is twice as long as it is wide. What are the dimensions of the pool table? b. The length of a rectangle is 4 in. greater than the width. The perimeter of the rectangle is 24 in. Find the dimensions of the rectangle. c. The sum of four consecutive odd integers is 26. Find the four integers. 3. Use a proportion to solve. a. You are riding your bicycle. It takes you 28 min to go 8 mi. If you continue traveling at the same rate, how long will it take you to go 5 mi? b. A blueprint is in : 2 ft. The width of a building is 48 ft. What is the width of the building on the blueprint? 4. Find the slope and y intercept of each equation. a. y 2x = 3 b. y 6 = 2x 5. For each equation below, find the x and y intercepts. a. 2x + 3y = 6 b. y = 2.5 c. x = 3 6. Write an equation in slope intercept form for the line through the given points, or through the given point with the given slope. a. ( 5, 3) and ( 0, 9) b. ( 2, 3) and m = c. (, 2) and m undefined d. (7, 5) and m = 0 2
3 7. Find the slope of a line parallel to the graph of each equation. a. y = x + b. 6x + 2y = 4 c. x = 4 d. y 3 = 0 8. Write an equation for the line that is perpendicular to the given line and that passes through the given point. a. (6, 4) and y = 3x 2 b. ( 5, 5) and y = 5x Tell whether the lines for each pair of equations are parallel, perpendicular, or neither. a. y = 3x 8 b. 9x + 3y = 6 c. y = 4 d. x = 0 3x y = 3x + 9y = 6 y = 4 y = 2 0. Solve each system using substitution. Each may have a unique solution, no solution, or infinite solutions. Show your work. a. 3x + 2y = 6 b. 4x = 6y x + y = 6 2x 3y = 2. Solve by elimination. Show your work. a. 3x + 8y = 8 b. 8x 6y = 22 c. 8x 2y = 58 5x 6y = 39 4x + 6y = 94 9x y = 0 2. Use a system of linear equations to solve: a. Your teacher is giving you a test worth 00 points containing 40 questions. There are two-point and four-point questions on the test. How many of each type of question are on the test? 3. Solve each system of equations. (Use the processes you used in Exercises and 2) a. 0 x + 2 y = x + 3 y = 2 2 b. y = 5 3 x x + 5 y = 0 4. Simplify each expression. a b. (6)(2 2 ) c. ( 9) 2 d. 9 2 e
4 5. Simplify a. (2x x) (2 + 2x 2 5x) c. (x 3 + 3x) (x x) b. (3 + 5x 3 + 2x) (x + 2x 2 + 4x 3 ) d. (2x + 3) (x 4) + (x + 2) 6. Simplify a. (3x + 5)(5x 7) b. (x 5)(2x 2 7x 2) c. (4x 7)(2x 5) d. (y 2 4w 2 ) 2 e. (4a 3y) 2 f. (3y + 2a)(3y 2a) 7. Find the midpoint of segment XY given the endpoints. a. X(3, 8) and Y( 5, 3) b. X(7, 0) and Y(5, 8) 8. The coordinates of point B are given. The midpoint of segment AB is (5, 8). Find the coordinates of point A. a. B(0, 4) b. B( 2, 8) 9. Find the distance between the pair of points. Round your answer to the nearest thousandth. a. (7, 2) and (, 2) b. ( 3, 5) and ( 8, 3) 20. You want to make a rectangular banner measuring 2.5 ft. wide and 5 ft. high. To the nearest square yard, how much material do you need? 2. Rectangle BACD has coordinates B( 4, 3), A(, 7), C(3, 4), and D(0, 0). Find the slope of each side, then determine which sides are parallel, perpendicular, or neither. 22. Triangle QRC has coordinates Q(3, 6), R(3, 2), and C( 3, 2). Find the slope of each side, then determine which sides are parallel, perpendicular, or neither. 4
5 23. Graph each figure in Exercise 2 and 22 on the two coordinates planes, then find the perimeter and area of each figure. 24. You want to frame a picture that is 5 in. by 7 in. with a 2.5 in.-wide frame. a. What is the perimeter of the picture? b. What is the perimeter of the outside edge of the frame? c. What is the area of the picture? d. What is the area of the frame? 25. Solve each proportion. a. 5x+3 2x = 3 4 b. 3x+4 6 = 5x Solve each equation. a. 3x 5 = 2( x 5) b. 3x 3(4 + x) = 3 (3x + 2) Find the circumference and area of each circle. a. b. 5
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