Science Park High School Math Summer Assignment

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1 Name: Science Park High School Math Summer Assignment Review of Math Skills for Students Entering Geometry and/or Algebra II DUE THE FIRST DAY OF SCHOOL The problems in this packet are designed to help you review topics that are important to your success in Geometry and/or Algebra II. We expect that you come to class knowing this material and ready to continue learning. Answer all questions in the space provided. SHOW ALL WORK. This assignment will be collected on the first day of school. It will count as the first grade of the cycle. Tutorials: Enjoy your summer. See you in September! -Science Park High School Math Department

2 PART I - Multiple Choice: Show all of your work for these questions in the space provided below. Then, place a circle around the letter that best answers the question. You will be graded on the accuracy of your answers. However, work must be shown to receive full credit (-5) = (a) -26 (b) 26 (c) 14 (d) 10 (e) none of these 2 5a 4b b a 5 5a (a) 2 24b 24b (b) 5 5a 2 (c) 10b 3a (d) 10 3a (e) none of these 3. (2y 3) 2 = (a) 4y b) 4y 2 6y + 9 (c) 4y 2 12y + 9 (d) 4y 2 +12y + 9 (e) none of these 4. One number is 8 less than another. If twice the larger number is equal to four times the smaller, what is the smaller number? (a) 8 (b) 4 (c) 12 (d) 16 (e) none of these

3 5. 3x 2x x (a) 10 x 3x (b) 10 (c) 17x 20 (d) 33x 20 (e) none of these 6. Which of these are equivalent? I. x > 3 II. x 4 < 8 III. 2x < 8 (a) I and I only (b) I and III only (c) I, II, and III (d) none of them 7. If x 3y = 8 and y = 2x + 1, then x = (a) -1 (b) 11 5 (c) 5 7 (d) 1 (e) none of these 8. Solve the equation 3(x 2) + 4 = 4(x 2) + 1 (a) 3 (b) -17 (c) 5 (d) -7 (e) none of these

4 9. The daily cost of renting a car is $30 plus $0.10 per mile. If John paid $52.50 for a 1-day rental, how many miles did John travel? (a) 23 (b) 225 (c) 525 (d) 825 (e) none of these 10. Simplify (x 2 7x + 10) + (3x 2 14x + 33) (x 2 + 4x 4) (a) 3x 2 25x + 47 (b) 3x 2 17x + 39 (c) 5x 2 25x + 47 (d) 5x 2 17x + 39 (e) none of these 11. Find the area of the rectangle written as a simplified polynomial 5x + 9 2x 5 (a) 14x + 8 (b) 7x 2 + 4x 45 (c) 7x 2 7x + 45 (d) none of these 12. Find the slope of the line that contains (-7, -5) and (-4, -6) (a) -13 (b) -3 (c) -1 / 3 (d) 1 (e) none of these

5 13. Which best describes the relationship between the lines with equations 8x + y = 6 and 16x + 2y = 0 (a) Perpendicular (b) Parallel (c) Same line (d) Neither parallel nor perpendicular Find f(-2) given that f(x) = 4x 2 2x - 25 (a) 20 (b) -5 (c) -29 (d) -17 (e) none of these What is the equation of a vertical line through (-8, 10)? (a) y = -8 (b) y = 10 (c) x = -8 (d) x = 10 (e) none of these Find the point-slope form of an equation of the line that passes through the given point and has the given slope (-3, -2) m = ½ (a) y + 2 = ½ (x 3) (b) y 2 = ½ (x 3) (c) y 2 = ½ (x 3) (d) y + 2 = ½ (x + 3) Find the greatest common divisor of 20 and 36. (a) 180 (b) 108 (c) 56 (d) 4 (e) 2

6 18. Convert 2¼ yards to inches. (a) 27 in. (b) 36 in. (c) 72 in. (d) 81 in. (e) 96 in. 19. What is the midpoint of the line segment that runs between ( 3, 1) and (1, 5)? (a) ( 2, 2) (b) ( 2, 2) (c) ( 2, 6) (d) (2, 6) (e) ( 1, 3) 20. One factor of 3x 2-6x + 9 is (a) x 2-2x + 3 (b) x 2-6x + 9 (c) x 2-2x + 9 (d) x + 3 (e) none of these Which of the following is equivalent to (p x ) y? (a) p x+y (b) pxy (c) yp x (d) p xy (e) none of these The perimeter of the figure with semicircular top is: (a) 21 (b) (c) (d) (e) none of these

7 23. In the triangle shown below the measure of angle C is (x ). The measure of angle A is (a) (60 x) 0 (b) (90 x) 0 (c) (120 x) 0 (d) (x 60) 0 (e) (x 120) Lines l and m intersect line k. Assume angles 4 and 7 are supplementary. Then we can conclude that: (a) lines l and m are perpendicular (b) angle 8 and angle 1 are congruent (c) lines l and m are parallel (d) angles 1 and 2 are complementary (e) angles 1 and 5 are supplementary 25. Subtract 5x 2-9 from 7x 2 - x + 1 (a) 2x 2 - x +10 (b) -2x 2 + x 10 (c) 12x 2 - x 8 (d) 2x 2 - x 8 (e) none of these u(3u + 4) + 3u(2u +1) = (a) 6u 2 +11u (b) 12u u (c) 12u 2 + 5u (d) 12u (e) none of these

8 27. A bookstore's markup for textbooks is 40%. What is the wholesale price for a textbook that sells for $50.75? (a) $36.25 (b) $71.05 (c) $30.45 (d) $8.67 (e) $ Which is the equation of the corresponding graph? (a) y = 2x (b) x = y + 2 (c) 2x + y = 1 (d) y = x (e) y = If a > 0, the shaded region below is best represented by a. y ax + b b. y ax + b c. y > ax +b d. y > ax + b e. none of these If c = - 2, then 2 c 3c = (a) 6 (b) 6 (c) 10 (d) 2 (e)

9 31. Betty wished to build a rectangular dog run along the side of her garage. The garage will serve as one of the longer sides of the run. If she has 50 feet of fencing and wishes the run to be 3 times longer than it is wide, how many square feet will the fencing enclose? (a) 80 sq. ft. (b) / 8 sq. ft. (c) 250 sq. ft. (d) 300 sq. ft. (e) 468 ¾ sq ft What is the next term in the geometric series 16, -4, 1, -1 / 4,...? (a) -1 / 8 (b) 0 (c) 1 / 16 (d) 1 / 8 (e) ½ As shown in the figure to the right, ABC is isosceles with the length of AB equal to the length of AC. The measure of angle A is 40 o and points B, C, and D are collinear. What is the measure of ACD? (a) 70 o (b) 80 o (c) 110 o (d) 140 o (e) 160 o

10 PART II: Show all of your work for these questions (including all formulas used) on the answer sheet provided at the end of this document. You will be graded on the correctness of your method as well as the accuracy of your answers. Work must be shown to receive full credit. 34. Find the area of region composed of rectangles and/or right triangles. Indicate units. 35. Express shaded area of region composed of rectangles as fractions of total area a. b. 36. Find area of triangle. Indicate units. 37. Find area of circle or semicircle given radius or diameter. Indicate units.

11 38. Find x in each of the following right triangles. 39. A flagpole has cracked 7 feet from the ground and fallen as if hinged. The top of the flagpole hit the ground 24 feet from the base. How tall was the flagpole before it fell? For #40-43, find the slope of the line through each pair of points. 40. and 41. and 42. and 43. and For #44-46, determine the equation for each line using the information given. 44. slope 5, containing the point (3, 2) 45. containing the points (0, 2) and (2, 0) 46. parallel to the line y = -2x + 3, containing the point (-2, -1) For #47-54, solve for x x + 3 = (6x 8) (5x + 9) = x 8x + 4 = 5x (x 2) = (3x + 2) 2(x + 4) = = 6 54.

12 For #55 and #56, determine the area and perimeter of each figure described: 55. Rectangle with length 3.6cm and width 4.2 cm 56. Square with sides of length 9mm For #57-60, simplify completely x 3 x (5x 3 y 2 ) 2 For #61-63, solve each equation either by factoring or by using the Quadratic Formula. 61. x 2 + 3x = x 2 5x 24 = x 2 + x 4 = 0

13 Entering Geometry and/or Algebra II Summer Assignment Answer Sheet Name: Part I: Answer #1-33 on the summer packet. Be sure to show all work. Part II: Show all work (including formulas used) and box your answers to #34-63 on this answer sheet 34. (a) (b) 35. (a) (b) 36. (a) (b) 37. (a) (b) 38. (a) (b) 39.

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