WARREN COUNTY TECHNICAL SCHOOL SUMMER ASSIGNMENT FOR GEOMETRY

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1 Name: Mr. Lamson and Mrs. Colabella, Summer 2017 WARREN COUNTY TECHNICAL SCHOOL SUMMER ASSIGNMENT FOR GEOMETRY Success in geometry depends on skills that you learned in Algebra 1. These skills will also be important for the PSAT and ASVAB tests that many of you will take next year. We do not have time to fully reteach these skills, so you will need to start the year with them fresh in your mind. You are expected to have this packet completed by the first day of school. You will lose credit for each day the packet is late. In addition, you will be given a test on the material in Parts 1 and 2 after we have reviewed the packet. Your answers can be written on this packet or on a separate paper. If you use a separate paper, you do not have to print out the packet. Please complete each problem to the best of your ability. An answer key is provided for most of the problems so you can check your work. Because of this, you must SHOW WORK or provide an explanation for your answer. NO CREDIT will be given for answers alone. Also, please try to do these problems without using a calculator because the test you will take will be at least partially noncalculator. (This is because the ASVAB does not permit the use of a calculator.) You may notice that the problems in the last section are more difficult. These are problems from the College Board s practice PSAT test. Try your best. You will receive credit for your effort even if your answer is wrong. Working on these types of questions may help improve your score on the PSAT and SAT. If you need help with a concept, videos on most of these topics are easily available online. I suggest Khan Academy which is free and has excellent explanations of most topics. Start at and go to Algebra 1 or Pre-Algebra under Math by Topic. Feel free to at colabellap@wctech.org. I will be checking my regularly. Have a great summer! Mrs. Colabella

2 PART 1 Algebra Review Evaluate the expression: 1) ) ) ) 7 + ( 2) 5) 1 ( 12) 6) ) 7 3 ( 10 3 ) 8) ) Solve the Equation: 10) 8x + 6 = 30 11) n 4 = 2 12) x x = ) 3x 5 5x = 7 14) 8x 3(2x + 5) = 13 15) 3 (x + 2) = 6 2 Solve the equation if possible. State if it has no solution or is an identity (with infinitely many solutions). 16) 6(2x + 10) = 3(4x 3) 17) 4(x 3) = 2(6 2x)

3 Solve each word problem by writing and solving an equation: 18) Daenerys paid $2500 for a delivery of dragon food. It cost 2.50 per pound plus a $300 delivery fee. How many pounds of food did she buy? 19) A roofing contractor gives an estimate for shingling a 20 foot by 10 foot section of a roof. The contractor estimates $27.50 per square foot for materials, $17.00 per square foot for labor and a flat fee of $750 for the miscellaneous expenses to be incurred on the job. Write and solve an equation for the total amount of his estimate. 20) You need to choose between two internet providers. One has free installation and charges $57.95 per month. The other charges $60 for installation and $42.95 per month. After how many months will the charge be the same for either provider? Write and solve an equation to determine when the two amounts charged will be equal. Solve the proportion: 21) = n 36 22) 3k 27 = ) n n 12 = 9 5 Solve each word problem by writing and solving a proportion: 24) A scale model of the aircraft carrier USS Dwight D. Eisenhower was built using a scale of 1 ft : 50 ft. The length of the actual carrier is 1,092 ft. What is the length of the model to the nearest inch. 25) A recipe that yields 12 buttermilk biscuits calls for 2 cups of flour. How much flour is needed to make 30 biscuits?

4 Rewrite each equation into slope intercept form (y = mx + b). 26) 3x + y = 5 27) 18x + 2y = 26 Graph each equation: 28) y = 2x 4 29) 3x 6y = 12 Find the slope of the line that passes through the points: 30) ( 1, 11) and (2, 10) 31) ( 3, 1) and ( 3, 4)

5 Find the x and y intercepts of the graph of the equation: 32) 3x 3y = 9 33) 2x + y = 10 Evaluate the function for the given value: 34) f(x) = 4x when x = ) g(x) = 5 x 6 when x = 2 2 Write an equation in slope-intercept form of the line with the given characteristics: 36) slope = 3 and y-intercept = 10 37) Through ( 3, 1) with slope m = 4; 38) Through the points (4,7) and (5,1)

6 Solve the inequality. Graph the solution. 39) 2g + 11 < 25 40) 1 3x x Solve the linear system: 41) 8x + 3y = 9 42) 3x + 2y = 5 8x + y = 29 x y = 10 Find the sum or difference: 43) (7x 3 4x 2 2x + 1) + (x 3 1) 44) (3x 2 4x + 1) (8x 2 4x + 17) Find the product: 45) (x + 3)(x 3) 46) (4x 5)(7x 3) 47) (x + 4) 2

7 PART 2 Basic Geometry Concepts 1) Find both the perimeter and the area of a rectangle with a length of 20 feet and a width of 4 feet. 2) Find both the perimeter and the area of a square with a side length of 3 inches. 3) a) What is the formula for the area of a triangle? b) Find the area of the triangle to the right if s = 8 and h = 6.9 4) a) What is the formula for the volume of a rectangular prism? b) Find the volume of the box to the right. c) Find the surface area of the box. 5) a) What is the Pythagorean theorem? Write the equation. b) In the triangle to the right, which side is the hypotenuse? c) What is the length of c if a = 6 and b = 8?

8 Memorization Head Start - Perform an internet search and define the following terms. Sketch an example if possible. 1. Point 2. Line 3. Plane 4. Line Segment 5. Ray 6. Parallel Lines 7. Skew Lines 8. Perpendicular Lines 9. Angle 10. Angle bisector 11. Complementary angles 12. Supplementary angles 13. Adjacent angles 14. Linear pair 15. Vertical angles 16. Perimeter 17. Circumference 18. Area 19. Volume 20. Congruent

9 PART 3 Sample ASVAB Questions 1) If the tire of a car rotates at a constant speed of 552 times in one minute, how many times will the tire rotate in half-an-hour? a) 276 b) 5,520 c) 8,280 d) 16,560 2) One in every 9 people in a town vote for party A. All others vote for party B. How many people vote for party B in a town of 810? a) 90 b) 720 c) 801 d) 819 3) A motorcycle cost $7,250. If it depreciates by 12% per year, how much will it be worth after one year? a) $870 b) $1,250 c) $5,920 d) $6,380 4) 27 3 a) 3 b) 3 c) 9 d) 12 5) The volume of the box to the right is a) 15 b) 36 c) 44 d) 96 6) If x y 0, then x2 y 2 x y = a) x + y b) x y c) x + 2y d) 2x y

10 PART 4 - Sample PSAT Questions This is a part of Practice Test 1 from the College Board web site. You are encouraged to go to the web site which includes two full practice tests, including sections on language arts, as well as answers and explanations -

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14 ANSWER KEY: PART 1 Alg. Review / / no solution 17. identity pounds 19. $9, at 4 months ft or 21 ft, 10 in cups 26. y=3x y=-9x /3 31. undefined (3/0) 32. (3,0) and (0,-3) 33. (5,0) and (0, 10) 34. f(2. 5) = g( 2) = 11 PART 2 - Geometry 1. Per = 48 ft Area = 80 sq. ft. 2. Per = 12 in Area = 9 sq. in. 3. A = 1 2 bh 3b square units 4. V = l w h 4b. 80 cubic cm. 4c. 132 sq. cm. 5. a 2 + b 2 = c 2 5b. c 5c. 10 PART 2 ASVAB 1. d 2. b 3. d 4. b 5. d 6. a PART 3 PSAT 1. A 2. B 3. A 4. D 5. B 6. B 7. A 8. D 9. B 10. D 11. C 12. A 13. D 36. y=3x y=4x y=-6x (-3, 5) 42. (3, -7)