美国高中数学测试题13-14MathPlacement (1).pdf

Emma Willard School Troy, New York 12180 MATHEMATICS PLACEMENT TEST Purpose: The tests in this booklet are to help determine proper mathematics placement and minimize the need for course changes after the start of the academic year. It is important that the student work independently so that the test will give us a fair representation of her current knowledge and skills. The tests are for placement purposes only. They do not affect admissions decisions in any way. However, it is important to answer questions to the best of your ability in order for the mathematics department to place you properly. Date student received test:_ Name: (please print)_ Date test taken:_ Circle grade you are entering at Emma Willard School: 9 10 11 12 PG Phone number (with area code): _ E-mail address: _ (print legibly please) Name of most recent school attended and the city and state/country where it is located. _ What math course did you take this year, and what is your average grade at the time you are taking this test? _ Have you taken a full-year course called Geometry? Circle your answer. YES NO If you were remaining in your current school district or at your current school, what would be the name of the course you would take next year? _ How do you view yourself as a mathematics student? Please read the following carefully: Directions to Parents: Please see that your daughter has a quiet place to complete the test in one sitting. The test has four levels. Each level is designed to be completed in less than an hour. Calculators may be used (EXCEPT on the Level One test), but texts and notes should not be used. We do not recommend extensive review prior to taking the test. It is meant to reflect your daughters accessible knowledge of her retained mathematics knowledge. It is not to your daughters advantage to obtain help on this test since proper placement is contingent on accurate assessment of her current knowledge of mathematics. Directions to the Student: This booklet contains four tests, Level One, Level Two, Level Three, and Level Four. Do as much of all four parts of the tests as you can. The sooner you complete the tests and return them to the school, the sooner we can properly place you and start the process of creating your schedule for the fall. Print out the levels you wish to complete. Be sure to check that all diagrams and problems have printed correctly. Please mail in all parts that you have completed as soon as possible after you complete them. You may use a calculator except on Level One. It is important that you give these tests your serious consideration as they will be the main factor in determining the math course in which you are enrolled. Please show your work neatly next to the problem (including scratch work) as it is useful in our evaluation of your methods and skills. Do not use extra paper, and simplify all answers. Showing your work helps us see where your mistakes were and adds to proper assessment of your understanding and hence proper placement. Calculator Use: It is important to note that all Emma Willard mathematics students will use the Texas Instruments TI-84 PLUS Graphing Calculator in all of our courses. These may be purchased at cost in our school store. While we teach students to use their calculators proficiently, we also stress the need to recognize problems that do not need a calculator and may require students to solve those problems without one. For this reason, on these placement tests we ask that you do as many problems as possible without the use of a calculator. On the Level One test, NO calculators are allowed. Please complete as many questions as you can on all levels of the four tests. For example, if you are an entering freshman and have only completed an eighth grade math course, and are only capable of completing a few problems on the Level One part, THIS IS FINE. If you are an entering junior, and hope to have proper placement, complete as much as you can of all four tests. The purpose of these tests is not to make a judgment about your mathematical ability. It is to assess how well you have been prepared for the sequence of courses at Emma Willard. We strive to place new students in the course in which they will find the most appropriate challenge. Revised 4/12 Level 1 1 of 6 Level One Test (total points = 108) In all questions, SHOW YOUR WORK in the space under the question and place your final answer on the line provided to the right. Do NOT use a calculator on this test. 1. A suit that is regularly sold for $120 is now advertised on sale at 30% off. What is the sale price of the suit? 1. _ (3 pts) 2. A schools ratio of boys to girls is 4:5. If there are 360 students, how many girls attend the school? 2. _ (3 pts) 3. Evaluate 249 2 xx when x = -1. 3. _ (3 pts) In 4-8, simplify the expression. 4. 3678xx+ 4. _ (3 pts) 5. 325()()xx x 5. _ (3 pts) Level 1 2 of 6 6. 343 762ccc+ 6. _ (3 pts) 7. aa a 46 2 7. _ (3 pts) 8. (3x)3 8. _ (3 pts) In 9-12 solve the equation. 9. += 369d 9. _ (3 pts) 10. 25652xx+= 10. _ (3 pts) 11. The formula 9 5 32FC=+ converts Celsius temperature (C) to Fahrenheit (F). What is the Fahrenheit equivalent of 20oC? 11. _ (3 pts) Level 1 3 of 6 12. Solve for Cin the formula 9 32 5 FC=+. 12. _ (3 pts) 13. Multiple Choice. To rent a truck for a day, a driver pays a $15 fee. She pays an additional 18 cents for each mile she drives. If the total cost in dollars is c and she drives d miles, then A) dc=+15018. B) dc=+01815. C) cd=+15018. D) cd=+01815. 13. _ (3 pts) 14. Solve the equation for y. 236xy= 14. _ (3 pts) 15. Is (1, 3) a solution ofyx=25? (Support your answer with work below.) 15. _ (3 pts) 16. Graph the line yx= 2 5 3 using slope & y-intercept. Do not use a table of values. (1 square = 1 unit) 16. (3 pts) x y Level 1 4 of 6 17. Given the line graphed to the right, a. Find its numerical slope. b. Write an equation to represent the line. 17. a. _ (3 pts) b. _ (3 pts) 18. A line passes through the points (4, -2) and (-9, 8). a. Find the slope of the line. Show work. b. Write an equation for this line. 18. a. _ (3 pts) b. _ (3 pts) 19. Given the slope of a line is 5 3 and the point (-8, 2) is on the line. Write an equation for the line. 20. Solve the system: 62 22 = =+ yx yx 19. _ (3 pts) 20. _ (3 pts) 21. Multiply: ()()21 35xx+ 21. _ (3 pts) 2 3 x y Level 1 5 of 6 22. Simplify: ()x +8 2 22. _ (3 pts) In 23-26, factor (using integers) the polynomial expression. 23. Factor: 515 32 aba b 23. _ (3 pts) 24. Factor: x225 24. _ (3 pts) 25. Factor: xx 2 412+ 26. Factor: 12x25x 2 25. _ (3 pts) 26. _ (3 pts) 27. Solve for x: ()()xx+=530 27. _ (3 pts) 28. Solve the equation: 35 24t = + 28. _ (3 pts) Level 1 6 of 6 29. Rewrite 24 in simplified radical form. 29. _ (3 pts) 30. Solve for x: 2 70 x = 30. _ (3 pts) 31. Solve for x: 2 4137x + = 31. _ (3 pts) 32. Simplify: 2 3 () 4 6 () 32. _ (3 pts) 33. Simplify: 8 53 5+ 33. _ (3 pts) 34. Use the quadratic formula, x bbac a = 2 4 2 to solve the equation: 260 2 xx=. 34. _ (3 pts) Level 2 1 of 8 Level Two Test (total points = 100) In all questions, SHOW YOUR WORK in the space under the question and place your final answer on the line provided to the right. You may use a scientific or graphing calculator. 1. Measure of angle x = ? 1. _ (2 pts) 2. In the figure, |m nand 50 .m x = Find m y . 2. _ (2 pts) 3. ?m y = 3. _ (2 pts) 4. In the figure, 90m Q=and 40m SRT=. ?m P= 4. _ (2 pts) 5. If is parallel to ABCD, then ?m x = 5. _ (2 pts) 15 x 55 65 n m x y 70 55 y 40 T S R Q P DC BA 35 80 x Level 2 2 of 8 6. In the plane figure, MN=NT=TV. Find the measure of TMN. 6. _ (2 pts) 7. Which of the following reasons can always be used to prove two triangles congruent? Circle all that apply. No partial credit. (2 pts) SSS AAA SAS SSA AAS ASA 8. Given the figure withDEBC?, which of the following proportions is not true? No partial credit. 8. _ (2 pts) A. 4 56 x = B. 4 512 y = C. 45 6x = D. 4 96 x x = + 9. Which one of the following sets of points is not collinear? A. B & D B. D, A & H C. D, B & G D. G, C &B 9. _ (2 pts) 10. Refer to the diagram in #9. The intersection of plane P and plane Q is: 10. _ (2 pts) A. line KC B. line AC C. line GC D. line PQ E. point C N 35 V T M 12 y 4 5 x 6 E A B C D C G B P A D K Q H Level 2 3 of 8 11. Given ABC such that 50m A=and 64m B=. The longest side of the triangle is A. AB B. AC C. BC D. all sides are equal E. not enough information is given 11. _ (2 pts) 12. Two similar triangles have areas in the ratio 4:9. The ratio of a pair of corresponding sides is 12. _ (2 pts) A. 4:9 B. 16:81 C. 9:4 D. 2:3 E:2 :3 13. ABCD is a parallelogram. Solve for x. 13. _ (2 pts) 14. If the side of an equilateral triangle measures 6, then what is the measure of an altitude of the triangle? 14. _ (3 pts) 15. What is the radius of circle O if PQ=12. 15. _ (3 pts) 16. Find the sum of the interior angles in a hexagon. 16. _ (3 pts) x+20 x-12 D A B C Q O P Level 2 4 of 8 17. A 6 foot ladder leans against a wall. Its top touches a point on the wall 4 feet above the floor. How many feet is the bottom of the ladder from the base of the wall? Draw a diagram and put your answer in simplest radical form. 17. _ (3 pts) 18. A rhombus has diagonals of 20 and 16. What is the perimeter of the rhombus? Draw a diagram and put your answer in simplest radical form. 18. _ (3 pts) 19. In right triangle ABC, AC=12. What is the perimeter of the triangle? 19. _ (3 pts) 20. Find the area and perimeter of the rectangle below. 20. Area = _ (2 pts) Perimeter = _ (2 pts) 30 A C B x y (-1, 1) (3, 1) (-1, -2) (3, -2) Level 2 5 of 8 21. Write the following proof either in a two-column format or written in paragraph form. (6 pts) Given: DA bisects BDC BD=DC Prove: AB=AC 22. What is the area of ADBin square units? 22. _ (3 pts) 23. What is the area of parallelogram ABCD in square units? 23. _ (3 pts) A B C D 8 4 6 CB A D 12 108 D AB C Level 2 6 of 8 24. What is the area of a circle whose circumference is12. 24. _ (2 pts) 25. Square ABCD is inscribed in circle O. OA=4. What is area of the shaded region in square units? 25. _ (3 pts) 26. In the circle below, what is the degree measure of arc AB? 26. _ (3 pts) 27. The edge of a cube is 2 cm. Find the total surface area of the cube. Include units of measurements in your answer. 27. _ (3 pts) 28. The diameter and height of a cone both measures 4 cm. What is the volume of the cone? 28. _ (3 pts) 40 A B O DC AB Level 2 7 of 8 29. Find the distance between the points (-2, 3) and (1, -4). 29. _ (3 pts) 30. Write an equation of the line perpendicular to 1 5 2 yx=+going through the point (3, 4). 30. _ (3 pts) 31. Given the line segment with endpoints (1, -4) and (3, 2), determine the coordinates (x, y) of the midpoint. 31. _ (3 pts) 32. List the letters of the answer(s) that give (s) you enough information to determine that the quadrilateral is a parallelogram. No partial credit. A. Both pairs of opposite sides are parallel. B. Two pairs of consecutive sides are congruent. C. Diagonals are congruent. D. Consecutive angles supplementary. 32. _ (3 pts) 33. Name the vector from A(3, 5) to B(7, 0). 33. _ (2 pts) Level 2 8 of 8 In 34-39, define the geometric term in your own words, a diagram alone is NOT sufficient. (2 pts each) 34. Complementary Angles 35. Isosceles Right Triangle 36. Alternate Interior Angles 37. Altitude of a Triangle 38. Rhombus 39. Median of a Triangle Level 3 1 of 6 Level Three Test (total points = 101) In all questions, SHOW YOUR WORK in the space under the question and place your final answer on the line provided to the right. You may use a scientific or graphing calculator. 1. Write an equation of a line perpendicular to 523xy+=and containing the point (4, -1). 1. _ (3 pts) 2. State the radius and center of the circle with the equation: 22 (3)16xy+= 2. Radius:_ (1 pts) Center:_ (2 pts) 3. State the domain & range of the relation graphed below. 3. Domain:_ (1 pts) Range:_ (1 pts) 4. Is the relation in #3 a function? Explain why or why not? 4. _ (3 pts) 5. Identify whether the function 2 ( )3g xx= is an even function, odd function or neither. 5. _ (3 pts) (2, -1) x y Level 3 2 of 6 6. Given the point (1, -3) is on the graph( )yf x=, what point is on the graph of. a. 3 ( )yf x= b. (3)3yf x=+ c. 2 ( )3yf x= + 6. a. _ (3 pts) b. _ (3 pts) c. _ (3 pts) 7. Let 2 ( )1f xx=+and ( )23g xx=. Find ( ( )g f xand simplify. 7. _ (3 pts) 8. If ( )32f xx=, then 1( ) fx =_?_ 8. _ (3 pts) 9. Find the EXACT (no decimals) x-intercept(s), y-intercept, and vertex of the parabola 2 2810yxx=algebraically. Show your work below. 9. x-int:_ (2 pts) y-int:_ (1 pts) vertex:_ (3 pts) Level 3 3 of 6 10. Simplify over the set of complex numbers. a. 49 b. 2 (1 2 )i 10. a. _ (3 pts) b. _ (3 pts) 11. Simplify: 02 35 43 ()x yz x yz . Write your answer with positive exponents. 11. _ (3 pts) 12. Simplify: 23 64 27 . Write your answer as a simplified fraction. 12. _ (3 pts) 13. Graph the function 1 ( )f x x =. Be certain to plot at least three points and include any asymptotes as dashed lines. 13. (3 pts) (1 square =1 unit) 14. Write 2 39=in logarithmic form. 14. _ (3 pts) x y Level 3 4 of 6 15. Evaluate 2 log 8. 15. _ (3 pts) 16. Solve450 x =. Round to the nearest thousandth. 16. _ (3 pts) 17. Write as a single logarithm with base 6: 1 662log 9 log 5+. 17. _ (3 pts) 18. Graph. 2 ( )logf xx=. Be certain to plot at least three points and include any asymptotes as dashed lines. 18. (3 pts) (1 square =1 unit) 19. Write an equation for a polynomial function that has the roots 0, -5 and 1/3. There is no need to simplify your answer. 19. _ (3 pts) 20. What is the quotient when 32 1110 xxx+is divided by 2x? 20. _ (3 pts) x y Level 3 5 of 6 21. Calculate to the nearest tenth of a degree. 21. _ (3 pts) 22. Give the exact value (no decimal) ofsin240. 22. _ (3 pts) 23. Solve 1 cos 2 x= for x in degrees where0360 x. 23. _ (3 pts) 22. State the amplitude and period of the graph of3cos(2 )yx=. 22. Amp. =_ (1 pts) Period=_ (2 pts) 23. Graph at least one full period of ( )2tanf xx=. Be certain to plot at least three points and include any asymptotes as dashed lines. 23. (3 pts) 12 5 -2 -1 1 2 - 2 - 2 Level 3 6 of 6 24. Graph at least one full period of ( )sinf xx= . Be certain to plot at least three points and include any asymptotes as dashed lines. 24. (3 pts) 25. Give the exact solution (no decimals) of sin0 x =for x in radians02x. 25. _ (3 pts) 26. Find the exact radian value for 1 1 2 sin () . 26. _ (3 pts) 27. Give the exact solution (no decimals) of 3 2 cosx = for x in radians02x. 27. _ (3 pts) 28. Give the exact solu