University of Waterloo Faculty of Science Math Preparedness Test September 2012

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Universit of Waterloo Facult of Science Math Preparedness Test September 1 NAME: (Please Print) I.D.#: Instructions and Information for students: You have 75 minutes to complete the test.

1 Universit of Waterloo Facult of Science Math Preparedness Test September 1 NAME: (Please Print) I.D.#: Instructions and Information for students: You have 75 minutes to complete the test. No aids are permitted. This is NOT a term test. Your mark on this test will NOT be used to calculate our final grade in an of our courses. Its sole purpose is to assess our readiness for our first-ear calculus courses. The test consists of two parts. Part A consists of 15 questions and focuses on fundamental mathematical concepts. Each question in Part A is worth 1 mark. Part B consists of 5 questions and assesses not onl our understanding of mathematical concepts but also our problem solving skills. Each question in Part B is worth 3 marks. The test will be marked out of 3. Rough work ma be done beside questions, on the back of the preceding page, or on the blank sheet attached to the end of the test booklet. Print our name, student ID number and test version in the designated fields, as suggested in the diagram below. All other fields will be ignored and should be left blank. You are writing test version 1. This is test version 1. Fill in ovals 1 for the Card Number (or Test Master) on our computer answer card. Circle our answers on the test paper and also code our answers on the computer card using a soft lead PENCIL. Select onl one answer for each question. Check that ou have not missed or double marked an rows in the answer field. For eample, if our ID is , the ID Number section should be completed as shown, and if our answer to question #5 is C then the row labelled 5 should have the shaded, as shown above. Please hand in the computer card and this test booklet when ou have finished. Onl our computer card will be marked.

2 Math Prep Test (Fall 1) Version 1 Page of 8 Part A: Fundamentals (Questions 1-15 are worth 1 mark each.) In questions 1 through 6, the smbols a, b and c represent positive numbers. For each of these questions, indicate whether the equations are or. 1. 1? 1 1 = + a+ b a b. a+ b? a b = + c c c 3.? a+ b = a + b 4. ln a + ln b = ln( a+ b)? 5. ln a + ln b = ln( ab)? 6.? a+ b a b e = e + e

3 Math Prep Test (Fall 1) Version 1 Page 3 of 8 7. Solve the sstem of equations below for. + 3 = 1 4 = (C) (D) ½ 8. Solve the equation = for., 1 1, 4 (C), 4 (D), 1 4 1,4 9. Solve the equation 1 e = 3 for. ln 3 1 ln (C) ln (D) ln 3 + none of the above

4 Math Prep Test (Fall 1) Version 1 Page 4 of 8 1. Which of the following is a graph of = + 4? 6 4 (D) (C) Calculate the area of the triangle with vertices (1,1), (4,) and (1,4). 9 3/ (C) 9/ (D) 9/4 3/4

5 Math Prep Test (Fall 1) Version 1 Page 5 of 8 1. What is the simplest form for the epression below? a b a b a+ b b a + a b a+ b ab a (C) 1 (D) 1 a + b 13. What is the simplest form for the epression below? 3 ( + 7)( 3) (C) 3 9 (D) Simplif the epression below. 4 4 sin θ cos θ + cos θ sin θ cos θ (C) (D) 1

6 Math Prep Test (Fall 1) Version 1 Page 6 of If log 8( ) + log8 =, what is the value of? (C) 13 (D) 1 1 Part B: Problem Solving (Questions 16 through are worth 3 marks each.) 16. Determine the length marked in the diagram. 3 o 5 1 (C) 15 (D) 5 6 o Find length of the shadow of a 4 m pole when the sun is at a position as shown in the diagram. The answers are given in metres, m (C) 4 3 (D) 3 none of the above

7 Math Prep Test (Fall 1) Version 1 Page 7 of When Nicholas was four ears old, he was twice as old as Larissa. Larissa is now 9 ears old. How old is Nicholas? 9 1 (C) 11 (D) If sinθ = 3/5 and θ is between and π, then what is the value of cosθ? (C) (D) none of the above. Suppose a particle has position at time t given b t () 1 3 = + t [in metres, m] What is the speed of the particle when = 13 m? (C) (D) 1 m/s m/s 6 m/s 1 m/s none of the above

8 Math Prep Test (Fall 1) Version 1 Page 8 of 8 You ma use this page for rough work.

AP Calculus (AB/BC) Prerequisite Packet Paint Branch High School Math Department

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