2023W1_MATH_100B_ALL_2023W1.2Q5DY184P603.Diagnostic_Test

Kaitlyn Tse 2023W1 MATH 100B ALL 2023W1 Assignment Diagnostic Test due 09/15/2023 at 11:59pm PDT Problem 1. (1 point) This problem set serves as both a review of pre-calculus mate- rial and as a diagnostic tool to determine whether or not you are adequately prepared for this calculus course. The problems will be marked for completion only and your an- swers will not affect your enrolment status. That means you don’t have to get the answers correct, but you do have to answer all the questions to get credit for completing the test. It is for your own benefit to honestly assess your precalculus knowledge. Since all your calculus tests will be written individu- ally and will be timed, we strongly suggest that you not use any outside sources (textbooks, online resources, peers, tutors), and that you time yourself at one hour and be sure to submit all the answers by then. You will have only one chance to submit an answer to each prob- lem. Before submitting each answer, you can and should use the ”Preview Answers” button. This will allow you to preview your answer to ensure that the answer you have entered is the answer you intend to submit. Once you are satisfied with your answer, press the ”Check Answer” button to submit your answer. This test will not affect your enrolment status, so please take the above advice: individual work only, no outside resources, and one hour limit . When you finish this test, your final score will indicate which pre- calculus skills you will want to review. Problem 2. (1000 points) Given the expression p = 2 q + r qr , solve for r in terms of p and q only. Multiple-choice: [/A/B/C/D/E/F/G/H/I] A. r = 2 q + r pq F. r = 2 p B. r = 2 q - p q - 1 G. r = 2 q - p q C. r = 2 q pq - 1 H. r = 2 pq q - p D. r = pqr - 2 q I. r is canceled out so it is impossible to solve for r . E. r = 2 pq + pr q Answer(s) submitted: • no response submitted: (incorrect) recorded: (incorrect) Problem 3. (1100 points) We are given that kx 2 + kx + 6 = 0. Then an expression for x as a function of k is Multiple-choice: [/A/B/C/D/E] A. x = - k ± √ k 2 - 24 2 k B. x = - k ± √ k 2 - 6 k 2 k C. x = - 1 2 ± √ k - 24 2 D. x = - 1 2 ± √ k 2 - 24 k 2 k E. x = - k ± √ k 2 - 24 k 2 Answer(s) submitted: • no response submitted: (incorrect) recorded: (incorrect) 1

Problem 4. (1000 points) Factor ( x 2 - 1 )( 2 x 2 + 6 x - 14 ) - ( x 2 - 1 )( x 2 + 3 x + 4 ) . Multiple-choice: [/A/B/C/D/E/F/G/H/I/J] A. ( x - 1 )( x + 1 )( x - 2 )( x - 5 ) F. ( x - 1 )( x + 1 )( x + 1 )( x - 10 ) B. ( x - 1 )( x + 1 )( x - 2 )( x + 5 ) G. ( x - 1 )( x + 1 )( x - 3 )( x - 6 ) C. ( x - 1 )( x + 1 )( x + 2 )( x - 5 ) H. ( x - 1 )( x + 1 )( x - 3 )( x + 6 ) D. ( x - 1 )( x + 1 )( x + 2 )( x + 5 ) I. ( x - 1 )( x + 1 )( x + 3 )( x - 6 ) E. ( x - 1 )( x + 1 )( x - 1 )( x + 10 ) J. ( x - 1 )( x + 1 )( x + 3 )( x + 6 ) Answer(s) submitted: • no response submitted: (incorrect) recorded: (incorrect) Problem 5. (200 points) Which of the following describes all the values of x satisfying x 2 + 4 ≥ 5? Multiple-choice: [/A/B/C/D/E/F/G/H/I/J] A. x ≥ 1 F. x ≥ ± 3 B. x ≥ ± 1 G. - 3 ≤ x ≤ 3 C. - 1 ≤ x ≤ 1 H. x ≤ - 3 or x ≥ 3 D. x ≤ - 1 or x ≥ 1 I. all x ∈ R E. x ≥ 3 J. no real solutions for x Answer(s) submitted: • no response submitted: (incorrect) recorded: (incorrect) Problem 6. (10 points) Consider the graph of the function y = f ( t ) as drawn below. If f ( - x ) = 3, find x . Click the image for a larger version. x = Answer(s) submitted: • no response submitted: (incorrect) recorded: (incorrect) Problem 7. (10 points) Let f ( x ) = ( 3 x 2 - 1 ) 7 be a composite function. Which is the cor- rect decomposition of f ( x ) ? Multiple-choice: [/A/B/C/D/E/F/G/H] A. a ( x ) = 3 x 2 - 1 , b ( x ) = x 7 , f ( x ) = b ( a ( x )) F. a ( x ) = 3 x 7 , b ( x ) = x 2 - 1 , f ( x ) = B. a ( x ) = 3 x 7 , b ( x ) = x 2 - 1 , f ( x ) = a ( b ( x )) G. a ( x ) = 3 x - 1 , b ( x ) = x 9 , f ( x ) = C. a ( x ) = 3 x 2 - 1 , b ( x ) = ( 3 x 2 - 1 ) 7 , f ( x ) = b ( a ( x )) H. None of these D. a ( x ) = 3 x 2 - 1 , b ( x ) = x 7 , f ( x ) = a ( b ( x )) E. a ( x ) = 3 x 2 - 1 , b ( x ) = ( 3 x 2 - 1 ) 7 , f ( x ) = a ( b ( x )) Answer(s) submitted: • no response submitted: (incorrect) recorded: (incorrect) 2

• G. None of the above Answer(s) submitted: • no response submitted: (incorrect) recorded: (incorrect) Problem 11. (1000 points) Which of the following is equal to 2 √ 6 - √ 2 ? Multiple-choice: [/A/B/C/D/E/F/G/H/I/J] A. 1 √ 3 + √ 1 F. √ 3 - √ 1 B. 1 √ 3 - √ 1 G. √ 6 + √ 2 2 C. √ 6 + √ 2 4 H. √ 6 - √ 2 2 D. √ 6 - √ 2 4 I. 1 E. √ 3 + √ 1 J. 1 2 Answer(s) submitted: • no response submitted: (incorrect) recorded: (incorrect) Problem 12. (2000 points) The length of a rectangular garden is 10 meters longer than its width. If the garden’s perimeter is 212 meters, what is the area of the garden in square meters? m 2 Answer(s) submitted: • no response submitted: (incorrect) recorded: (incorrect) Problem 13. (10 points) The domain of the function f ( x ) = x 2 - 16 x 2 + 3 x is Multiple-choice: [/A/B/C/D/E/F/G/H/I/J] A. - 3 < x < 0 F. x 6 = 0 B. x < - 3 or x > 0 G. x 6 = - 3 C. x ≥ - 3 H. x 6 = 0 and x 6 = - 3 D. x < - 4 or x > 4 I. x 6 = - 4 and x 6 = 4 E. x > - 3 J. x 6 = 0 , x 6 = - 3 , x 6 = - 4 and x 6 = 4 Answer(s) submitted: • no response submitted: (incorrect) recorded: (incorrect) Problem 14. (10 points) The values of f ( x ) at a few points are given in the table below. Find f ( f ( 3 )) . x -3 -2 -1 0 1 2 3 f ( x ) 0 -3 1 2 3 1 -2 f ( f ( 3 )) = Answer(s) submitted: • no response submitted: (incorrect) recorded: (incorrect) Problem 15. (10 points) The figure below shows the graph of a ( x ) in blue and the graph of b ( x ) in red: Based on the figure above, graph the function c ( x ) = a ( x ) · b ( x ) . Hint: There is not enough information to determine formulas for a ( x ) and b ( x ) , but you do have enough information to sketch a graph whose main features are reflected below. Which of the graphs below labeled A-E most accurately matches your graph? (enter the corresponding letter) None of these graphs A B C D E Answer(s) submitted: • no response submitted: (incorrect) recorded: (incorrect) 4

Problem 16. (1000 points) Simplify 3 2 + h - 3 h h . Multiple-choice: [/A/B/C/D/E/F/G/H/I/J] A. 2 h - 6 h ( 2 + h ) F. 2 h - 6 h B. 2 h - 6 2 + h G. - 6 h C. 6 h H. - 6 h ( 2 + h ) D. - 6 h 2 ( 2 + h ) I. 2 h - 6 h 2 ( 2 + h ) E. 3 2 h J. - 6 2 + h Answer(s) submitted: • no response submitted: (incorrect) recorded: (incorrect) Problem 17. (1000 points) Simplify x 1 / 2 y ( xy - 3 ) 2 . Multiple-choice: [/A/B/C/D/E/F/G/H/I] A. y 7 F. y 2 x 3 / 2 B. y 7 x 4 G. 1 y 5 C. y 7 x 3 / 2 H. 1 x 4 y 5 D. y 2 I. 1 x 3 / 2 y 5 E. y 2 x 4 Answer(s) submitted: • no response submitted: (incorrect) recorded: (incorrect) Problem 18. (100 points) Solve the following equation. If necessary, enter your answer as an expression involving natural logarithms or as a decimal approx- imation that is correct to at least five decimal places. 12 e x - 15 = 13 x = Answer(s) submitted: • no response submitted: (incorrect) recorded: (incorrect) Problem 19. (200 points) Which of the following expression is the correct relation between the area of a circle, A , and its circumference, C ? Multiple-choice: [/A/B/C/D/E/F/G/H/I/J] A. A = C 2 2 π F. A = 4 π C 2 B. A = C 2 4 π G. A = π C C. A = C π H. A = 2 π C D. A = C 2 π I. A = C 2 2 E. A = π C 2 J. A = C 2 4 Answer(s) submitted: • no response submitted: (incorrect) recorded: (incorrect) 5