Algebra 2 with Trigonometry. Practice Exam #1 Answer Key

Transcription

1 Algebra with Trigonometr Practice Eam # Answer Ke Answer all 9 questions in this eamination. Write our answers to the Part I multiple-choice questions on the separate answer sheet. No partial credit will be allowed on the multiple-choice section. For Parts II, III, and IV, clearl indicate the necessar steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in these parts, a correct numerical answer with no work shown will receive onl credit. A reference sheet that ou ma need to answer some questions in this eamination is included. Scrap paper is not permitted for an part of this eamination, but ou ma use the blank spaces in this eamination as scrap paper. Scrap graph paper is provided at the end of this eamination for an question for which graphing ma be helpful but is not required. An work done on this sheet of scrap graph paper will not be scored. Write all our work in pen, ecept graphs and drawings, which should be done in pencil. Note: A graphing calculator and a straightedge (ruler) must be available for ou to use while taking this eamination. ALGEBRA WITH TRIGONOMETRY, SAMPLE EXAMS emathinstruction, RED HOOK, NY 7, 009

2 Part I Answer all 7 questions in this part. Each correct answer will receive credits. No partial credit will be allowed. For each question, write on the separate answer sheet the numeral preceding the word or epression that best completes the statement or answers the question. []. If sin () 7 then cos = cos sin 8 7 (). If the sum of i and 7 8i were plotted in the comple plane, the result would fall in which of the following quadrants? I III () II IV i 7 8i 6i, 6 Quadrant II (). The solution set to the quadratic inequalit or () 7 0 or is 0 or Now test values to finish.. The largest solution, to the nearest degree, of the equation 0 60 is which of the following? sin 9sin 0 on the interval 68 () 78 This problem is most easil solved b graphing sin 9sin and then finding its largest -intercept using our graphing calculator.. The smallest root of 8 0 is approimatel..8 ().7.6 Graph the function 8 and use our calculator to find the smallest zero of this function, which is approimatel ALGEBRA WITH TRIGONOMETRY, SAMPLE EXAMS emathinstruction, RED HOOK, NY 7, 009

3 6. A quadratic function of the form a b c has a leading coefficient, a, that is positive and a turning point at 6,. Which of the following represents the range of the quadratic function?,, () 6, 6, A leading coefficient that is positive indicates that the parabola opens upwards and has a minimum -value of but no maimum -value. 7. Eight finalists for the New York State math championship are competing. Different prizes are awarded for the top four finishers. Assuming no ties are possible, in how man was can these prizes be given out? 8! 8 C ()! 8 P T st nd rd th n n n n n P 8 8. Which of the following represents the inverse of 0? 0 () The value of sin00 can be epressed equivalentl as sin0 sin0 cos0 () sin0 cos0 cos 0 sin 0 Using sin A sin Acos A we have: sin 00 sin 0 sin 0 cos 0 0. The interquartile range of the data set, 7,,,7, 0 is 7 (). 0 Q 7 found using the calculator Q 7 found using calculator IQR Q Q 0 ALGEBRA WITH TRIGONOMETRY, SAMPLE EXAMS emathinstruction, RED HOOK, NY 7, 009

4 . Which of the following quadratics would have roots that sum to? () b sum a. Which of the following represents the range of the function,0 0, (),0 0, sin 6? min ma Range:, 0 (). A function, f, has a -intercept of 7. What is the -intercept of the function f 0? 9 () 0 f 0 7 f An angle is drawn in standard position. If its terminal ra lies in the lies in the second quadrant and intersects the unit circle at an -coordinate of, then the -coordinate of intersection is (). In the triangle shown below, what is the measure of the smallest angle, to the nearest degree? due to Quad. II cos cos () 7 76 cos 9 86 ALGEBRA WITH TRIGONOMETRY, SAMPLE EXAMS emathinstruction, RED HOOK, NY 7, 009

5 6. On a multiple choice test with choices per question, which of the following gives the probabilit of getting eactl seven out of ten questions correct? () P C C P Binomial probabilit with: p, q, n 0, and r 7 C () 7. For an angle A where 90 A 80 it is given that sin A cos A? 9 () 8. Which of the following sets gives the -coordinates where the parabola 7 0 intersect when drawn in the coordinate plane?. Which of the following is the value of cos A cos A cos A 9 9 cos A 9 Quad II cos A () 0 and the line, 8 0, (), 0, or 9. In which of the following situations would it be most appropriate to use an entire population instead of a sample? when determining the average age of teachers in a school district () when determining the average weight of freshmen in American high schools when determining the average speed of drivers on an interstate highwa when determining the average thickness of the ozone laer surrounding the planet It is onl appropriate to use the entire population when we can be certain that ever member of the population will be surveed. In all other choices, surveing the entire population is not possible because of its size. 0. In MNP, mn 0, MN 0 and MP 6. Given this information angle P could be acute onl acute or obtuse () right onl obtuse onl sin P sin 0 sin P P 6. or.6 Both work with 0. ALGEBRA WITH TRIGONOMETRY, SAMPLE EXAMS emathinstruction, RED HOOK, NY 7, 009

6 . The comple fraction can be simplified as 6 () For an arithmetic sequence whose third term is and whose common difference is four, which of the following gives the value of the 0 th term? () 76 8 a 0 a a a 9d Which of the following is the value of j? j 8 () 0 8 (). If the graph of sin was compared to the graph of sin which of the following? then the phase shift would be () 6 sin sin. Which of the following values of solves: () 6 6? ALGEBRA WITH TRIGONOMETRY, SAMPLE EXAMS emathinstruction, RED HOOK, NY 7, 009

7 6. Which of the following inequalities represents the graph shown below? () Since the parabola opens downward a 0. As well, since the curve is dashed, the equalit is not included. () 7. The solution set to the equation, 0, 6 (),0, 0 is or Part II Answer all 8 questions in this part. Each correct answer will receive credits. Clearl indicate the necessar steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive onl credit. [6] 8. Benjamin is choosing three jell filled donut holes out of a bo. If the bo contains eight strawberr and si blueberr filled donuts, find the probabilit that Benjamin will choose two strawberr and one blueberr b randoml choosing his three donuts. P n n two strawberr n one blueberr C C total sets of donuts C two strawberr and one blueberr or 9. Find the following product in simplest form: ALGEBRA WITH TRIGONOMETRY, SAMPLE EXAMS emathinstruction, RED HOOK, NY 7, 009

8 0. Solve the equation shown below for all values of in simplest radical form Find the sum of the comple numbers i and i. Epress our answer in a bi form and then plot the result on the comple plane below. Imaginar i i i, Real. Eplain wh the triangle shown below cannot eist. sin sin sin 0 sin. 8 But sin. Thus this triangle cannot eist For a particular real number a and base b it is known that log.7 log b a. a. Determine the value of b a ba log log.7 8. b ALGEBRA WITH TRIGONOMETRY, SAMPLE EXAMS emathinstruction, RED HOOK, NY 7, 009

9 . The graph below can be described b an equation of the form cos and B and show the calculations that lead to our answers. A B. Determine the values of A min and ma A ma min. B min ma.. A drug compan found that a sample of 0 people who took their new diet pill lost an average of.7 pounds over a two week period. If their results were normall distributed with a standard deviation of pounds, then approimatel how man people lost more than 8.7 pounds? 's above the mean Percent greater % Number of people Part III Answer all questions in this part. Each correct answer will receive credits. Clearl indicate the necessar steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive onl credit. [] 6. In quadrilateral ABCD it is known that AB 6, BC, CD 6, mc and mabd 6. Determine, to the nearest tenth the length of AD. 6 6 cos cos A D 6 6 B 6 C ALGEBRA WITH TRIGONOMETRY, SAMPLE EXAMS emathinstruction, RED HOOK, NY 7, 009

10 7. Combine and simplif the following subtraction Solve the following equation for all value(s) of : or 9 or 6 or 6 Be sure to check and reject! Part IV Answer the question from this part. The correct answer will receive 6 credits. Clearl indicate the necessar steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. A correct numerical answer with no work shown will receive onl credit. [6] 9. Algebraicall determine the intersection point(s) of the two logarithmic functions given below. log 6 and log log 6 log log 6 log log or 9 We still need the coordinate of intersection: log 9 6 log Intersection at: 9, is an etraneous root and must be rejected ALGEBRA WITH TRIGONOMETRY, SAMPLE EXAMS emathinstruction, RED HOOK, NY 7, 009

11 ALGEBRA WITH TRIGONOMETRY PRACTICE EXAM ANSWER SHEET Answer Ke Student. Teacher. School () Your answers to Part I should be recorded on this answer sheet. Part I Answer all 7 questions in this part () () () () () () Your answers for Parts II, III, and IV should be written in the test booklet. ALGEBRA WITH TRIGONOMETRY, SAMPLE EXAMS emathinstruction, RED HOOK, NY 7, 009