Math 3201 Sample Exam. PART I Total Value: 50% 1. Given the Venn diagram below, what is the number of elements in both A and B, n(aub)?

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1 Math 0 Sample Eam PART I Total : 50%. Given the Venn diagram below, what is the number of elements in both A and B, n(aub)? 6 8 A green white black blue red ellow B purple orange. Given the Venn diagram below, which element(s) is (are) in sets A, B or C, A B C? {0, 0, 0, 50} {0, 0, 60, 70, 80, 90} {0} {0, 0, 0, 0, 0, 50, 60, 70, 80, 90}. There are 6 students in a classroom. students have blonde hair (H), 6 have brown ees (E), 6 do not have blonde hair or brown ees, and have blonde hair or brown ees, but not both. How man of these students have both blonde hair and brown ees, H E? 7 0. A is the set of positive even integers less than. B is the set of multiples of between and 0. Which element(s) is (are) not in the intersection of A and B, (A B)? A C B {,, 8, 9, 0, 5, 8} {,, 8, 9, 0,, 5, 8} {6} {6,} 5. A student incorrectl wrote! =. To produce a correct solution for!, what operation should be applied to. add divide b multipl b subtract 6. Consider the word CAR. In how man different was can the letters be arranged? 6 7. A student must select a protective case for her new cell phone. She must choose a colour and a stle for her case. Given the selections below, how man protective case choices does she have? Case Colour Case Stle Red Blue hard Green Black White soft Silver 8 5 0

2 8. Simplif: n n ( n )! n! n n n n n n 9. In the grid below, a person must travel from A to B b onl heading East (E) or South (S). One eample of a route is shown representing three moves East followed b two moves South (EEESS). Under these rules, which represents the total number of possible routes that can be taken to get from A to B? A B W N S E Eample: A E E E S S B Route: EEESS 5!!! 6!!! 5! 6! 0. There are 7 marbles in a bowl: white, green and blue. If taken out one at a time, in how man different was can all 7 marbles be taken out of the bowl? A soccer plaer has 7 attempts on net and 6 goals scored. What are the odds in favour of her scoring a goal on her net attempt? 6 : 6 : 7 : 6 7 : 6. A committee of three people will be randoml chosen from a group of nine people; 5 females and males. Which represents the probabilit of selecting a committee that has at least one male and at least one female member? C C C C 5 5 C 9 9C 5C 9C 5C C C 5 C C C C C 9 9C C 9C C C C 5. A and B are mutuall eclusive events. The probabilit that either A or B will occur, P(AB), is 56%. If the probabilit of A occurring, P, is 7%, what is the probabilit of B not occurring, P? 7% 9% 6% 7%. You have a si-sided die with each side numbered one through si. You also have a coin with heads on one side and tails on the other. What is the probabilit of rolling a number greater than with the die and tossing heads with the coin? 6 Mathematics 0 Sample Eamination Page of 0

3 5. A deck of 0 cards consists of different coloured sets: red, blue, green and ellow. Each set is numbered from 0 to 9 as shown below. If two cards are randoml picked from the deck, what is the probabilit that the first card is blue or green and the second card is also blue or green? Card Colour Cards red blue green ellow What are the non-permissible values for the rational epression? 5 (),,,5,,,5 7. What is the simplified form of, O,5? What epression is equivalent to 5,? Simplif: 8,,,,,,,, 0. Simplif: 6 9, 0 9, 0 8, 0 8 9, 0 Page of0 Mathematics 0 Sample Eamination

4 . Simplif: 5 6 9,,,, ( ) ( ). What is the range of the function f( ) shown in the graph below?, R, R, R, R =f() What is the -intercept of the graph of the function f( )?. Which graph best represents a function with the characteristics listed below? Three -intercepts Etending from Quadrant II to Quadrant IV 5. Given the table, the scatter plot and the curve of best fit of the polnomial f(), what is the value of f(5)? =f() From which quadrants does the graph of f( ) etend? II to I II to IV III to I III to IV Mathematics 0 Sample Eamination Page of 0

5 7. Which function passes through the point, 7? f( ) f( ) 8. Which is a decreasing eponential function? ( ) 5 f ( ) 7 f ( ) 7 f f ( ) f ( ) f ( ) 9. Which eponential function best represents the graph shown? f ( ) f ( ) f ( ) f ( ) 6 0. The population of a strain of bacteria growing in a Petri dish is modeled b the function Pt ( ) 000 t where P(t) represents the number of bacteria and t represents the time in hours after the initial count. How much time will it take for the number of bacteria to reach 000? h 8 h 6 h h. Solve for :. Which is true of the table given below? (ears) (amount) Initial Amount Amount Growth 0 doubles ever three ears 0 triples ever two ears 0 doubles ever three ears 0 triples ever two ears At ( ) 00. The function that models the deca of carbon- is 570 t, where A(t) is the number of grams of carbon- present at time t, in ears. Which statement is true? The amount of carbon- doubles ever 570 ears. There are 50 g of carbon- present initiall. g will be present after 50 ears. 50 g of carbon- will be present after 570 ears. Page 5 of0 Mathematics 0 Sample Eamination

6 . Which graph best represents ln? 5. What is log log written as a single logarithm? log log log6 log 6. Evaluate: log What is the logarithmic form of C 5 d? d log5 C d log C 5 C log5 d C log d 5 8. Solve for : 7 log log7 log7 log log log7 t 9. The equation A() t Ao log7 log represents a radioactive sample after t ears. How much time will it take for 5% of the sample to remain? 0.7 ears 0.9 ears 8. ears 0.0 ears 0. What is the midline equation for the graph shown below? = = = 0 = Mathematics 0 Sample Eamination Page 6 of 0

7 . What are the amplitude and maimum value for the function f ( ) sin 60? Amplitude Maimum. The graph of which function has a period of 80 0? cos cos 80 cos 80 cos. What is 9 radians in degrees? What is the domain of the function cos? 6, R R 6, R R 5. The graph of the function cos has its amplitude doubled and its period halved. Which represents the new function? cos cos6 8cos 8cos6 6. The interest rate on the loan shown in the chart below is 5% compounded monthl. How much of the second pament is the interest toward the loan? Pament Period (month) Pament ($) Principal Paid ($) Balance ($) 0 5, , , ,8.65 $59.6 $60.89 $6.50 $ bi-weekl paments are required to pa off a loan. How man ears does this represent? 6 ears ears ears 6 ears 8. A represents a bank loan that is compounded annuall. What is the interest rate? % % 6% 8% Page 7 of0 Mathematics 0 Sample Eamination

8 9. Which represents the lowest interest that would be paid? Interest rate Compounded % dail % monthl 9% dail 9% monthl 50. A student repaid a total of $880.7 for a loan including the principal and interest. If the interest rate was 9% compounded monthl for ears, what was the principal amount of the loan, to the nearest dollar? $0 $00 $6 $795 PART II Total : 50% Answer ALL items in the space provided. Show ALL workings students wrote eams in Math, Biolog and English. The Venn Diagram below represents the percentage of those who wrote the eams. Algebraicall determine the percentage of students who wrote all three eams, and determine the number of students that this represents. Biolog ( -7)% % % (6 )% % Math % ( +7)% English 5.(a) In how man was can a teacher seat four girls and two bos in a row of si seats if the two bos must be seated net to each other? 5.(b) Algebraicall solve for n: P n 5.(c) Four students are to be chosen from a group of to fill the positions of president, vice-president, treasurer and secretar. In how man was can this be accomplished? 5.(a) If a 5-digit number is generated at random from the digits,,, 5 and 8 (with no repetition), what is the probabilit that it will be an odd number? 5.(b) A person will be randoml selected from a group to draw a marble from a bag. The odds of selecting a female from the group is 7:8 and the odds of drawing a red marble from the bag are :. What is the probabilit of a non-red marble being drawn from the bag b a male from the group? 5.(a) Simplif and state restrictions: Mathematics 0 Sample Eamination Page 8 of 0 8 8

9 5.(b) Pat and Chris can paint the house in 5 hours if the work together. Pat is a professional painter and can paint twice as fast as Chris. How long would it take Pat to paint the house b himself? 55.(a) Sketch two possible graphs that are different, et are both cubic functions with negative leading coefficients and negative -intercepts. Eplain wh the graphs ou have sketched are different. Graph : Graph : 55.(b) Given the function characteristics. f( ) 5, complete the table to describe its () (i) -intercept end behaviour (left and right) Ma # of possible -intercepts () (ii) Eplain wh the graph of this function is not a parabola. 56.(a) Algebraicall solve for : 7 56.(b) Nora is about to invest $5000 in an account that pas 6% interest a ear compounded monthl for the net ears. A different financial institution offers 6.5% interest a ear compounded semi-annuall for the net ears. Write a function that models the growth of Nora s investment for each situation. Should Nora invest her mone in this financial institution instead? Eplain wh or wh not. Page 9 of0 Mathematics 0 Sample Eamination

10 57.(a) Algebraicall solve for : (b) The ph scale is used to measure the acidit of a solution. The ph, p(), is defined b the equation p( ) log, where the concentration of hdrogen ions,, in a solution is measured in moles per litre (mol/l). () (i) Black coffee has a ph of 5. What is its hdrogen ion concentration? () (ii) Baking soda has a ph of 9. In terms of concentration, how much more acidic is black coffee than baking soda? 6 58.(a) Use the sinusoidal function shown below to answer the questions that follow () (i) Determine the amplitude, period, equation of midline and the range. () (ii) Use the information from part (i) to determine a function that represents the graph in the form acos b d. 59. Pat borrowed $500 at a rate of 8% compounded monthl for ears. How much interest will Pat be charged for borrowing the mone?. A. D. B. A 5. C 6. D 7. B 8. A 9. A 0. B. A. A. C. B 5. C 6. C 7. C 8. D 9. B 0. A. C. D.A.A 5. C 6. C 7. A 8. D 9. D 0. B. D. A. D.A 5. A 6. B 7. A 8. B 9. C 0. B. A. D. B. B 5. D 6. B 7. B 8. D 9. B 50. A 5. 6%=7STUDENTS 5.A. 0WAYS 5.B. n = (n=- IS A RESTRICTION) 5.C.,880 5.A. 8/0=.0=0% 5.B. / * 8/5 = /5 5.A. +(X-)/ X CANNOT EQUAL, / 5.B. X = 7.5 Pat's work per hour is /5 does this mean he take 7.5 hours? 55A. Draw two downward starting cubics with a different number of -intercepts Different Number of -int.s 55Bi. -int = - Q to Q Ma # of int= ii. Parabolas have a maimum degree of, while cubics have a maimum degree of 56a. = b. I eilds $598.0, while II eild $ so Institution II eild higher ROI 57a. = bi mol/L 57b ii mol/L or 0^ or 0000 times more acidic (each ph increase equals a magnatude of 0 increase) 58ai. a= period=0 degrees midline =- range (-less or equal less than equal, is all real) ii. =cos- 59. A = $75.59 I = A-P so total interest is $ Mathematics 0 Sample Eamination Page 0 of 0