Deakin University MATH SIT191 11MM Exam 2 Revision Sem 2Revision Exam 2 Semester 2 REVISION FOR EXAM 2 – 2021

Document Content and Description Below

Deakin University MATH SIT191 11MM Exam 2 Revision Sem 2Revision Exam 2 Semester 2 REVISION FOR EXAM 2 – 2021 MULTIPLE CHOICE QUESTIONS Bound Book of Notes & CAS Calculator permitted 1. can ... be simplified to: 3. The equation is true when __________________________________________ 4. The graph y=4x+2-1 has an asymptote and y-intercept respectively as: 5. The value of x correct to three decimal places that solves the equation 0.5x-1=0.42 x is: __________________________________________ 6. log6(72)+log6(3) equals: __________________________________________ 7. The value of x that satisfies the equation 2log4 (7 x )-5=0 is: __________________________________________ 8. The value of x that satisfies the equation log2 (x )-log2 (x-1)=2 is: Exponential and Logarithmic Functions Revision Exam 2 Semester 2 9. The function +¿→ R f :R¿ where f ( x )=log2(3 x ) , has an inverse function f -1 . The rule for f -1 is given by: __________________________________________ 10. The graph below is best described by the equation: A y = log10(x + 1) + 2 B y = log10(x + 1) + 3 C y = log10(x - 1) + 2 D y = log10(x - 1) + 3 E y = log10(x + 2) + 3 1. An exact value of √3 3 corresponds to: A cos (300) B tan (1500) C sin (3300) D cos (3300) E tan (2100) __________________________________________ 2. The radian equivalent of 330º is: __________________________________________ 3. An angle is measured as 2x radians. The measure of the angle in degrees is: __________________________________________ 4. If sin(a)= 12 13 and 90º < a < 180º, then cos(a) must equal: __________________________________________ 5. The smallest value of 1-3 cos (θ) is: A -5 B -4 C -3 D -2 E -1 __________________________________________ 6. The solution to the equation 4 sin( x° )-3=0 , to the nearest degree, over the domain [0°, 360°] is: Circular Functions Revision Exam 2 Semester 2 __________________________________________ 7. The graph depicted below could have the equation: A y=2 tan(x ) B y=tan(x) C y=tan (2 x) D y=2tan (π x ) E y=tan( x __________________________________________ 8. The period and amplitude respectively for the graph with equation y=-sin (4 x) are: _____________________________________________ 9. The solutions to the equation 2 cos(x )-√2=0 over the domain [-p, p] is: __________________________________________ 10. The height of a swing above the ground can be modelled by the equation H=1+sin 3t (H in metres and t in seconds). When t = 5 seconds, H is approximately: A 1.26 m B 1.65 m C 0.65 m D 0.26 m E 1.71 m __________________________________________ 1. lim x→4(xx2--16 4 ) is equal to: A undefined B __________________________________________ 2. f ' (-5) for f (x)=-x2-x is equal to: 3. A function that has a gradient function equal to -3 x2 + 10 x - 6 could be: __________________________________________ 4. If ' (x )=¿ 4 x3 , then f (x) could equal: __________________________________________ 5. For f (x)=x3-3 x2-24 x+8 , the values of x where the gradient is zero are: A -8 and 1 Calculus Revision Exam 2 Semester 2 B -1 and 8 C -4 and -2 D -6 and 4 E -2 and 4 __________________________________________ 6. For f (x)=x3-3 x2-24 x+8 , the stationary points are: A (-8, -504) and (1, -18) B (-2, 36) and (4, -72) C (-6, -172) and (4, -72) D (-4, -8) and (-2, 36) E (-1, 28) and (8, 136) __________________________________________ 7. The gradient function for a particular curve has the rule . If the curve passes through the point (4, 4), then the equation of the curve is: __________________________________________ 8. If f¢ (x) = 5x4 - 6x2 and f (2) = 15 , then f (x) is: 9. The definite integral ∫ 3 1 (8 x3-12 x ) dx is equal to: A 104 B 192 C 112 D -26 E -8 __________________________________________ 10. An expression for the derivative of 1x using first principles would look like: A lim 1. A café has a choice of 3 entrees, 5 main meals and 4 desserts. If a customer intends having one of each course, how many combinations does she have? E 1518 __________________________________________ 3. If (n+2) ! = 132 n ! , then n is: Counting Methods Revision Exam 2 Semester 2 A 12 B 11 C 10 D 9 E 8 __________________________________________ 4. In the game of Scrabble, each player is issued with 7 letters. If a player receives these letters ‘O, U, M, E, S, T, H’, the number of different arrangements using all seven letters and beginning and ending in a vowel is: A 5040 B 180 C 720 D 28 E 120 __________________________________________ 5. Four people are selected from 6 men and 5 women to form a committee. The probability that the committee will consist of 2 men and 2 women is: EXTENDED RESPONSE On the actual exam you will be required to complete 2 Extended Response questions. They may be on any 2 of the 4 topics (Differentiation and Antidifferentiation count as one topic) that we have studied. Four practice questions are provided here. Unless stated otherwise, exact answers must be given. Question 1 EXPONENTIAL and LOGARITHMIC FUNCTIONS A bacterial culture is growing so that the number of bacteria present at time t hours is represented by N=A×4 kt . There are 52 000 present after 1 hour and 416 000 present after 4 hours. a) Write an equation to represent the number of bacteria present after 1 hour in terms of A and k. b) Write an equation to represent the number of bacteria present after 4 hours in terms of A and k. c) Use the two equations from parts (a) and (b) to solve simultaneously for A and k. What does the value of A represent? d) What is the number of bacteria present after 5 hours? e) How long does it take for the bacteria to reach 10 times its initial number? Question 2 CIRCULAR FUNCTIONS The population of wombats in a particular location varies according to the rule where n is the number of wombats and t is the number of months after 1 March 2013. (a) What is the initial population of wombats in this location? Revision Exam 2 Semester 2 (b) Find the period and amplitude of the function n. How many times does the wombat population complete its cycle over a year? (c) Between what figures does the population fluctuate? (d) On what date does the population first reach its lowest value? (e) (f) Find n(10). Over the 12 months from 1 March 2013, find the fraction of time when the population of wombats in this location was less than n(10). Question 3 CALCULUS Phil Hotham is a construction engineer working to build a new ski resort at Fool’s Creek. Part of the plan of the This section of the mountain, from A to B, is modelled by the curve with equation The x-axis represents the level at which the village will be built. T is the highest point of the ski run and L is the loqest point. All distances are measures in metres. a. Find the coordinates of A and B. Revision Exam 2 Semester 2 b. Find the height of the top of the mountain above the village. c. Find the coordinates of L. d. Find the average gradient of the ski run from T to L. Phil is planning a chairlift to take the skiers to the top of the mountain from the village. He plans to build the village at the point V, which is 40 m from A. The path of the chairlift is shown on the diagram below from V to T. e. Find the equation of the line which models the path of the chairlift. Phil has found that the chairlift will reach the mountainside at the point C before it gets to the top of the mountain. He decides to build a tunnel to complete the journey to the top, T. f. Find the coordinates of point C. g. Find the length of the tunnel required to get to the top of the mountain from C to T. State your answer in metres correct to 2 decimal places. The developers of Fool’s Creek would like to entice visitors all year round. Phil discovers the when the snow melts, a pond is formed in the valley between P and B, as shown in the diagram below. Revision Exam 2 Semester 2 h. Find the area of the cross-section of the pond. Question 4 COUNTING METHODS Lakeside Rebels is an A-League soccer team. There are 17 players in the squad of which 2 are goalies, 8 are forwards and 7 are defenders. 11 players make up a full team which consists of 1 goalie, 5 forwards and 5 defenders. a. In how many ways can a full team be chosen? b. How many teams are possible now? c. How many teams are possible now? d. In how many ways can these 4 people be seated? e. What is the probability that Jerry and the coach sit in the middle chairs? Revision Exam 2 Semester 2 f. In how many ways can the team assemble for the photo? g. In how many ways can the team line up? ANSWERS: (Multiple Choice) (Extended Response) 1. (a) 52 000 = A × 4k (b) 416 000 = A × 44 k (c) A = 26 000, k = ½. A is the initial number of bacteria. (d) 832 000 (e) log4(100) 2. (a)1600 (b) period = 6 months, amplitude = 400. It runs through its cycle twice in one year. (c) Population fluctuates between 800 & 1600. (d) @ t = 3 which corresponds to 1 June 2013 (e) 1000 (f) 1/3 Revision Exam 2 Semester 2 Revision Exam 2 Semester 2 [Show More]

Last updated: 3 years ago

Preview 1 out of 12 pages