Questions

14 couples 28 people take part in a contest where 14 people are to be selected at random to win a 100 prize Part a How many possible different combinations of winners are there If rounding use at least four digits after the decimal in your answer Part b What is the probability that one person from each of the 14 couples wins a prize If rounding use at least four digits after the decimal in your answer

15 9 Determine the first step to subtract fractions when the denominators are different Choose the correct answer below A Find the least common multiple of the denominators That number is the least common denominator LCD OB Subtract the numerators and subtract the denominators n Multiply by 1 using an appropriate notation to express each number in terms of the least common n denominator CD Subtract the numerators and keep the larger denominator Determine the LCD The LCD is 0 0

PRE LAB QUESTIONS Read through the lab introduction and procedures and answer the following questions a How does the movement of molecules compare between solutions at room temperature versus 45 degrees Celsius b Which solution would have a faster rate of diffusion What is osmosis C d This movement or diffusion of water across a membrane is called e What is a concentration gradient f What is meant by a steeper concentration gradient g Elodea is a plant that lives in fresh water ponds The pond water has a lower concentration of dissolved particles than inside of a cell so fresh water will tend to move into the cell Is freshwater hypotonic isotonic or hypertonic compared to the Elodea cells h You can tell that the water fills the whole cell because the green chloroplasts are free to spread everywhere even out to the edges against the cell wall Would a cell in fresh water be considered lysed turgid crenated or plasmolyzed Explain PART 1 OSMOSIS AND TEMPERATURE 3 Hypothesis regarding the relationship of the rate of osmosis and temperature

100 10 8 OB Multiply by 1 using an appropriate notation to express each number in terms of the LCD n OC Simplify if possible D Find the least common multiple of the denominators That number is the least common denominator LCD The LCD is 40 What is the next step in adding fractions when denominators are different OA Add the numerators keeping the same denominators OB Simplify if possible OC Multiply by 1 using an appropriate notation OD Add the numerators and the denominators n to express each number in terms of the LCD n

Table 1 Osmosis and Temperature Results Initial Weight g Final Weight g Weight Change g Change 60 Karo s dyed blue 60 Karo s dyed blue 23 31 22 24 Strinew scol b How does the percent weight gain of the artificial cell relate to the rate of osmosis C Based on your results summarize the rate of osmosis and temperature d What are the dependent and independent variables in this experiment Initial Weight g Final Weight g Weight Change g Table 2 Osmosis and Concentration Gradient Results Change PART 2 OSMOSIS AND CONCENTRATION GRADIENT a Hypothesis regarding the effect of different concentration gradients on the rate of osmosis 80 Karo s dyed red 24 77 OM diH 0 16 83 0 1M 6 07 PREGN Sucrose Concentrations 0 2M 0 4M 0 6M Bo finia sPERSO Buzos HAS b Which sucrose solution of yours caused the potatoes to have the greatest weight gain 0 8M

Regarding the MNS blood group which point is correct O Anti M and anti s are a cause of HTRS O Anti M and anti S are lgG O Anti s and anti S are a cause HTR O None is correct O Anti M Ant N Anti S and Anti s are a cause HTR

Nikki wants to put money away in an account to buy a car that costs 18 500 The account pays 5 per annum compounded semi annually a How much money should Nikki put into the account if she wants to buy it in 3 years 4 marks

Use the balance equation below 2 H g O g 2 H O l If 10 grams of H gas is reacted with 48 grams of O gas Which reactant is the limiting reactant How much H O is produced Show all working

Students should change the blades of their scalpels on a regular base or wil broken O TRUE OFALSE D BladerLASK CE

The eigenvalues of the matrix A O a 1 3 Ob 3 2 1 O c None Od 1 3 2 Clear my choice 3 001 220 1 0 1 are

4 12 pts A graph of a piecewise defined function is shown Find a formula for its function rule and also describe the domain and range of this function S 3 h 12 So S 7 5x K

One of the following functions is a solution of the second linear ODE y 9y 0 a y x cos 3x b y x cos 2x None O d y x cos r C

4 Listen 2 00 For what value s of x does f x 3 State the domain of the function Evaluate f x for x 3 Use the graph of the function to answer each part Some choices may be used more than once State the range of the function 6 2 2 2 4 1 0 00 2 00 3 U 3 00 3 3 U 3 0 4 00 3 U 3 0 5 undefined or does not exist 6 3

The table shows the number of hours of daylight on the 15th of each month in Queenstown New Zealand Month Hours of daylight Jan 15 23 Feb 13 92 Mar 12 45 Apr 10 85 Jun Jul Aug May 9 52 8 78 9 07 10 20 Sep Oct Nov 11 72 13 27 14 75 Dec 15 58 Model the data with a sine function whose value of a is positive and whose x values represent the month numbers so that Jan 1 Feb 2 and so on Use the data for September to determine the phase shift Enter your answer by filling in the boxes Round to two decimal places where needed

Master mix 1 GFP pUC19 F 5 CCAGGCTTTACACTTTATGCTTCC 3 GFP PUC19 R 5 CTTTGATTCCATTCTTTTGTTTGTCTGCC 3 Master mix 2 GFP PBR322 F 5 GATGACGATGAGCGCATTGTTA 3 GFP PBR322 R 5 CTTTGATTCCATTCTTTTGTTTGTCTGCC 3 Reagents Sterile water Taq buffer dNTPs Forward primer Reverse primer Bacterial DNA Taq polymerase Stock concentration 10X 2mM 2 M 2 M Final concentration 1X 0 2mM 0 2 M 0 2 M Final volume Volume L 1 reaction 2 L 1 L 20 L 7 reactions 126 L Question Fill in the required volumes for the PCR table above 6 Place your labelled PCR tubes in the PCR machine closest to you Once you and the group opposite you have loaded your tubes into the machine program the following conditions

M 3 4 1 7 2 4 1 3

Suppose we have two strings ABCBDAB and BDCAB What is the longest common subsequence of them B BC ABAB

sinx 0789 7 X 107 0 8 x 7 The standard factored form of integer r 5 733 sinxx lim 20 71 e e 0 q 1 X O using the unique factorization theorem is d 04 O a 23 3 72 O b 13 441 O c 32 72 13 O d 73 32 2 0 Ra 40 40x2 va vb lak laksa azoto 201 20 vb 1 2u 1 e ej ze 0 Ud

14 y T 3 21 1 H H 2 3 5 cos e 90 180 270 360 450 540

Alte is Frying 98 ft off the ground and its string is oulec taut The angle of elevation of the site is 53 Find the length of the string Round your answer to t nearest tenth 3 D

Using the equation below describe the transformations from the parent function s x x 7 8

7 x 8 4 x 1 6 4 2 8 6 2 2 8 2 2

An object falls freely in a straight line and experiences air resistance proportional to its speed this means its acceleration is a t kv t where k is a positive constant and v is the object s velocity The speed of the object decreases from 1200 ft s to 1100 ft s over a distance of 1400 ft Approximate the time required for this deceleration to occur Hint Note that a t v t and v t x t Write the velocity of the object as a function of time v t XXX

At noon a child s temperature is 101 2 F and is rising at an increasing rate At 1 p m the child is given medicine After 2 p m the temperature is still increasing but at a decreasing rate The temperature reaches a peak of 103 6 F at 3 p m and decreases to 100 F by 6 p m Draw a possible graph of the function T t the child s temperature at time t Choose the correct graph below O A AT t 105 100 noon 5 t 10 Q G OB AT t 105 100 noon Q Q O C 105 100 AT t noon Q OD 105 AT 1 100 noon Q G

Refer to the graph at the right to answer the following questions At which labeled points is the function increasing At which labeled points is the graph concave up Which labeled point has the most positive slope The function is increasing at the labeled point s Use a comma to separate answers as needed C AB C y f x E F

Graph each of the trig function using degrees the period and faze shift 13 y 4sin 0 in 40 90 180 270 360 450 540

2 8 f x X fool 6 4 3 2 8 6f 4 2 2 N y 6 4 8 x

Roughly 12 000 people in a certain country are diagnosed with thyroid cancer every year which accounts for 1 of all cancer cases It occurs in women three times as frequently as in men Fort thyroid cancer can be treated successfully in many cases with radioactive iodine or 1 131 This unstable form of iodine has a half life of 8 days and is given in small doses measured in millicuries a Suppose a patient is given an initial dose of 100 millicuries Find the function that gives the amount of 1 131 in the body after 120 days b How long does it take for the amount of 1 131 to reach 15 of the initial dose c Finding the initial dose to give a particular patient is a critical calculation How does the time to reach 15 of the initial dose change if the initial dose is increased by 5 a Suppose a patient is given an initial dose of 100 millicuries Find the function that gives the amount of 1 131 in the body after 120 days y t Tyne an expression Round coefficients to six decimal places as needed

Devise an exponential decay function that fits the given data then answer the accompanying question Be sure to identify the reference point t 0 and units of time The homicide rate decreases at a rate of 3 per year in a city that had 900 homicides yr in 2006 At this rate when will the homicide rate reach 800 homicides yr What is the reference point t 0 OA the initial number of homicides 900 B the rate 3 C the year 2006 OD the future number of homicides 800 What are the units of time A years B percents C cities OD homicides yr Write the exponential decay function y t 900 0 030 Type an expression Round coefficients to three decimal places as needed In what year will the homicide rate reach 800 homicides yr final answer Then round to the nearest whole number as needed

K Describe the following graph Your description should include each of the six categories On which interval s is the function increasing Select the correct choice below and if necessary fill in the answer box to complete your choice OA CILE Type your answer in interval notation Type an integer or a decimal OB There is no interval on which the function is increasing 16

Construct the perpendicular bisector of side AB of each triangle 3 4 B A B

Suppose the acceleration of an object moving along a line is given by a t kv t where k is a positive constant and v is the object s velocity Assume that the initial velocity and position are given E v 0 4 and s 0 0 respectively Complete parts a through c a Use a t v t to find the velocity of the object as a function of time v t 4e kt b Use v t s t to find the position of the object as a function of time s t K 1 4

Let f be a differentiable function Suppose that f 1 8 f 5 3 f 1 5 and f 5 6 5 Further suppose that that f x dx 9 Then the integral 25 rf x dx is equal to 0

Draw the graph of the function y f x that satisfies the following properties Both the function and the slope increase as x increases Select all graphs that satisfy both properties A Q Q G B Q CELE C D

Triangle P Q R is a dilation of triangle PQR using center Cand scale factor 1 5 1 Q in 3 9 3 1 1 Is triangle P Q R larger or smaller than triangle PQR Explain how you know 2 What is the length of segment P Q Explain how you know

Which functions have the property that the slope always decreases as x increases A B Q Q C Select the correct choice below and if necessary fill in the answer box to complete your choice O A Type A B C or D Use a comma to separate answers as needed OB None of the functions have the property that the slope always decreases as x increases

Suppose the acceleration of an object moving along a line is given by a t kv t where k is a positive constant and v is the object s velocity Assume that the initial velocity and position are given by v 0 4 and s 0 0 respectively Complete parts a through c a Use a t v t to find the velocity of the object as a function of time v t CI

Describe the way the slope of the graph on the right changes from left to right C For x 2 which of the following statements is true OA The slope of the graph is increasing from left to right OB The slope of the graph is decreasing from left to right OC The slope of the graph is neither increasing or decreasing from left to right 10 8 8 6 X 6 8 10

K Describe the following graph Your description should include each of the six categories SIL On which interval s is the function increasing Select the correct choice below and if necessary fill in the answer box to complete your choice O A Type your answer in interval notation Type an integer or a decimal Use a comma to separate answers as needed B There is no interval on which the function is increasing 10 10 17

In the year 2000 the population of a certain country was 285 million with an estimated growth rate of 0 5 per year a Based on these figures find the doubling time and project the population in 2150 b Suppose the actual growth rates are just 0 2 percentage points lower and higher than 0 5 per year 0 3 and 0 7 What are the resulting doubling times and projected 2

1 31 f cos t 2 dt 33 3 1 7x dx wo

2 Find h and r if y 15 A 31 r 43 h

2 P x 15x 29x 17x 3 x 3 5

53 If f is continuous and f f x dx 10 find 2x dx

Devise an exponential decay function that fits the given data then answer the accompanying questions Be sure to identify the reference point t 0 and units of t The pressure of a certain planet s atmosphere at sea level is approximately 900 millibars and decreases exponentially with elevation At an elevation of 25 000 ft the pressure is one third of the sea leve pressure At what elevation is the pressure half of the sea level pressure At what elevation is it 3 of the sea level pressure What is the reference point t 0 A the elevation at sea level 0 ft B the elevation 25 000 ft C 3 of the sea level pressure OD the pressure at sea level 900 millibars What are the units of t OA millibars B feet C pressure levels At what elevation is the pressure half of the sea level pressure 15 773 feet Do not round until the final answer Then round to the nearest whole number as needed At what elevation is the pressure 3 of the sea level pressure

17 sec 0 tan 0 de

1 f x 1 2x x dx

Say you want to start a college fund for a newborn You would like to make sure the account has 20 000 in it on their eighteenth birthday The account you found has a 6 fixed interest rate that compounds monthly What monthly payments do you need to make to make sure there is 20 000 in 18 years Round to the nearest cent and don t include the dollar sign A

The population of a town with a 2016 population of 63 000 grows at a rate of 1 8 per year a Find the rate constant k and use it to devise an exponential growth function that fits the given data b In what year will the population reach 105 000

Find the area of the surface generated by revolving x 12y y2 on the interval 3 y 7 about the y axis The area is 16x square units Simplify your answer Type an exact answer using x as needed