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Mathematics function
创建日期：2024-08-31 15:34:41
所属分类：数学mathematics
标签： Mathematics
Mathematics function

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Mathematics C

Term 2 Final Examination Paper

Question 1 (12 marks) Use a SEPARATE book clearly marked Question 1

(i)        For the set of scores  3,5,5,5,7,8,9,11,13,  find the value of:

(a)       the median.

(b)       the standard deviation.

(iv)      For a given function f (x), f '(x) = 4x and f (-1) = 3. Evaluate f (2) .

(v)       In a particular town, 40% of the population are aged under 30 years

and 45% are aged from 30 years to 60 years inclusive. If this information is represented on a sector graph, find the size of the sector angle representing the percentage of the population aged over  60 years.

(vi)      A box contains 3 blue and 5 yellow balls. Two balls are withdrawn from the box without

replacement. Find the probability that the two balls will be of the same colour.

(vii)     From the frequency histogram below:

(a)        calculate the mean.

(b)       write down the mode.

(c)       write down the median.


Question 2      (12 marks) Use a SEPARATE book clearly marked Question 2

(i)        Differentiate each of the following with respect to x giving your answers

in simplest form.

(ii)       Find the value of k so that the following is a valid probability density function:

(iii)      A game has 3 possible outcomes for a player. The player can win $130,

win $10 or lose $10. The respective probabilities of these outcomes are 5%, 15% and  80%. Determine whether or not the game is fair.

(iv)      A factory produces pens in large numbers. It is known that 2% of the pens produced

are defective. Find the probability, in unsimplified form, that in a sample of 40  pens:

(a)       no pens are defective.

(b)       at least one pen is defective.

(c)        exactly seven pens are defective.

(v)       In the expansion of  (2 + 3x) 14    show that the coefficients of x 8   and x9  are equal.


Question 4      (12 marks) Use a SEPARATE book clearly marked Question 4

(i)        A cashbox contains  6  ten cent coins and  4  twenty cent coins.  Two coins are

removed randomly from the box, one after the other, without replacement. The possible total value of the two coins is recorded as the random variable X.

(a)        Construct the probability distribution table for X.

(b)       Calculate the expected total value of the two coins.

(ii)       In this question, you may use the table of areas under the standard normal curve, which can be found at the end of this examination paper.

The life expectancy of fluorescent light tubes is normally distributed with a mean of 7 000  hours and a standard deviation of  1 000 hours.

(a)       Find the probability that a fluorescent light tube will have a life expectancy of less than  5 000   hours.

(b)       In a batch of  20 000   fluorescent light tubes, find the number of tubes  that

could be expected to last between   6 000  and  8 000   hours.  Answer correct to the nearest  100  tubes.

(c)       The manufacturer’s guarantee requires them to replace free of charge any

fluorescent light tubes which do not last a specified minimum number of hours (x hours). If 2%  of fluorescent light tubes are replaced free of charge because of the guarantee, find  the value of x.

(iii)            Maintenance costs for an apartment complex generally increase as the complex gets

older.  Management determines that the rate of increase in maintenance costs of an

apartment complex is given by  dt/dM = 90t2 + 5000  where  $M is the total

accumulated maintenance costs t years after the complex was built.  Find the total maintenance costs during the seventh year after the apartment complex was built.

Question 5 (12 marks) Use a SEPARATE book clearly marked Question 5

(i) The curves y = 2x 一 x2  and are shown below for the domain   一 0 . 25 ≤ x ≤ 3 . 5.

(a)       If the curves intersect at the point R , in the first quadrant, show that R is the point

(b)       Find the area bounded by the two curves and the y axis.

(ii)       Consider the function f(x) = x + 1+ x2/4.

(a)       Find the asymptotes of the curve y = f (x).

(b)       Show that f (一 2) = 0 .

(c)       Show that the function has only one stationary point and determine its nature.

(d)       Find values of x for which the graph of y = f (x) is concave upwards.

(e)       Sketch the curve y = f (x) showing its essential features.

(f)        If the equation x +1+ x2/4 = k has exactly two solutions, find the value of k.



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关键词一 关键词二 关键词三 关键词四 关键词五 和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 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EARN 5 FE 825 IERG 5130 STAT 8178 EE161 ADS2 G54FUZ CS326 113B ECN 226 QBUS6860 ELEC3202 COMP9334 MGT11B MET CS 777 STA238 00099F Python SMM306 CMT206 EC116 SP MAST90084 CS480/680 BCPM0091 CMPT 300 ECON2209 FY20 STAT 432 CVEN9625 MATH1712 CMP9771M CMP3750M CIS 325 AI506 MAT344H1S MGT7180 PSTAT 160B CSYS5010 1D STAT 453/558 ME152B STA304H1F CSCI-128 ME428 CO3002 FINE 7640 COMP3234 ECSE 223 EE497 – 3D MATH5905 ECS648U ENG5009 MATH10242 EC665 A CPI221 ISOM5220 MACE40402 MGT B456F COMP9315 AFM 113 STAT 778 CS 564 MA231 CS 230 CS 124 COMP5511 CSC317 ITEC1010 ELEC207 INFT 3019 7CCMFM06 EE 161 5G ECLT5810 MATH 7349 CS526 O2 COMP90054 ELE00063M ACCT5034 ARC1015 CSCI 40 CSCI E40 FIN 524B CS 462 389COM CMT309 MFIN703 COMP4250 STA304 STA304H1S STA 1003 FIN 448 BUFN 732 CS520 CVEN3701 ECMT6006 PHAS0100 CSIT314 MDIA 5028 CSCI 2134 MAT 451 CMPT 459 STAT 457 INFO20003 COMP4141 IELE8066 F540 ECM9 CSE 6321 FIN 430 MATH3911 BFC5916 COMP1011 EEE 6209 STATS 240 CW3 COMP206 COMP1003 4331W ISE 530 CMPT 295 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MATH20602 COMP532 MAS275 COMP5318 COMP4002 FIT5086 MAST20004 FIT3152 FIT5129 CIS2380 CS521 COMP 1005 EECMS CITS5501 ECE 462 ECON 6002 ENG 4051 CSC 648 CMT654 MECHENG 713 PHYS1002 AMME 2000 FP0060 DDES3200 MECHENG 743 BINF90002 FIT2081 ISYS90081 ELECTENG 722 BUS 360 ECOS3010 BUS2810 ETF2100 ENG2048 STAT5002 COMP2017 CEME 2003 MATS3004 COMP9319 PHYS1001 COMP5349 AMME2261 COMP-381 FIT3173 COSC2757 ENG4025 QBUS2820 COMP9414 MATH2021 EOSC118 MFIN6690 PMATH 321 CSE-141L MATH575A COMPSCI5002 COMP1511 management comp2123 FINS3616 COMP 3331 COMS30034 DTSC 71 AcF 702 AcF702 DTSC71 MAT021 ELE8083 ACFI213 EG-127J 127J FIT5163 FIT2001 ELE00113M CMT310 CS 245 ENGL 1101 MTH6115 EE497 CS 325 Math 124A MTH5130 MBA502 MGT 5380 ARCH 1261 F033800 20LLP109 ELE4009 FINANCIAL COMP3331 Computer ECE4179 20T3 COMP9311 COMP9311 UNSW MFIN6210 ACCT 5930 EE590 ENG2029 ECO100 SIT315 ACCT3610 COMP3600 STK2100 FIT2004 COMP30020 ACTL1101 Stat 101B BANA 200 COSC2473 ENGG1400 AI COMP90043 MMF 1914H PHYS 127 CS584 CIVL2010 ECMT2150 CS 333 CP1406 KIT308 Economics 701 ECON3740 ECE 5759 BFC3340 FINC2012 COMP4500 MATH3871 FIT3080 18-819C Economic ECO202Y5Y PHY100 FINC-780 Econ 100B EC602 IE582 EE450 COMP9517 WRDS 150B ECON 570 LECTURE 2 ECA5101 ECE 4420 ADAD9311 FIT3031 CS 544 MF 703 CS 6140 KIT501 ENGSCI 344 CSC171 IE 332 FINM8007 21S2 COSC 1114 FE545 E471 SIT102 CSC108 MAT301 IAE 101 COP3503 STAT2004 EC 303 CS1026 STAT1203 MATH3171 ISOM5160 IFN657 FIT2014 ACCT2102 DSCI550 STATS 330 ELEC421 COMP3670 QBUS6840 MEES:698B MAST30027 MIET1077 Economics IFT 6758 FIT5122 BUSN5101 CptS 111 HRMT5502 Math2018 PP 312 INFS3200 CZ3005 CSSE1001 SENG 2011 MKTG 553Q BUFN 640 COMP507 ETF5952 DATA 311 ECE4043 BANK3011 finance M3H623544 HW1 INFS 7410 AI6103 STAT3888 INFS3208 ACCT7103 ECOS3013 PSYCH 20B F79MA STAT3006 ENGG952 2X MGSC 7000 ECE4132 MSF 526 MATH 3033 CDS 511 EEEE4120 EEET2465 ECA5103 MATH2070 ELEC3104 BU51019 EEE8147 ENGR20003 COSC 1107 ETF3200 FNCE 435 MSFI 435 ISyE6420 GENG4405 HW ETC5523 IE 7315 MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A 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