In: Science

Submitted By KhuanChinn
Words 794
Pages 4

1.1 Exponential and Logarithm Equations

1. Evaluate each expression (a) [pic] (b) [pic] (c) [pic]

2. Solve the following exponential equations.

(a) [pic] (b) [pic]

(c) [pic]

3. Solve each of the following equations.

(a) [pic] (b) [pic]

(c) [pic]

4. Solve the logarithmic equations for [pic]

(a) [pic] (b) [pic]

(c) [pic]

5. Solve the following equations: (i) [pic] (ii) 32x+ 2 – 28 (3x) + 3 = 0 (iii) [pic] (iv) [pic] (v) [pic]

6. Solve the following equations: (i) [pic] (ii) log2 x + 3logx 2 = 4 (iii) [pic] (iv) [pic] (v) [pic]

7. Solve the following simultaneous equations: (i) [pic] [pic]

(ii) [pic] [pic]

(iii) [pic] [pic]

8. Find the smallest positive integer n such that (i) [pic] (ii) [pic] (iii) [pic]

9. (a) If[pic], prove that[pic]. (b) Given [pic]solve for x.

1.2 Complex Numbers

10. Evaluate the expression and write the result in the form [pic]

(a) [pic] (b) [pic]

(c) [pic] (d) [pic]

(e) [pic] (f) [pic]

(g) [pic] (h) [pic]

11. Given that [pic], find the values of p and q.

12. Find [pic] in the form [pic], where [pic]

13. If [pic] and [pic], find

(a) [pic] [pic] (b) [pic] [pic]

14. Solve the following equation for the values of x and y:


15. Express the following complex numbers in the form a + bi. (i) [pic] (ii) [pic] (iii) [pic] (iv) [pic] (v) [pic] (vi) [pic] (vii) [pic] (viii) [pic] (ix) [pic] (x) [pic] (xi) [pic] (xii) [pic]

16. Express z = [pic] in the form x + yi, where x and y are real numbers. Draw an Argand diagram to show the location of z. Hence, find the modulus and argument of z.

17. Find the value of x and y, [pic], for the…...

Similar Documents

Math Investigation

...OBLONG, OBLONG WHERE DO WE BELONG? (Oblong Numbers) I. Introduction Math investigations engage one’s mind to formulate conjectures from observed numerical phenomenon. Patterns are being observed and these patterns are then translated into mathematical expressions such as the equation. Thus this investigation would lead to mathematical models that need to be proven. However, the formulation of a mathematical model is not an easy task. It requires skills and experience to device such. Then, after the modeling, it requires testing the model by verifying extreme cases and later proves that this model is true to all cases. This investigation involved two cases: (1) relationship exists between the number of columns and the number of dots (oblong numbers) and (2) relationship exists between the number of rows and the number of dots (oblong numbers). As we go further with the investigation, we’d come up with a mathematical model that leads to answer the aforementioned cases. Moreover, we are looking for the possible extent if there are still existing mathematical facts involving these cases that are uncovered and waiting to be explored. Situation: OBLONG NUMBERS are numbers which can be represented in a rectangular array having one dimension one unit longer than the other. [pic] II. Statement of the Problem This mathematical investigation aimed to ascertain the relationships exist between the number of columns/rows and the number of dots (oblong...

Words: 1847 - Pages: 8


...|Read this week’s Electronic Reserve Readings. | | | |Participation |Participate in class discussion. | |2 | |Discussion Questions |Respond to weekly discussion questions. | |1 | |Individual |Resource: Ch. 10 of The Art of Thinking | |6 | |Questioning and | | | | |Investigation |Suppose you live in a new suburban community that combines all the amenities and | | | | |benefits of a close, small community with the benefits of living near the big city. Some| | | | |years pass and several children and adults in the community start developing extensive | | | | |and similar illnesses. You think this is clearly not a case of genetics, and you become | | | | |suspicious that something has gone wrong in the development planning and execution of | | ...

Words: 4724 - Pages: 19

Economic Investigation

...Dr. Stella Madueme. / International Journal of Engineering Science and Technology Vol. 2(4), 2010, 610-617 Gas Flaring activities of major oil companies in Nigeria: An economic investigation. Dr. Stella Madueme Department of Economics University of Nigeria, Nsukka Enugu State, Nigeria Abstract This paper reveals the general trends in gas flaring in seven major oil companies in Nigeria from 2000 to 2008. It reveals which company’s flaring activities constitutes the greatest hazard. Data was collected through archival sources. Gas flaring activities was highest between 2000 to2002 but presently only about a quarter of all gas produced is flared. TEXACO and PAN OCEAN has been flaring more than 95% of its gas from 2000 to 2008. SHELL was discovered to maintain the best record in terms of the fact that its flaring activities has been decreasing consistently over the years. Some of the recommendations are planned targeted policies towards gas flaring reduction, increased government taxation on gas flaring and governmental reward packages to companies with lowest flaring activities are also necessitated. Keywords: Oil company. Gas. Flaring, economic, environmental, hazard Introduction and literature review Gas flaring has been recognised as an economic waste and a great environmental hazard. Various researchers have written extensively on various issues in the gas sector. Blasing, Hand and Kimberly (2007) worked on monthly carbon emissions from natural gas flaring and cement......

Words: 2578 - Pages: 11

Criminal Investigation

...Police Department CRIMINAL INVESTIGATION Policy Number: OPS-6.02 REFERENCE: TPDM Policy OPS-6.02.1 Effective Date: June 1, 2000 Revised Date: October 20, 2004 Accreditation Standards: Mass. Gen. Law: Chap. 90, Sec.22B, MRCP 14(a)(1)(A)(viii) Other: Comm. v. DiGiambattista, District Attorney’s Guidelines on Identification Procedures _________________________ POLICY: It shall be the policy of the Truro Police Department to conduct criminal investigations for the purpose of clearing crimes by arrest and/or complaint; to prosecute lawbreakers; and to recover stolen property. Whenever members of this department conduct an investigation, which requires the interrogation of a suspect, or an interview, connected therewith, all constitutional and statutory rights guaranteed under the law shall be afforded to the individual. The Truro Police Department will ensure that there is a screening of all reported offenses to assure adequate follow-up investigation whenever appropriate. Whenever possible, the District Attorney’s Guidelines on Identification Procedures with attached forms and checklists will be used when dealing with photo line ups, arrays, show ups and taped interrogations and identifications. (Revised October 20, 2004) PROCEDURES: 1. UNIFORM PATROLMEN CONDUCT PRELIMINARY INVESTIGATIONS: Most preliminary investigations will be conducted by members of the patrol force since they are usually the first to arrive at the scene and can start the investigation without delay.......

Words: 4250 - Pages: 17

Soil Investigation

...DETAIL SOIL INVESTIGATION INTRODUCTION SOIL INVESTIGATION is carried out to design a right type of foundation safely and economically. A designer requires adequate information about the physical properties and the arrangement of the materials underground. The field and laboratory investigations needed to get this necessary information is known as soil exploration. The study of complete soil investigations can be grouped as follows : • Objectives or purposes, • Preliminary investigations, • Methods of site exploration, • Depth and spacing of trial pits and bore holes, • Choice of a method, • Recording of data. The investigation of the geology and previous uses of any site, together with the determination of its engineering, environmental and contamination characteristics is fundamental to both safe and economic development. [pic] SOIL TESTING • Soil tests can be conducted on samples that truly represent the soil at the site. • Soil sampling, testing and test interpretation must be conducted with guidance from specially trained and experienced personnel. • Proper soil testing is proven to be a reliable basis for the design of foundations and commonly used in site investigations to indicate their potential use and limitations. • Based on the premise that the behavior of soil masses under imposed conditions can be predicted if certain soil properties can be measured. • The results of soil tests must be interpreted based on past......

Words: 1681 - Pages: 7

Parabola Investigation

...Parabola Investigation In this task, I will investigate the patterns in the intersections of parabolas and the lines y=x and y=2x, then I will prove my conjectures and to broaden the scope of the investigation to include other lines and other types of polynomials. 1. Consider the parabola y=(x-3)2 +2=x2-6x+11 and the lines y=x and y=2x. The original graph is shown below (graph 1.1) Find the intersections of the parabola with y=x and y=2x, Graph 1.2. Also, label the x-values of the intersections with the line y=x as they appear from left to right on the x-axis as a1 and a2; label the x-values of the intersections with the line y=2x as b1 and b2. Now, I will using the graph and graph calculator, find the values of a1-b1 and b2-a2 and name them respectively SL and SR. SL=a1-b1=2.381966-1.763932=0.618034 SR=b2-a2=6.236068-4.618034=1.618034 Now, calculate the quantity D= │SL-SR│ D= │SL-SR│=│0.618034-1.618034│=1 By algebra calculation, D=│SL-SR│ =│ a1-b1-(b2-a2) │ =│ a1-b1-b2+a2 │ =│ (a1+ a2 )-(b1+b2) │ Now, I will try other parabolas of the form y=ax2+bx+c, a>0, with vertices in quadrant 1, intersected by the lines y=x and y=2x. y=x2+2x+1 [pic] From the graph we can see there is no intersection of the parabola and y=x, y=2x. Using the algebra way: Solve: (a) x2+2x+1=x (b)......

Words: 566 - Pages: 3


...existence that proved highly effective and efficient for business firms. “Social media marketing is the process of gaining website traffic or attention through social media sites. Social media marketing programs usually center on efforts to create content that attracts attention and encourages readers to share it across their social network” (Wikipedia, 2014). As said by Nielsen’s (2011), State of the Media: Social Media reports that 70% of social media users are engaged in online shopping (Nielsen, 2011).Consumers can access any site and get their needs fulfilled from any part of the world. Multi-national companies such as Apple, Samsung etc. have taken advantage of the growing opportunities in the field of social media marketing. This investigation focusses on the topic advantages and tools of social media marketing for various business firms. Social media marketing proves advantageous in providing a competent for companies that include social media marketing within their marketing strategies , one of the major advantage of social media marketing is the cost effectiveness , companies can communicate their ideas to large wide spread community all over the world in a minimum cost , this not only reduces the overall costs but also helps companies understand the consumer behavior and feedback of variety of consumers towards their respective product or service that they are providing which can help them innovate and improve the existing product or service, . Social media......

Words: 796 - Pages: 4

Individual Investigation

...The Welsh Baccalaureate Individual Investigation ‘A comparison of underage drinking in Wales and England’ Ismail Ibrahim Cathays High School 68720 The Individual Investigation Checklist Name: Form: |Have you? |Student Check |Teacher Check | |Planning | |Looked at example Investigations | | | |Used the booklets and help sheets given to you | | | |Chosen a topic and checked it with staff | | | |Looked at the topic in Wales and another country | | | |Checked that there is enough data on the topic | | | |Chosen and checked a suitable title | | | |Mind mapped your ideas | | | |Filled in and printed your planning sheet ...

Words: 5009 - Pages: 21

Scientific Investigation and Non-Scientific Investigation

...Law, K.Y. School of Arts and Social Sciences The Open University of Hong Kong Abstract The paper reviews the main difference between scientific investigation and non-scientific investigation and the change of the scientific principles from different approach. In the first section of the text, the author describes the definitions of scientific investigation and non-scientific investigation and the different of both researches. Furthermore, Using the example to explain the difference between the two, so that a better understanding. The second section of this study is to present three styles of scientific principles; it’s divided to positivist search, interpretive search and critical search. It’s analyze the different of the above search and described their characteristic and feature Introduction Scientific investigation is the way in which scientists and researchers use a systematic approach to answer questions about the world around the people. A scientific investigation is an empirical (measurable) study of a question using the scientific method. The main parts are listed below: (1) problem: the question people intend to answer, (2) hypothesis: the best anticipated guess to the outcome of the question, (3) experiment: study is carried out and the results are measured, (4) Results: the data/information measured during the experiment is organized in a meaningful way. Charts/graphs/tables are made, (5)discussion/analysis: the results are......

Words: 1386 - Pages: 6

Investigation Report

...U.S. CHEMIC AL S AFETY AND H AZ ARD INVESTIG ATION BOARD INVESTIGATION REPORT LPG FIRE AT VALERO – MCKEE REFINERY (Four Injured, Total Refinery Evacuation, and Extended Shutdown) Photo: Associated Press VALERO ENERGY CORPORATION SUNRAY, TEXAS FEBRUARY 16, 2007 KEY ISSUES: • FREEZE PROTECTION OF DEAD-LEGS • EMERGENCY ISOLATION OF EQUIPMENT • FIREPROOFING OF SUPPORT STEEL • FIRE PROTECTION FOR HIGH PRESSURE LPG SERVICE • CHLORINE RELEASE REPORT NO. 2007-05-I-TX JULY 2008 Valero - Sunray July 2008 Contents EXECUTIVE SUMMARY ..........................................................................................................................6 1.0 INTRODUCTION .........................................................................................................................10 1.1 1.2 2.0 Background....................................................................................................................... 10 Investigative Process......................................................................................................... 10 VALERO ENERGY CORPORATION.........................................................................................11 2.1 2.2 McKee Refinery................................................................................................................ 11 2.3 3.0 Company History .......................................................................................

Words: 13395 - Pages: 54

Soil Investigation

...Soil investigation is often neglected or rejected by most clients on the basis of cost, despite the fact that the cost of carrying out a soil investigation is very little compared to the cost of the project Soil investigation is done for various purposes. In engineering, soil investigation is very necessary. It is essential to investigate the soil of the selected plot on which a structure will be constructed. Based on soil investigation a soil report is prepared for the purpose of designing the building foundation. When an engineer designs building foundation he/she must carefully read the report and design the foundation based on the data provided in the report. Soil investigation is required for the following purposes - To know the allowable bearing capacity of foundation for proposed building. To know the depth and type of foundation for the proposed building. To know the allowable passive resistance for the foundation of proposed building. To know the type, grading and nature of soil. To know the ground water level. Typical steps of soil investigation Soil investigation involves following steps –  Details planning for the sequence of operations.  Collecting the samples of soil from the plot.  Determining the soil characteristics by conducting field tests.  Study the condition of ground water level.  Collecting ground water sample for chemical analysis.  Soil exploration.  Testing all collected samples in the laboratory.  Preparation of......

Words: 1233 - Pages: 5

Principles of Investigation

...1. The success of an interview or interrogation depends on a number of personal characteristics and commitments of the investigator. Planning for and controlling the events surrounding both interviews and interrogations are important but are generally viewed as more critical to the success of an interrogation. The success of the interviewer or interrogator and of the interview or interrogation is often determined by the time and dedication committed to preparing for the conversation. The interviewer must become familiar with the facts of the case under investigation and with the victim. The interrogator must learn as much as possible about the offense, the victim(s) and the suspect through the process of collecting, assessing, and analyzing data and theorizing about the motivations and thought processes of the suspect. These are some reasons that planning for an interview or interrogation are important and in many ways similar. In planning for an interview or interrogation, one must determine what questions will be asked to ensure they are good questions that will lead the interviewer or interrogator to the conclusions they are trying to reach. There are some instances where only moderate planning or preparation is necessary for an interview while extensive planning and preparation is needed to conduct an interrogation. The most common type of interview is an on-the-scene interview where extensive planning is not always a possibility. An examples of this is......

Words: 1863 - Pages: 8

Crime Investigation

...International Journal For Technological Research In Engineering Volume 1, Issue 9, May-2014 ISSN (Online): 2347 - 4718 DATA MINING TECHNIQUES TO ANALYZE CRIME DATA R. G. Uthra, M. Tech (CS) Bharathidasan University, Trichy, India. Abstract: In data mining, Crime management is an interesting application where it plays an important role in handling of crime data. Crime investigation has very significant role of police system in any country. There had been an enormous increase in the crime in recent years. With rapid popularity of the internet, crime information maintained in web is becoming increasingly rampant. In this paper the data mining techniques are used to analyze the web data. This paper presents detailed study on classification and clustering. Classification is the process of classifying the crime type Clustering is the process of combining data object into groups. The construct of scenario is to extract the attributes and relations in the web page and reconstruct the scenario for crime mining. Key words: Crime data analysis, classification, clustering. I. INTRODUCTION Crime is one of the dangerous factors for any country. Crime analysis is the activity in which analysis is done on crime activities. Today criminals have maximum use of all modern technologies and hi-tech methods in committing crimes. The law enforcers have to effectively meet out challenges of crime control and maintenance of public order. One challenge to law......

Words: 1699 - Pages: 7


...Jamel Vilmont 10/26/15 Investigation #3 Analyzing Evidence 1. The solvents are the three sample, Water, Hexane and Ethanol used. The sample are the coo laid used which was red blue and yellow and the markers used which was orange, blue, black, red, and green. 3. The solvent of water mixed with the Kool-Aid created a mixed color of red and yellow for the red Kool-Aid and high streak for the blue Kool-Aid and a disappearance of the yellow Kool-Aid. With markers dipped in ethanol, it created a yellowish orange streak, s short blue streak with little bit of red at the top and a long black streak. 4. the two that I found very similar in my experiment was the H2O blue Kool-Aid with similar features as the blue ethanol. The H20 orange, blue and black markers with the hexane orange blue and black markers as well. Interpreting Evidence 1. from my results we come to a conclusion that the Kool-aid where more soluble in water while the markers weren’t. 2. the one with the highest number of components was the read kool-aid that was dipped in water and the orange and blue markers that was dipped in ethanol. No matter what the Kool-Aid reacted the most to each solvent Making Claims All the markers acted differently with in water, ethanol and hexon and all the coolaids acted the same way excepted with ethanol but for all of the yellow Kool-Aid, they all acted the same....

Words: 258 - Pages: 2

Criminal Investigation

...Phase 1: Individual Project 1 CJFI360-1601A-01: Introduction to Criminalistics Professor: Frank Smith Colorado Technical University Online Obaid Rahman January 11, 2016 As the lead investigator for your investigations unit you have been selected by your supervisor to develop  an updated list of qualifications for new prospective investigators who apply  to transfer into the unit. In particular your supervisor wants your feedback on several areas they feel will be key to the selection process. Keep in mind that your paper should be 4 to 5 pages in length, not counting the cover sheet, abstract, and reference section, and the paper should meet all APA6 standards and requirements. Assignment Guidelines Address the following in 750–1,000 words: What are some of the characteristics the unit should look for in a potential investigator? Explain. In particular, explain why honesty and integrity are critical qualities for investigators to possess. What would be the educational level you would recommend for the beginner investigator to possess before being accepted into the unit? Why? How would prior experience in the field play a role (if any) in your decision on your educational requirements? Explain. What role will previous work history and supervisory recommendations play in the decision making process? Why? Be sure to reference all sources using APA style. References Federal Law Enforcement Officers, 2004, Brian A. Reaves, Ph.D.(August 2008), Retrieve......

Words: 258 - Pages: 2