assessment test
Free Career Assessment Test
Please answer the following 15 questions to the best of your ability. Your answers will be used to identify the career selection(s) that is most suited to your habits, thoughts and actions.
Remember to follow your first instinct when answering the questions. You are not the first person to say some of the questions cannot be answered without our knowing the context of the situation. Do not over-analyze the quiz.
After you have completed the quiz, you will be notified as to which career choice is right for you. You may then begin your search for a college or school that offers the training you need to pursue a career in your field.
Only one answer per question required.
1. When making decisions do you try to remain objective and consider the facts or do you allow your feelings and the effect of the decision of others to influence your decision?
I remain objective.
I consider the effect on others but it doesn't affect my decision.
I don't like to consider too much of anything when I'm making a decision.
I struggle not to let feelings cloud my judgment but they often do.
I allow my feelings and the effect of this decision on others shape my decision.
2. Do you leave your options open when it comes to making a decision or do you prefer to have matters settled one way or another.
I like to leave my options open.
I narrow the options based on the options I think are best in this situation.
I have a hard time making a decision and prefer to be told what to do.
I like to make a decision but continuing weighing the options until it's time to act.
I like to make a decision quickly and move on to the next matter at hand.
3. Would you prefer to develop new and innovative systems or work to make existing systems more efficient?
I like to develop new, innovative systems.
I like to develop new systems but I also enjoying increasing efficiency of old ones.
I just like to work on things I already know and am comfortable with.
I like to make existing systems work efficiently and in doing so am occasionally innovative.
I just want to make existing systems we have work more efficiently.
4. Where would you say you fall in a scale between logical and analytical and personable and sensitive?
I am logical and analytical.
I am logical but I do have a heart, too.
I don't believe in being either logical or personable. I'm just here to work.
I am personable and sensitive but I can step back and see the big picture, too.
I am personable and sensitive to the exclusion of logic.
5. Would you say you are more of a practical, hands-on worker or more of an idea person?
I am a practical, hands-on worker.
I am a hands-on worker who comes up with the occasional idea.
I don't get paid to come up with ideas. I'm just here to work.
I am an idea person who sometimes finds it easier to be quiet and focus on work.
I am an idea person.
6. Are you a detail person or do you go with the flow?
I am a detail person.
I am a detail-oriented person but sometimes there's no time for that.
I don't focus on anything but getting the job done.
I like to go with the flow but sometimes details are important.
I don't sweat the small stuff.
7. On social occasions do you prefer listening to what is going on around you or do you prefer watching the goings-on?
I prefer to listen to what is going on around me.
I prefer to listen but sometimes I like to watch, too.
I don't like to be too aware of what other people are doing or saying.
I like to watch what's happening around me but I listen, too.
I like to watch what people are doing around me.
8. How do you prefer to learn -- by being shown diagrams and pictures or through experiments and activities?
I prefer to learn by viewing diagrams and pictures.
I like classes that mix visual and hands-on training.
For me, learning is a struggle whether it's done by seeing or by doing.
I prefer to do things myself but the occasional photo or diagram does help.
I prefer to learn by doing my own experiments.
9. When assigned a task, do you start by reading the instructions or do you start the task knowing you can figure it out as you go?
I like to read the directions first.
I glance at the directions but I have a pretty good idea how to proceed.
I feel uncomfortable undertaking a task until I have been trained in the procedures.
I think I can figure this out as I go but I will glance at the directions if needed.
I can figure things out as I go.
10. Which of the following best describes your ability to speak in a way that convinces others of your point of view.
I am always able to persuade others that I am right.
I am sometimes able to persuade others that I am right.
I am uncomfortable trying to persuade others.
I have a hard time persuading others.
I can never seem to convince others to share my point of view.
11. Which of the following best describes your ability to clearly explain complex matters verbally.
I am always able to describe complex matters verbally.
I am sometimes able to describe complex matters verbally.
I am uncomfortable trying to describe complex matters.
I struggle when trying to describe complex matters verbally.
I am never able to describe complex matters verbally.
12. Which of the following best describes your ability to write clear instructions.
I am never able to write clear instructions.
I am sometimes able to write clear instructions.
I am uncomfortable trying to write clear instructions.
I struggle when trying to write clear instructions.
I have no trouble writing clear instructions.
13. Which of the following best describes your ability to compute numbers quickly in your head.
I am always able to compute numbers in my head.
I am sometimes able to compute numbers in my head.
I am uncomfortable computing numbers in my head.
I struggle when computing numbers in my head.
I am not able to compute numbers in my head.
14. Are you drawn to find the reason why things are the way they are or are you content to accept them that way?
I accept that things are the way they are for good reason.
I accept things as they are but sometimes I can't help looking for the reason.
I am uncomfortable questioning things.
I sometimes question why things are the way they are but I accept them that way.
I question the reason why things are the way they are.
15. Which of the following describes your ability to visualize something in your mind and reproduce the visualization in an artistic form or design.
I am never able to create something based on a visualization I have experienced.
I am sometimes able to create something based on a visualization I have experienced.
Being artistic and creative is highly overrated.
I am sometimes able to turn a visualization into something more tangible.
I am always able to visualize something and make it come to life.
Remember to follow your first instinct when answering the questions. You are not the first person to say some of the questions cannot be answered without our knowing the context of the situation. Do not over-analyze the quiz.
After you have completed the quiz, you will be notified as to which career choice is right for you. You may then begin your search for a college or school that offers the training you need to pursue a career in your field.
Only one answer per question required.
1. When making decisions do you try to remain objective and consider the facts or do you allow your feelings and the effect of the decision of others to influence your decision?
I remain objective.
I consider the effect on others but it doesn't affect my decision.
I don't like to consider too much of anything when I'm making a decision.
I struggle not to let feelings cloud my judgment but they often do.
I allow my feelings and the effect of this decision on others shape my decision.
2. Do you leave your options open when it comes to making a decision or do you prefer to have matters settled one way or another.
I like to leave my options open.
I narrow the options based on the options I think are best in this situation.
I have a hard time making a decision and prefer to be told what to do.
I like to make a decision but continuing weighing the options until it's time to act.
I like to make a decision quickly and move on to the next matter at hand.
3. Would you prefer to develop new and innovative systems or work to make existing systems more efficient?
I like to develop new, innovative systems.
I like to develop new systems but I also enjoying increasing efficiency of old ones.
I just like to work on things I already know and am comfortable with.
I like to make existing systems work efficiently and in doing so am occasionally innovative.
I just want to make existing systems we have work more efficiently.
4. Where would you say you fall in a scale between logical and analytical and personable and sensitive?
I am logical and analytical.
I am logical but I do have a heart, too.
I don't believe in being either logical or personable. I'm just here to work.
I am personable and sensitive but I can step back and see the big picture, too.
I am personable and sensitive to the exclusion of logic.
5. Would you say you are more of a practical, hands-on worker or more of an idea person?
I am a practical, hands-on worker.
I am a hands-on worker who comes up with the occasional idea.
I don't get paid to come up with ideas. I'm just here to work.
I am an idea person who sometimes finds it easier to be quiet and focus on work.
I am an idea person.
6. Are you a detail person or do you go with the flow?
I am a detail person.
I am a detail-oriented person but sometimes there's no time for that.
I don't focus on anything but getting the job done.
I like to go with the flow but sometimes details are important.
I don't sweat the small stuff.
7. On social occasions do you prefer listening to what is going on around you or do you prefer watching the goings-on?
I prefer to listen to what is going on around me.
I prefer to listen but sometimes I like to watch, too.
I don't like to be too aware of what other people are doing or saying.
I like to watch what's happening around me but I listen, too.
I like to watch what people are doing around me.
8. How do you prefer to learn -- by being shown diagrams and pictures or through experiments and activities?
I prefer to learn by viewing diagrams and pictures.
I like classes that mix visual and hands-on training.
For me, learning is a struggle whether it's done by seeing or by doing.
I prefer to do things myself but the occasional photo or diagram does help.
I prefer to learn by doing my own experiments.
9. When assigned a task, do you start by reading the instructions or do you start the task knowing you can figure it out as you go?
I like to read the directions first.
I glance at the directions but I have a pretty good idea how to proceed.
I feel uncomfortable undertaking a task until I have been trained in the procedures.
I think I can figure this out as I go but I will glance at the directions if needed.
I can figure things out as I go.
10. Which of the following best describes your ability to speak in a way that convinces others of your point of view.
I am always able to persuade others that I am right.
I am sometimes able to persuade others that I am right.
I am uncomfortable trying to persuade others.
I have a hard time persuading others.
I can never seem to convince others to share my point of view.
11. Which of the following best describes your ability to clearly explain complex matters verbally.
I am always able to describe complex matters verbally.
I am sometimes able to describe complex matters verbally.
I am uncomfortable trying to describe complex matters.
I struggle when trying to describe complex matters verbally.
I am never able to describe complex matters verbally.
12. Which of the following best describes your ability to write clear instructions.
I am never able to write clear instructions.
I am sometimes able to write clear instructions.
I am uncomfortable trying to write clear instructions.
I struggle when trying to write clear instructions.
I have no trouble writing clear instructions.
13. Which of the following best describes your ability to compute numbers quickly in your head.
I am always able to compute numbers in my head.
I am sometimes able to compute numbers in my head.
I am uncomfortable computing numbers in my head.
I struggle when computing numbers in my head.
I am not able to compute numbers in my head.
14. Are you drawn to find the reason why things are the way they are or are you content to accept them that way?
I accept that things are the way they are for good reason.
I accept things as they are but sometimes I can't help looking for the reason.
I am uncomfortable questioning things.
I sometimes question why things are the way they are but I accept them that way.
I question the reason why things are the way they are.
15. Which of the following describes your ability to visualize something in your mind and reproduce the visualization in an artistic form or design.
I am never able to create something based on a visualization I have experienced.
I am sometimes able to create something based on a visualization I have experienced.
Being artistic and creative is highly overrated.
I am sometimes able to turn a visualization into something more tangible.
I am always able to visualize something and make it come to life.
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ability test
Ability Tests
Ability tests have a long and established reputation for reliably predicting job performance and can prove invaluable in helping to select individuals for roles. Cubiks is able to offer clients a series of ability tests in online and paper formats. We provide versions for use in both supervised and unsupervised conditions.
As well as providing standard ability tests, we also have a proven track record in developing bespoke online ability test item banks for large-scale corporate and graduate recruitment.
In all cases, the questions in our tests are designed to be relevant to a business context and to be broadly reflective of the reasoning skills required in most jobs. This guarantees credibility and ensures that candidates perceive the tests as true measures of ability.
The following tests are available to clients via the Cubiks Online assessment platform:
Reasoning for Business ability test series
Problem-solving
Reasoning for Business
The Reasoning for Business ability tests series includes a variety of tests that cover different areas of business reasoning. The tests have been designed for two key levels of application - Managerial & Graduate and Business Support.
Managerial & Graduate
VerbalThis assessment has been designed to examine an individual’s ability to comprehend written information and to understand and analyse the logic of written arguments. Questions ask individuals to interpret and draw inferences from business-oriented data and then solve problems related to this information.
NumericalThis assessment measures an individual’s ability to analyse and draw logical inferences from numerical data using basic arithmetic and computational skills that are common to the workplace. It has been designed to determine an individual’s ability to work with numbers and involves questions based on data presented in a variety of forms including graphs, diagrams and statistical tables.
Diagrammatic (Inductive Reasoning)This assessment measures an individual’s ability to analyse and draw logical inferences from diagrammatically presented data, and as such is a test of reasoning ability that is independent of pre-existing numerical or verbal skills. The test taker is required to identify similarities and differences between groups of patterns and then to apply this understanding to help categorise additional patterns.
VerbalThis assessment has been designed to examine an individual’s ability to comprehend written information and to understand and analyse the logic of written arguments. Questions ask individuals to interpret and draw inferences from business-oriented data and then solve problems related to this information.
NumericalThis assessment measures an individual’s ability to analyse and draw logical inferences from numerical data using basic arithmetic and computational skills that are common to the workplace. It has been designed to determine an individual’s ability to work with numbers and involves questions based on data presented in a variety of forms including graphs, diagrams and statistical tables.
Diagrammatic (Inductive Reasoning)This assessment measures an individual’s ability to analyse and draw logical inferences from diagrammatically presented data, and as such is a test of reasoning ability that is independent of pre-existing numerical or verbal skills. The test taker is required to identify similarities and differences between groups of patterns and then to apply this understanding to help categorise additional patterns.
Business Support
VerbalThis assessment also measures an individual’s ability to comprehend written information and to understand and analyse the logic of written arguments. It has been designed to assess Business Support staff.
NumericalThis assessment has been designed to measure an individual's ability to analyse and draw logical inferences from numerical data using basic arithmetic and computational skills.
Antonyms
The participant must choose which word from a group of five has the opposite meaning to another word.
Deviation from category
The participant must decide which one of five words has a different meaning from the others.
Pairs of concepts
The participant has to decide whether two words have the same meaning, the opposite meaning, or neither the same nor the opposite meaning.
Verbal analogy
The participant has to decide whether the underlying meaning or idea in two statements is the same, the opposite, or neither the same nor the opposite.
Logical reasoning
The participant is shown three statements and is asked to decide whether the logic is correct, incorrect, or not possible to deduce.
Series of numbers
The participant has to complete a series of numbers by determining the underlying rule that connects the construction of the series.
Simple calculations
The participant has to make simple calculations.
Complex calculations
The participant has to make complex calculations.
In some situations, companies will choose to test clients more than once, and for this reason, Problem Solving exists in a number of different versions.
VerbalThis assessment also measures an individual’s ability to comprehend written information and to understand and analyse the logic of written arguments. It has been designed to assess Business Support staff.
NumericalThis assessment has been designed to measure an individual's ability to analyse and draw logical inferences from numerical data using basic arithmetic and computational skills.
Problem-Solving
Our Problem-Solving test series has been designed to assess how quickly and accurately an individual can solve new problems. It contains a series of questions that cover both numerical and verbal problems.
The verbal questions include:
Antonyms
The participant must choose which word from a group of five has the opposite meaning to another word.
Deviation from category
The participant must decide which one of five words has a different meaning from the others.
Pairs of concepts
The participant has to decide whether two words have the same meaning, the opposite meaning, or neither the same nor the opposite meaning.
Verbal analogy
The participant has to decide whether the underlying meaning or idea in two statements is the same, the opposite, or neither the same nor the opposite.
Logical reasoning
The participant is shown three statements and is asked to decide whether the logic is correct, incorrect, or not possible to deduce.
The numerical problems cover:
Series of numbers
The participant has to complete a series of numbers by determining the underlying rule that connects the construction of the series.
Simple calculations
The participant has to make simple calculations.
Complex calculations
The participant has to make complex calculations.
In some situations, companies will choose to test clients more than once, and for this reason, Problem Solving exists in a number of different versions.
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reasoning test
Numerical Reasoning Tests
The term ‘numerical reasoning test’ is often used interchangeably with ‘numerical ability test’ and ‘numerical aptitude test’. There is no widely accepted definition of the difference between numerical ability and numerical aptitude and as far as psychometric tests are concerned the two terms are interchangeable. However the same does not apply to the term ‘numerical reasoning’ which does have a specific meaning. The term ‘numerical reasoning test’ should really only be used to describe a specific type of numerical test.
This is best explained as follows: there are basically two types of numerical questions that appear in psychometric tests. Speed questions are so easy that with unlimited time most people taking the test could answer them all successfully. However, the time allowed to complete the test is so short that even the most able person is not expected to finish. This means that the result depends on the number of correct answers made in the relatively short time allowed.
In contrast, a power test contains questions that vary in difficulty and no one is expected to get all of the answers correct even with unlimited time. In practice, a definite but ample time is set for power tests.
Even though there are literally hundreds of numerical ability tests available to employers, the questions used in these tests can be classified into four basic types: Numerical computation, numerical estimation, numerical reasoning and data interpretation.
Numerical Speed Tests – Computation and Estimation
Numerical computation and numerical estimation are ‘speed’ questions. These questions involve basic arithmetic including: addition, subtraction, multiplication, division, percentages, ratios, fractions and decimals. To score well on these questions you will need to be able to make quick and accurate calculations without using a calculator.
Numerical Power Tests – Numerical Reasoning and Data Interpretation
A numerical reasoning test is a power test rather than a speed test because the questions require you to interpret the information provided and then apply the appropriate logic to answer them. In other words, you need to work out how to get the answer, rather than just doing the necessary calculations.
Preparing for a Numerical Reasoning Test
If you are told that you need to sit a numerical reasoning test as part of the job selection process and you want to prepare for it properly, then you should ask which type of questions it contains. Specifically, is it just numerical reasoning or does it also contain data interpretation, computation or estimation questions. Once you have the answer to this question you can run through the free downloadable practice papers on this website to give yourself the best chance of success in the real test.
Sample Numerical Reasoning Test
Identify the missing number at the end of the series.
| A | B | C | D | E | ||||||||||||||||||||||
| 1 | 3, 11, 19, 27, ? | 33 | 35 | 37 | 39 | 41 | ||||||||||||||||||||
| A | B | C | D | E | ||||||||||||||||||||||
| 2 | 3, 6, 11, 18, ? | 24 | 25 | 26 | 27 | 28 | ||||||||||||||||||||
| A | B | C | D | E | ||||||||||||||||||||||
| 3 | 516, 497, 478, 459, ? | 436 | 440 | 438 | 452 | 442 | ||||||||||||||||||||
| Identify the missing number within the series. | ||||||||||||||||||||||||||
| A | B | C | D | E | ||||||||||||||||||||||
| 4 | 33, ?, 19, 12, 5 | 31 | 26 | 29 | 27 | 24 | ||||||||||||||||||||
| A | B | C | D | E | ||||||||||||||||||||||
| 5 | 11, 19, ?, 41, 55 | 31 | 29 | 26 | 39 | 34 | ||||||||||||||||||||
| A | B | C | D | E | ||||||||||||||||||||||
| 6 | 98, 94, ?, 70, 38 | 89 | 85 | 86 | 87 | 88 | ||||||||||||||||||||
| 7 | Identify the missing number. | |||||||||||||||||||||||||
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| 8 | Identify the missing number. |
| ||||||||||||||||||||||||
| 9 | It costs a manufacturer X dollars per component to make the first 1,000 components. All subsequent components cost X÷3 each. When X = $1.50 How much will it cost to manufacture 4,000 components? |
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| 10 | A train traveling at 60 mph enters a tunnel that is 5 miles long. The train is one mile long. How many minutes does it take for the whole train to pass through the tunnel? |
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| 11 | In the Shelbyville election, the Republican candidate received one and a half times as many votes as the Democrat candidate. The Democrat candidate received one third more votes than the Independent candidate. 900 votes were cast for the Independent candidate. How many votes were cast for the Republican candidate? |
| ||||||||||||||||||||||||
| 12 | Anna and John both drive to their new home 400 miles away. Anna drives the family car at an average speed of 60 mph. John drives the removal truck at an average speed of 50 mph. During the journey, Anna stops for a total of 1 hour and 20 minutes, John stops for half as long. What is the difference in minutes between their arrival times? |
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Preparing for a Numerical Reasoning Test
Numerical reasoning tests are an increasingly popular way of assessing candidates during the job selection process. Many people who have been out of the education system for a while or who don’t use maths on a day-to-day basis feel intimidated by these types of test. The important thing to remember is that you don’t need to have studied mathematics to a high level to succeed. These are primarily tests of reasoning ability and the math needed is invariably straightforward. Although you may need to get back up to speed with percentages, ratios, proportions, fractions and decimals.
You will usually be allowed to use a calculator for these types of question and investing in one which can handle fractions and percentages is a good idea. You should also try to work through a few numerical computation practice papers to get back into swing of these types of calculation.
These sample question papers each contain 22 questions and have a suggested time limit of 20 minutes. The questions are presented in Letter/A4 format for easy printing and self-marking.
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what is an aptitude test
Aptitude Tests > Introduction
Aptitude and ability tests are designed to assess your logical reasoning or thinking performance. They consist of multiple choice questions and are administered under exam conditions. They are strictly timed and a typical test might allow 30 minutes for 30 or so questions. Your test result will be compared to that of a control group so that judgments can be made about your abilities.
You may be asked to answer the questions either on paper or online. The advantages of online testing include immediate availability of results and the fact that the test can be taken at employment agency premises or even at home. This makes online testing particularly suitable for initial screening as it is obviously very cost-effective.
Aptitude and ability tests can be classified as speed tests or power tests. In speed tests the questions are relatively straightforward and the test is concerned with how many questions you can answer correctly in the allotted time. Speed tests tend to be used in selection at the administrative and clerical level. A power test on the other hand will present a smaller number of more complex questions. Power tests tend to be used more at the professional or managerial level.
There are at least 5000 aptitude and ability tests on the market. Some of them contain only one type of question (for example, verbal ability, numeric reasoning ability etc) while others are made up of different types of question.
First Things First
The first thing to do is to determine which type of questions you are going to be asked. Don't waste time practicing questions that won't appear in the actual test. Types of question can be classified as follows:
Verbal Ability - Includes spelling, grammar, ability to understand analogies and follow detailed written instructions. These questions appear in most general aptitude tests because employers usually want to know how well you can communicate.
Numeric Ability - Includes basic arithmetic, number sequences and simple mathematics. In management level tests you will often be presented with charts and graphs that need to be interpreted. These questions appear in most general aptitude tests because employers usually want some indication of your ability to use numbers even if this is not a major part of the job.
Abstract Reasoning - Measures your ability to identify the underlying logic of a pattern and then determine the solution. Because abstract reasoning ability is believed to be the best indicator of fluid intelligence and your ability to learn new things quickly these questions appear in most general aptitude tests.
Spatial Ability - Measures your ability to manipulate shapes in two dimensions or to visualize three-dimensional objects presented as two-dimensional pictures. These questions not usually found in general aptitude tests unless the job specifically requires good spatial skills.
Mechanical Reasoning - Designed to assess your knowledge of physical and mechanical principles. Mechanical reasoning questions are used to select for a wide range of jobs including the military (Armed Services Vocational Aptitude Battery), police forces, fire services, as well as many craft, technical and engineering occupations.
Fault Diagnosis - These tests are used to select technical personnel who need to be able to find and repair faults in electronic and mechanical systems. As modern equipment of all types becomes more dependent on electronic control systems (and arguably more complex) the ability to approach problems logically in order to find the cause of the fault is increasingly important.
Data Checking - Measure how quickly and accurately errors can be detected in data and are used to select candidates for clerical and data input jobs.
Work Sample – Involves a sample of the work that you will be expected do. These types of test can be very broad ranging. They may involve exercises using a word processor or spreadsheet if the job is administrative or they may include giving a presentation or in-tray exercises if the job is management or supervisory level.
Don't Waste Time
Spend your preparation time wisely. Most people find themselves with only one or two weeks to prepare for aptitude tests - don't worry, this is enough time provided that you are systematic.
- You must find out what type of questions you are going to face even if this means asking.
- Use the information on this website to get an idea of the different types of questions.
- Download and look at a sample paper for each type of question you are expecting to face.
- Go through one paper of each type and see how you get on.
- Decide on a practice strategy.
- Practice one paper a day right up until the actual test.
If you are unsure what types of question to expect then ask the human resources people at the organization you are applying to. This will not count against you in any way and they should be only too happy to tell you. You have a right to prepare yourself for any tests you are asked to sit.
Don't Make Assumptions
Try not make any assumptions. For example, many people assume that they won't have any problems with verbal ability questions because they once got an 'A' in English. They may have a point if they got the 'A' a few months ago, but what if it was ten years ago? It is very easy to ignore the effects of not reading as much as you used to, and of letting your spell-checker take care of correcting your written English.
The same thing applies to numerical ability. Most people who have been out of education for more than a few years will have forgotten how to multiply fractions and calculate volumes. While it is easy to dismiss these as 'first grade' or elementary maths, most people simply don't do these things on a day-to-day basis. So, don't assume anything - it's better to know for sure.
Deciding on a Practice Strategy
You should make your own decision about which types of question to practice. You could either concentrate on your weakest area or you could try to elevate your score across all areas. Whichever strategy you choose - keep practicing. Because of the way that aptitude tests are marked, even small improvements to your raw score will have a big influence on your chances of getting the job.
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intelligence tests
Review Questions
| 1. | Evaluate the expression for the value x = 2. | |
| | (A) | 1/2 |
| | (B) | 4 |
| | (C) | 6 |
| | (D) | 8 |
| | (E) | 232/5 |
| | | |
| 2. | If a is even and negative, b is negative, and c is even, which of the following choices could be equal to a × b + c2 + 1? | |
| | (A) | –71 |
| | (B) | –16 |
| | (C) | 0 |
| | (D) | 4 |
| | (D) | 9 |
| | | |
| 3. | What is the absolute value of the difference between the LCM and GCF of 24 and 42? | |
| | (A) | 18 |
| | (B) | 162 |
| | (C) | 174 |
| | (D) | 498 |
| | (D) | 1002 |
| | | |
| 4. | Which of the following fractions is not equivalent to the others? | |
| | (A) | 6/14 |
| | (B) | -21/-49 |
| | (C) | 33/91 |
| | (D) | 9/21 |
| | (D) | 15/23 |
| | | |
| 5. | How many digits are in the number 533? | |
| | (A) | 23 |
| | (B) | 24 |
| | (C) | 25 |
| | (D) | 33 |
| | (D) | 38 |
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aptitude test
Exponents
An exponent defines the number of times a number is to be multiplied by itself. For example, in ab, where a is the base, and b the exponent, a is multiplied by itself b times. In a numerical example, 25 = 2 × 2 × 2 × 2 × 2. An exponent can also be referred to as a power: a number with an exponent of 2 is raised to the second power. There are some other terms that you should be familiar with:- Base. The base refers to the 3 in 35. It is the number that is being multiplied by itself however many times specified by the exponent.
- Exponent. The exponent (or power) is the 5 in 35. The exponent tells how many times the base is to be multiplied by itself.
- Square. Saying that a number is “squared” means that it has been raised to the second power, i.e., that it has an exponent of 2. In the expression 62, 6 has been squared.
- Cube. Saying that a number is “cubed” means that it has been raised to the third power, i.e., that it has an exponent of 3. In the expression 43, 4 has been cubed.
Common Exponents
It may be worth your while to memorize a few common exponents before the test. Knowing these regularly used exponents can save you the time it would take to calculate them during the test. Here is a list of squares from 1 through 10:
emorizing the first few cubes can be helpful as well:
Finally, the first few powers of two are useful for many applications:
Adding and Subtracting Numbers with Exponents
In order to add or subtract numbers with exponents, you have to first find the value of each power, and then add the two numbers. For example, to add 33 + 42, you must expand the exponents to get (3× 3 × 3) + (4 × 4), and then, finally, 27 + 16 = 43.If you’re dealing with algebraic expressions that have the same bases and exponents, such as 3x4 and 5x4, then they can simply be added and subtracted. For example, 3x4 + 5x4 = 8x4.
Multiplying and Dividing Numbers with Exponents
To multiply exponential numbers or terms that have the same base, add the exponents together:3 6 × 3 2 = 3 (6 + 2) = 3 8
x 4 × x 3 = x (4 + 3 )=x 7 To divide two same-base exponential numbers or terms, just subtract the exponents.
To multiply exponential numbers raised to the same exponent, raise their product to that exponent:4 3 × 5 3 = ( 4 × 5 3 = 20 3
a 5 × b 5 = ( a × b) 5=ab 5 To divide exponential numbers raised to the same exponent, raise their quotient to that exponent:
If you need to multiply or divide two exponential numbers that do not have the same base or exponent, you’ll just have to do your work the old-fashioned way: multiply the exponential numbers out and multiply or divide the result accordingly.Raising an Exponent to an Exponent
Occasionally you might encounter an exponent raised to another exponent, as seen in the following formats (32)4 and (x4)3. In such cases, multiply the powers:(32)4 = (3)2 × 4 = 3 8
(x4)3 = (x)4 × 3 = x 12
Exponents and Fractions
To raise a fraction to an exponent, raise both the numerator and denominator to that exponent:
Exponents and Negative Numbers
As we said in the section on negative numbers, when you multiply a negative number by another negative number, you get a positive number, and when you multiply a negative number by a positive number, you get a negative number. These rules affect how negative numbers function in reference to exponents.- When you raise a negative number to an even-number exponent, you get a positive number. For example (–2)4 = 16. To see why this is so, let’s break down the example. (–2)4 means –2 × –2 × –2 ×–2. When you multiply the first two –2s together, you get +4 because you are multiplying two negative numbers. Then, when you multiply the +4 by the next –2, you get –8, since you are multiplying a positive number by a negative number. Finally, you multiply the –8 by the last –2 and get +16, since you’re once again multiplying two negative numbers.
- When you raise a negative number to an odd power, you get a negative number. To see why, all you have to do is look at the example above and stop the process at –8, which equals (–2)3.
Special Exponents
There are a few special properties of certain exponents that you also need to know.Zero
Any base raised to the power of zero is equal to 1. If you see any exponent of the form x0, you should know that its value is 1. Note, however, that 00 is undefinded.One
Any base raised to the power of one is equal to itself. For example, 21 = 2, (–67)1 = –67 and x1 = x. This can be helpful when you’re attempting an operation on exponential terms with the same base. For example:3x6 × x = 3x6 × x1 = 3 =3x(6 + 1) = 3x 7
Fractional Exponents
Exponents can be fractions, too. When a number or term is raised to a fractional power, it is called taking the root of that number or term. This expression can be converted into a more convenient form:xa/b =6 √xa Or, for example, 213 ⁄ 5 is equal to the fifth root of 2 to the thirteenth power:
6 √213 = 6.063 The √ symbol is also known as the radical, and anything under the radical, in this case 2 13 ,is called the radicand. For a more familiar example, look at 91⁄2, which is the same as √9
2 √91 = √9 = 3 Fractional exponents will play a large role on SAT II Math IC, so we are just giving you a quick introduction to the topic now. Don’t worry if some of this doesn’t quite make sense now; we’ll go over roots thoroughly in the next section.
Negative Exponents
Seeing a negative number as a power may be a little strange the first time around. But the principle at work is simple. Any number or term raised to a negative power is equal to the reciprocal of that base raised to the opposite power. For example:
Or, a slightly more complicated example:
With that, you’ve got the four rules of special exponents. Here are some examples to firm up your knowledge:
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