The Construction And Skilled Trades (CAST) test assesses the aptitude of candidates in roles such as electrical repair, vehicle maintenance and other skilled trades. It is frequently administered during the application process for these types of roles in order to quickly and efficiently screen out unsuitable candidates.

This course will help you increase your mechanical aptitude test score and get your dream job, with a comprehensive coverage of video-based studying and computer-based practicing.On average, our students score 27% higher than the average test-taker.

**✓** **Deep video-based learning** - Every module of this course covers the topics in the test in great depth. We make use of video-based guides in order to maximize your learning.

**✓** **Preparation for any level of difficulty** - The difficulty faced on the CAST can vary. In order to make sure you are 100% covered for any of these tests, we have designed our course to teach you everything from the ground up.

**✓** **Lighting fast tactics** - There are 14 key question categories identified in mechanical aptitude tests. This course offers the optimal strategy for answering every one of these questions.

**✓** **How to approach mechanical questions effectively** - this course is structured to build you mechanical knowledge in such a way that develops your intuitive understanding of mechanical concepts.

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- Question 1 of 8
##### 1. Question

**The floor plan of a house is shown below:****Answer the questions 1 – 8 considering the information given in this floor plan.****What are the dimensions of each of the 4 rooms if they are all identical?**CorrectIncorrect - Question 2 of 8
##### 2. Question

**The floor plan of a house is shown below:****Answer the questions 1 – 8 considering the information given in this floor plan.****What is the length of the long side of the kitchen if its surface area is 1.4 times greater than that of the bathroom?**CorrectIncorrect - Question 3 of 8
##### 3. Question

**The floor plan of a house is shown below:****Answer the questions 1 – 8 considering the information given in this floor plan.****What is the perimeter of the living room if its southern wall intersects the lateral walls of rooms 2 and 4 at their respective middles?**CorrectIncorrect - Question 4 of 8
##### 4. Question

**The floor plan of a house is shown below:****Answer the questions 1 – 8 considering the information given in this floor plan.****What is the volume of the house if it is 9 ft high?**CorrectIncorrect - Question 5 of 8
##### 5. Question

**The floor plan of a house is shown below:****Answer the questions 1 – 8 considering the information given in this floor plan.****How much percent of the entire area of the house are bedrooms? Write the answer at two decimal places.**CorrectIncorrect - Question 6 of 8
##### 6. Question

**The floor plan of a house is shown below:****Answer the questions 1 – 8 considering the information given in this floor plan.****If the length of kitchen is 1.4 times greater than that of bathroom and the width of the kitchen is half the width of bedroom 2, calculate the surface area of the bathroom.**CorrectIncorrect - Question 7 of 8
##### 7. Question

**The floor plan of a house is shown below:****Answer the questions 1 – 8 considering the information given in this floor plan.****How many 6 in. × 6 in. tiles must be used to pave the floors of the all 4 bedrooms?**CorrectIncorrect - Question 8 of 8
##### 8. Question

**The floor plan of a house is shown below:****Answer the questions 1 – 8 considering the information given in this floor plan.****Before paving the building, a layer of a special chemical solution must be used to insulate it from moisture. The solution must be used up to 2 feet inside the building in all outer walls (the colored region in the figure). How many kg of solutions must be used if the rate is 1 kg solution for every 10 ft**^{2}of surface?CorrectIncorrect

If you’ve been asked to take the CAST test, you probably don’t have a lot of time between now and sitting the exam. **Time is short, and you need a quick fix.**

Whether you are confident with mechanical concepts or haven’t looked at them since high school, this course has something to offer.

This CAST Test Preparation Pack is perfect for:

- Inexperienced test-takers who need to learn the mechanical concepts covered in the CAST Test from scratch
- Individuals who are well-versed with mechanical concepts who wish to sharpen their skills and jog their memory in order to maximise their chances of success.

This course has been meticulously designed, making use of years of expertise in order to put together the most comprehensive and concise CAST Test preparation course available on the market. Our in-house mechanical and educational specialists have composed the text-based and video guides on this course in order to ensure that you are equipped with everything you could possibly need for the test.

Mechanical Aptitude Tests are administered by a wide variety of employers to screen out unsuitable candidates. If you’ve applied for a job position and have been asked to take this test, there won’t be any do-overs; if you fail, other candidates who have succeeded will fill the role you wanted. You need to get this right, and you need to get it right the first time. This course has been specifically designed to prepare test-takers for any CAST Test by examining every possible question type in great depth so that you will not only know how to answer the questions, but also understand them fundamentally so you can be prepared for anything.

One of the largest difficulties when learning the concepts contained within the CAST Test is visualization. Frequently, test-takers will struggle to visually understand the concepts presented when reading it in simple text. In order to combat this and maximize your learning potential, we have produced a series of video guides for this course. Using video-based guides alongside our written content, you will be on the fast-track to test success. This course is the only CAST course on the market which comprehensively covers these topics in a video-based format.

Being asked to take a test you’ve never taken can be pretty daunting. Taking a test you’ve not performed so well on in the past can also be a scary prospect. Our expect in-house psychometric experts understand this, and have produced this course with that in mind. This course is designed to provide you with bulletproof protection against any question type, by teaching you the principles involved from the ground up. Instead of using ineffective and unreliable online resources, you can ensure your success with the best course on the market. When you’re taking a test like this, every second of your time is precious; why waste time trawling through questionable resources when you can secure success here and now?

What sets this course apart from the others is a comprehensive approach to teaching the concepts. Free resources found online are far from sufficient, and other courses on the market focus almost entirely on practice questions without any substantial instructional content. We offer a comprehensive approach to all question types on the CAST Test and curated practice tests, presented in an accessible and easy-to-understand curriculum so that you can spend less time deciphering the course and more time preparing for the test.

Do you want to secure your success in the screening process and take one step closer to that dream job? Don’t let your competitors get the upper hand - get started with this course now, and fix the odds in your favor with this comprehensive CAST Test Preparation Pack today!

The Construction And Skilled Trades (CAST) test assesses the aptitude of candidates in roles such as electrical repair, vehicle maintenance and other skilled trades. It is frequently administered during the application process for these types of roles in order to quickly and efficiently screen out unsuitable candidates.

This course will help you increase your mechanical aptitude test score and get your dream job, with a comprehensive coverage of video-based studying and computer-based practicing.On average, our students score 27% higher than the average test-taker.

$ 64.90 $ 138 53% off###### Prices are in USD. Limited Time Offer

- Lifetime access
- 15 Full-Length Mechanical Guides
- 4 Full-Length Mathematical Guides
- 3 Full-Length Verbal Guides
- Video-based learning
- Suitable for all applicants taking the CAST test, as well as other mechanical tests

- TAKE THE FREE PRACTICE TEST NOW
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- Question 1 of 49
##### 1. Question

**What is the mechanical advantage of the system in figure? (Pulleys are weightless)**CorrectIncorrect - Question 2 of 49
##### 2. Question

**Which diagram below shows the working principle of clothes pegs?**CorrectIncorrect - Question 3 of 49
##### 3. Question

**In the figure below, 6 meshed gears are shown. If the third gear rotates anticlockwise, then the direction of rotation for the first and the sixth gear are respectively…………………..**CorrectIncorrect - Question 4 of 49
##### 4. Question

**What is the rotation velocity and direction of wheel C if the wheel A makes 30 rot / min? (R**_{A}**= 3R**_{B}**and R**_{C}**= 2R**_{B}**).**CorrectIncorrect - Question 5 of 49
##### 5. Question

**A 40cm long spring by constant 2000 N/m is hanged on a hook 1.2m above the ground. A solid sphere of radius 5 cm is hanged at the lowest end of the spring. What is the maximum weight of the solid sphere so that it doesn’t touch the ground?**CorrectIncorrect - Question 6 of 49
##### 6. Question

**Which statement is CORRECT?**CorrectIncorrect - Question 7 of 49
##### 7. Question

**When centripetal force acting on an object on the ground stops, the object makes………….**CorrectIncorrect - Question 8 of 49
##### 8. Question

**What is the force needed to lift a 200 N load L as shown in the figure, if the axle diameter d is 8cm and the wheel radius R is 40cm?**CorrectIncorrect - Question 9 of 49
##### 9. Question

**Calculate the density of liquid 2 in the figure if the density of liquid 1 is 1200 kg/ m**^{3}**.**CorrectIncorrect - Question 10 of 49
##### 10. Question

**What is the main difference between a cell and a capacitor?**CorrectIncorrect - Question 11 of 49
##### 11. Question

**We use ……………………………….. to measure air pressure**CorrectIncorrect - Question 12 of 49
##### 12. Question

**What happens to the current passing through the main branch in the circuit shown in the figure if one the bulbs smashes?**CorrectIncorrect - Question 13 of 49
##### 13. Question

**A kettle draws 5A current when operating at mains electricity system (V = 240 V). What is the power of this kettle in kW?**CorrectIncorrect - Question 14 of 49
##### 14. Question

**What is the wavelength of a sound wave which has a frequency of 500 Hz? Take the speed of sound equal to 340 m/s.**CorrectIncorrect - Question 15 of 49
##### 15. Question

**Which statement below is CORRECT?**CorrectIncorrect - Question 16 of 49
##### 16. Question

**If an object is sinking, density of this object is ……. than density of the liquid.**CorrectIncorrect - Question 17 of 49
##### 17. Question

**The image of an object formed by a concave mirror is inverted and has the same size as the object. Find the distance between the mirror and the object (in cm) if the focal length of the mirror is 30 cm?**CorrectIncorrect - Question 18 of 49
##### 18. Question

**In a laboratory a student mixes 200 g water at 70**^{0}C with 100 g water at 40^{0}C. Find the final temperature of the mixture. (c_{water}=4186 J/kg^{0}C)CorrectIncorrect - Question 19 of 49
##### 19. Question

**A third class lever has a mechanical advantage**CorrectIncorrect - Question 20 of 49
##### 20. Question

**What is the mechanical advantage of the system of meshed gears shown in the figure below? (The large gear is considered as driving gear and the small one as driven gear)**CorrectIncorrect - Question 21 of 49
##### 21. Question

**If gear A rotates in the clockwise direction, what will the direction of wheels B, C and D be?**CorrectIncorrect - Question 22 of 49
##### 22. Question

**If the weight of each pulley is equal to the load, what is the ratio between the pulling force F and the load L? (F / L = ?)**CorrectIncorrect - Question 23 of 49
##### 23. Question

**A spring has a constant of 1200 N/m. What is the mass of the object hung on the spring if it extends by 10 cm? Take g = 9.81 m/s****2****. Write the answer at 3 s.f.**CorrectIncorrect - Question 24 of 49
##### 24. Question

**Two identical objects A and B are at the same height as shown in the figure. The object A is released down and the object B is thrown horizontally at a certain speed v. If air resistance is neglected, which object will fall first on the ground?**CorrectIncorrect - Question 25 of 49
##### 25. Question

**What force prevents a car from skidding away when it moves along a curved path?**CorrectIncorrect - Question 26 of 49
##### 26. Question

**What class of levers does the inclined plane represent?**CorrectIncorrect - Question 27 of 49
##### 27. Question

**How do the pressures at bottoms of the containers shown in the figure compare if there is the same liquid in all containers?**CorrectIncorrect - Question 28 of 49
##### 28. Question

**Which one of the followings is equal to the unit of resistance?**CorrectIncorrect - Question 29 of 49
##### 29. Question

**All manometers shown in the figure are at the same temperature. What is the relationship among the pressures of the gases X, Y and Z?**CorrectIncorrect - Question 30 of 49
##### 30. Question

**In parallel combination of bulbs, when a bulb smashes, the other bulbs……………….**CorrectIncorrect - Question 31 of 49
##### 31. Question

**If an electrical device dissipates 180 000 J in 5 minutes, what is the power of the device in Watts?**CorrectIncorrect - Question 32 of 49
##### 32. Question

**What is the sound intensity of a washing machine which emits sound of level equal to 70 dB? The intensity of hearing threshold is 10**^{-12}**W/m**^{2}**.**CorrectIncorrect - Question 33 of 49
##### 33. Question

**Which is correct for the names of forces shown in the figure?**CorrectIncorrect - Question 34 of 49
##### 34. Question

**What additional mass (in kg) is to be put on the wooden block of 0.3 m**^{3}volume, if it is to be completely immersed in the alcohol as in figure? (ρ_{wood}= 600 kg/m^{3}, ρ_{alcohol}= 900 kg/m^{3})CorrectIncorrect - Question 35 of 49
##### 35. Question

**An object is placed 20 cm before a diverging lens by focal length 12 cm. Where is image formed?**CorrectIncorrect - Question 36 of 49
##### 36. Question

**A flask contains 2.5 L air at –173**^{0}C. What will the volume be if the temperature is increased to 127^{0}C, by keeping the pressure constant?CorrectIncorrect - Question 37 of 49
##### 37. Question

**Which direction will the rack move in the rack and pinion system shown in the figure?**CorrectIncorrect - Question 38 of 49
##### 38. Question

**What is the value of F in terms of the weight of the object P, if the system is in equilibrium and the pulleys are weightless?**CorrectIncorrect - Question 39 of 49
##### 39. Question

**Which statement is CORRECT about ballistics?**CorrectIncorrect - Question 40 of 49
##### 40. Question

**Which force causes a string to straighten and thus generate a tension in the string when a stone is pulled by it around a circular path?**CorrectIncorrect - Question 41 of 49
##### 41. Question

**A screw is a combination of ……………………….**CorrectIncorrect - Question 42 of 49
##### 42. Question

**If the objects in the figure are made from****the same material,****what is the ratio of their pressures P**_{1}**/ P**_{2}**exerted on the ground?**CorrectIncorrect - Question 43 of 49
##### 43. Question

**Electrons in a circuit flow from a place where there are ………..electrons to a place where there are ………..electrons.**CorrectIncorrect - Question 44 of 49
##### 44. Question

**A gas is compressed to one third of its original volume as shown in the figure. Which of the changes below is correct concerning the gas?**CorrectIncorrect - Question 45 of 49
##### 45. Question

**What is the current I****x****for the circuit in the figure?**CorrectIncorrect - Question 46 of 49
##### 46. Question

**A person hears the sound of thunder 2.4s after having seen the flash of lightning. How far does the lightning occur? Take the speed of sound in air equal at 343 m/s.**CorrectIncorrect - Question 47 of 49
##### 47. Question

**The interior of a hot air balloon contains 1200 m**^{3}**of hot air with density 0.8 kg/m**^{3}**. The mass of the balloon without including the hot air is 320 kg. The density of the surrounding air is 1.3 kg/m**^{3}**. What is the net (resultant) force acting on the balloon? Take g = 9.81 m/s**^{2}**.**CorrectIncorrect - Question 48 of 49
##### 48. Question

**What is the power of a converging lens if the image produced by an object placed 25 cm before the lens, is formed 100 cm after the lens?**CorrectIncorrect - Question 49 of 49
##### 49. Question

**A weather forecast announces that the expected daytime temperature is 41**^{o}**F. What is the temperature in**^{o}**C?**CorrectIncorrect - Graphic Arithmetic - 16 questions administered in the space of 30 minutes
- Mechanical Concepts - 44 questions administered in the space of 20 minutes
- Reading Comprehension - 32 questions administered in the space of 30 minutes
- Mathematical Usage- 18 questions administered in the space of 7 minutes
- Introduction to the CAST Test
- Course Structure
- Time Management Factor
- The Right Approach

**1****2****3****4****5****Not categorized 0%****1****2****3****4****5****Answered****Review****Question 1 of 5****1. Question****The long side of a crowbar (up to the turning point) has a length of 0.80 m. it is**

**used to pull out a nail from a board. The nail is 5 cm away from the turning point.**

**Calculate the force to be used if the nail can take a maximum force of 3000 N.****Correct****Incorrect****Question 2 of 5****2. Question****A wheelbarrow weighs 20 kg when empty. A 600 N load is carried using it. The load is concentrated at a point which horizontally is 50 cm away from the wheel. The wheelbarrow, which is 2m long, has also its center of mass at this point. How much easier do we lift the load instead of carrying it on shoulders? (Take the gravity equal to 10 m/s2 if needed)****Correct****Incorrect****Question 3 of 5****3. Question****A third class lever has a mechanical advantage****Correct****Incorrect****Question 4 of 5****4. Question****Which one of the following are correct for levers?****I.If there is a gain in force, there is a loss in distance****II.The mechanical advantage is the ratio of the load to the force****III. In simple machines there is a gain in work****Correct****Incorrect****Question 5 of 5****5. Question****Which diagram below shows the working principle of pliers?****A.****B.****C.****Correct****Incorrect****What are levers?***They can change the direction of a force*- They can change the magnitude of force
- They can change both of the above
- The part that tends to rotate the system anticlockwise (in the figure above, the force F
_{1}exerted perpendicular to the rigid rod at the distance d_{1}from the pivot, tends to rotate the rigid bar anticlockwise. - The part that tends to rotate the system clockwise (in the figure above, the force F
_{2}exerted perpendicular to the rigid rod at the distance d_{2}from the pivot, tends to rotate the rigid bar clockwise. - Pivot located between load and force,
- Load located between pivot and force, and
- Force acting between pivot and load
- They can change the direction of a force
- They can change the magnitude of force
- They can change both of the above
- Pivot located between load and force, (L-P-F or F-P-L) [First class levers]

(Examples of first class levers include seesaw, can-opener, scissors, equal-arm balance, crowbar etc.) - Load located between pivot and force, and (P-L-F or F-L-P) [Second class levers]

(Examples of second class levers include wheelbarrow, can-opener, nutcracker etc.) - Force acting between pivot and load (P-F-L or L-F-P) [Third class levers]

(Examples of third class levers include sugar tongs, tweezers, forearm etc.) - What are levers? – Theoretical background
- Equation of levers
- Mechanical advantage
- Types of levers – First, Second, Third Class
- Practice Questions

- Units and systems of units
- Vectors and Scalars.
- Force as a vector.
- What can a force do?
- Equal, different and opposite vectors.
- Operations with vectors.
- Components of a vector.
- Some important forces in Mechanics
- Work and energy.
- Types of energy.
- Power
- Practice Questions

- What is a fluid?
- What is Buoyancy? Buoyant Force.
- Calculation of Buoyant Force. Archimedes Principle.
- Density and Conditions for Floating.
- Buoyancy in the Air. Balloons.
- Practice Questions.

- What is Acoustics?
- What is sound? Sound as a kind of wave.
- Characteristics of sound waves.
- Amplitude and wavelength.
- Equation of sound waves.
- Speed of sound.
- Intensity and power of sound waves.
- Intensity as a function of distance from the source.
- Pitch and loudness.
- Echo.
- Audible sound. Ultra and infrasound.
- Musical notes.
- Sound level and decibel scale.
- Doppler Effect.
- Practice Questions

- What is light? How is light propagated?
- Luminous and non-luminous objects.
- Does light pass through all matter?
- Shadow.
- Speed of light.
- Reflection of light.
- Plane mirrors. Laws of reflection.
- Image formed by two plane mirrors.
- Curved mirrors. Special rays in curved mirrors.
- Image formation in concave mirrors.
- Image formation in convex mirrors.
- Lenses. Similarity between lenses and curved mirrors.
- Image formation in converging lenses.
- Image formation in diverging lenses.
- Equation of mirrors and lenses.
- Magnification of spherical mirrors and lenses.
- Refraction of light. Laws of refraction.
- Critical angle. Total internal reflection.
- Index of refraction. Snell’s Law.
- Light as an Electromagnetic Wave.
- Dispersion of light. Prisms.
- The human eye. Eye defects.
- Power of a lens.
- Practice Questions.

- Thermal energy, Heat and the difference between them.
- Temperature. Measurement of temperature.
- Thermal equilibrium. First Law of Thermodynamics.
- Thermal expansion and contraction.
- States of matter.
- Phase change.
- Units of heat.
- Specific heat capacity.
- Specific Latent Heat.
- Calorimetry. Heat exchange.
- Gas Laws
- Graph representation of Gas Laws
- Second Law of Thermodynamics
- The meaning of Entropy. Third Law of Thermodynamics.
- Heat transfer.
- Practice Questions.

- What is Pressure? – Theoretical Background
- Solid pressure
- Liquid Pressure
- Applications of hydrostatic pressure
- Practice Questions

- Theoretical background
- Mechanical vs Electric Power
- Power and efficiency
- Electric energy & Joule’s Law
- Joule or kWh? – Cost of electricity
- Practice Questions

- Combination of resistors – Series, Parallel, Complex
- Advantages and disadvantages of series and parallel combination of resistors
- Practice Questions

- Electric Charges
- Electric Circuits
- Electric Current
- Ohm’s Law
- What does resistance depend upon?
- Symbols of electric circuit elements
- Practice Questions

- Gas Pressure – Theoretical Background
- Air pressure – Evidence of air pressure
- How to measure air/gas pressure? – Apparatus and Units
- Pressure and Volume relation in gases
- Practice Questions

- Wheel and Axle
- Inclined Plane
- Screw
- Wedge
- Practice Questions

- What is circular motion? - Theoretical background
- Directions of Rotation
- Centripetal and centrifugal force
- Centripetal acceleration
- Practice Questions

- What is ballistics? - Theoretical background
- Equations of ballistics
- Practice Questions

- What are springs? – Theoretical background
- Combination of Springs – Series, Parallel, Mixed
- Practice Questions

- What are pulleys? – Theoretical background
- Types of pulleys – Fixed, Moveable, Combined
- Block and Tackle
- Practice Questions

- What are gears? – Theoretical background
- Thumb rules in meshed gears
- Practice Questions
- Systems of gears
- Rack and Pinion
- Relationship between the radius of the gear and its velocity of rotation

- What are wheels? – Theoretical background
- Mechanical advantage of wheels
- Combination of wheels and gears
- Advantages and limitations of wheel (and gear) systems
- Practice Questions

- PEMDAS
- Answering with a calculator
- Answering without a calculator
- Methodology
- Time-efficient solutions

- Proportion & direct proportion
- What are rates?
- Typical questions
- Methodology

- What are ratios?
- Dividing a quantity in a ratio
- Typical questions
- Methodology

- What are percentages?
- Percentages and decimals
- Calculating percentage change
- Typical questions

- Ordering Types
- Fraction Ordering
- Mixed Value Ordering
- Formula-Type Problems
- Practice Questions

- Linear Series
- Geometric Series
- Compound Series
- Layered Series
- Squared Series
- Exponential Series
- Practice Questions

- Word Problems Question Types
- Percentages Problems
- Rate and Ratio Problems
- Age Calculation Problems
- Time Trap Avoidance
- One-Variable Problems

- What are floor plans?
- What does a floor plan show?
- How to deal with calculations regarding floor plans

- Practice Test 1
- Practice Test 2

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Hi, and welcome to PrepTerminal’s Construction And Skilled Trade Test course. In the following modules, we’ll walk you through every concept contained within the CAST through a comprehensive series of guides composed by industry experts who have closely studied the CAST in order to ensure that this course is the most up-to-date preparation resource on the market. These guides contain in-depth explanations of the concepts covered by the CAST, as well as the best methods required to solve questions on the CAST test quickly and effectively. Time management is an essential skill in this test, and as such we have composed our guides with an emphasis on this so that you won’t be caught unprepared when taking the real test.

In this module, we will discuss the contents of the test, and the structure of the course. We’ll lay out the rationale behind creating this course, what makes it unique, and how best to study from it. After this, we’ll finish up with some of our best test-taking tips to get you started off on the right foot.

As you go through the modules, take your time - there is a lot of information to digest due to the nature of this test, and it’s vital that you absorb all of it to the best of your ability if you’re to maximize your performance in this test. It may be that you find yourself needing to pause and review parts of the videos or read the text transcript in order to consolidate your understanding; this is perfectly normal and is in fact encouraged so that you can be sure you haven’t missed any important details along the way.

Last but not least - we’re very pleased to see you here. We hope you enjoy the course, and that it’ll be of great benefit to you. Good luck!

**Test Structure**

The questions on the CAST course can vary in difficulty, though the concepts covered are not so advanced that a college education would be required to manage them - in fact, these questions are at a sixth-grade level. That being said, a learned knowledge of the concepts covered is a huge asset when it comes to understanding exactly how to approach questions quickly and subsequently achieving a high score.

The test itself is comprised of four individually-administered tests:

As you can see, the time limit can be extremely unforgiving, and it would be easy to trip up. That’s what we’re here for. While this information may seem overwhelming, **by the time you have finished this course you will be 100% prepared for any question.**

Because you’ll need to judiciously skip time-consuming questions, even one wrong answer could have a catastrophic effect on your overall score. After all, *every* point counts on the CAST. As such, when you are faced with a question, you must think critically and make decisions quickly. Success is contingent upon your capacity to work efficiently and intelligently; pre-existing knowledge is not as much of a factor.

By following the guidelines and methodology that we laid out for you, you’ll be able to easily filter out the questions which are and aren’t worth spending time on and guess strategically for a higher score. By understanding how test-takers design the test, we seek to ensure that you’ll be more than prepared when test day comes.

The CAST test is far more challenging than it seems. Far too often, hardworking and talented individuals are being turned away from jobs they were otherwise qualified for simply because their test scores were too low.

While the CAST can be useful as a general metric of mechanical comprehension, many highly competent individuals fail the test for no reason other than their unfamiliarity with the types of questions and time traps. The strategy and super quick tactics conveyed in our modules help test-takers solve questions well within the time constraints and immediately recognize & avoid time traps, thus allowing you to save precious time which can make the difference between success and failure in your exam.

We have created this course so that busy people such as yourself can prepare for this test as quickly as possible. Whether you’ve been out of school for a few years, or are just nervous, we seek to provide promising candidates the tools they need to effectively take on this challenging psychometric test.

While the CAST *is* difficult, anybody can succeed if they are armed with a proven test-taking strategy and well-prepared tactics for the CAST’s different question categories. We believe that nobody should be turned away from their dream job or institution just because they didn’t know what to expect from a standardized test.

This is one of the only online courses devoted solely to the CAST test. Being far more than a cursory review, our test prep modules are deeply focused upon the skills you need for success. Avoiding extraneous tips, needless steps and general nonsense, our resources are both incredibly comprehensive and extremely practical.

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Questions involving levers require the candidate to identify the correct position in which a force must be applied in order to establish the equilibrium between two parts of levers which have opposite tendencies of rotation. In addition, they require one to figure out the missing force at one side of the system to set the equilibrium, if the distances from the turning point are given.

Another important point of this module is working out the resultant turning effect (moment) of force if the equilibrium cannot be established. The situation can be more complex if the weight of the lever is also included in the calculations.

In the test, it is very important to approach questions with some urgency as time is extremely limited. One should take care not to linger too long on any single question as it takes up valuable time which would be better-allocated on other, more approachable questions. While this guide will explore the means by which to approach the questions regarding levers, it is vital that if you cannot identify a path to a solution within 10-12 seconds you take an educated guess and move on to the next question. Spending too much time on any single question can cost precious time which is better spent elsewhere on less challenging problems.

First, let’s have a quick view on levers, before entering into details, which will be discussed when the types of levers are explained.

**Levers** are one of the simplest types of simple machines. As such, they possess the main properties of simple machines, i.e.:

Levers consist on a rigid bar which can turn around a fixed point. This turning point is known as pivot or fulcrum.

The turning point divides the system into 2 main parts:

Thus, the equilibrium is settled when the turning effects (moments) caused by the two forces applied at the given distances from the turning point, cancel each other. In simplest words, the condition of equilibrium in this case is

Total clockwise moment of force=Total anticlockwise moment of force

**1.2 Equation of levers**

The mathematical equation of the abovementioned rule is

where

F_{1⊥} and F_{2⊥} are the components of acting forces on both sides of the bar which are perpendicular to the bar length, while d1 and d2 are the distances of the points where the forces act to the fulcrum.

In general, a lever is used to lift a load L using a force F. Therefore, instead of writing F_{1}, F_{2}, d_{1} and d_{2}, we can write L for F_{1}, dL for d_{1}, F for F_{2} and d_{L} for d_{2}.

Hence, the equation of levers becomes

L×d_{L}=F×d_{F}

For example, if the load in the figure below is 20N and the distance of the center of gravity of the load from the turning point is 2 m, the magnitude of force F will be

**1.3** **Mechanical advantage **

Another important quantity regarding levers is Mechanical Advantage (MA). It is calculated by the equation

It calculates how many times easier we can lift a load using the lever than if we simply lifted it by arms.

In our example, the mechanical advantage is

This means we can lift the load 2 times easier when using the lever instead of carrying it by hand.

**1.4 Types of levers**

We determine the class of the lever by noting the relative positions of the load (L), pivot (P) and force (F).

The three possible combinations are:

Each of these combinations gives a different class of levers.

**1.4.1 First class levers**

** A first class lever **is used to lift heavy loads with small forces. It has a fulcrum between the force and the load as in the figure of the previous example

If the system is in equilibrium there are two equal turning effects but in opposite directions. According to the law of levers we can write

The force applied to the lever can also be calculated from the law of conservation of energy. Look at the figure below:

Giving that

Work done on the load=Work done by the force

we obtain

From the similarity of triangles, we obtain

where k is a constant. Hence, we obtain

Substituting the last expression in the equation (1), we obtain

Simplifying k, we obtain

which is identical with the equation (2).

**1.4.1.1 Examples of first class levers in daily life**

There are many examples in daily life when the principles of first class levers are applied. Scissors, see-saws, can openers, equal-arm balances and crowbars are all examples of first class levers.

Scissors (first class lever)

Seesaw (first class lever)

Seesaw (first class lever)

Equal-arm balance (first class lever)

Crowbar (first class lever)

**Example:** Calculate the force needed to pull out a nail using a crowbar as in the figure. The nail can take a maximum force of 2000 N.

Solution: Crowbar is a first class lever, so, its fulcrum is As we see, the distance from the load to the turning point (dL) is 15cm = 0.15m and the distance from the force to the turning point (dF) is 1m. The maximum force the nail can take (2000 N) here represents the load L. Thus, for the force F needed to pull out the nail, we have

The mechanical advantage of this crowbar is

The same result can be obtained also by dividing the distance from the turning point. Thus, from the equation

we can write

As you can see, the result is the same in both cases.

**1.4.2 Second class levers**

A second class lever has the load between the force and the fulcrum as shown in the figure below

The equation of a second class lever is the same as for the first class lever, i.e.

And the equation of mechanical advantage is also the same:

The only difference here is that in most cases, force distance is equal to the total length of the lever.

Wheelbarrow, nutcracker and bottle opener are all examples of second class levers. Look at the figures below

Wheelbarrow (second class lever)

Nutcracker (second class lever)

Bottle opener (second class lever)

Example: A man carries a 600N load using a wheelbarrow. What is the force the man applies for the values given in the figure? Find the mechanical advantage of the wheelbarrow? Ignore the weight of wheelbarrow.

Solution: From the figure we can see that dL = 40cm = 0.4 m, dF = 120cm = 1.2m and L = 600N. Thus, using the levers equation

we can work out the force F.

The mechanical advantage of this wheelbarrow is

**1.4.3 Third class levers**

*A third class lever *has the force between the load and the fulcrum, as shown in the figure below

A third class lever also obeys the law of the lever

Sugar tongs, tweezers, forearm etc. are good examples of third class levers.

Sugar tongs and tweezers (third class lever)

Forearm (third class lever)

Example: Calculate the force needed to catch a 20g ball using the tweezers as in the figure above if the length of tweezers is 9 cm and the force is exerted at a point 6 cm from the turning point. What can you say about mechanical advantage of these tweezers? (Take the approximate value of 10 m/s^{2} for gravity in this example).

Solution: first, we have to work out the load L which is equivalent to the weight W. Giving that mass m = 20g = 0.02 kg, we obtain

Now, using the equation of levers

Substituting the values dL = dtotal = 9cm = 0.09m and dF = 6cm = 0.06m, we obtain

The mechanical advantage is

In this case the mechanical advantage is less than 1. This means the force needed to lift the load is greater than the load itself. For this reason, one may think this type of lever is useless as we have to use a greater force than needed to lift the load. However, third class levers are usually used to lift light objects. Thus, the force is also small.

The usefulness of third class levers consist on the fact that they are used when no other options are available. Ethics is also a reason why we use third class levers. It is not ethical

catching the sugar lumps with fingers. On the other hand, you cannot use the hands to move a burning wooden block but you would use tongs for this.

**Important note**: In all the above examples, the weight of levers was not mentioned. It is either very small to be taken in consideration, or it was taken together with the load.

**1.5 Finding the correct approach on the questions involving levers**

The diagram below represents a guide on how to approach the questions about levers.

**1.6 Summary**

Levers are one of the simplest types of simple machines. As such, they possess the main properties of simple machines, i.e.:

The equilibrium is established when the turning effects (moments) caused by the two forces applied at the given distances from the turning point, cancel each other. In simplest words, the condition of equilibrium in this case is

Total clockwise moment of force=Total anticlockwise moment of force

In symbols,

where

L is the load in Newtons,

F is the force in Newtons,

d_{L} is the distance from the load to the fulcrum, and

d_{F}is the distance from the force to the turning point.

The above equation is known as the equation of levers.

We determine the class of the lever by noting the relative positions of the load (L), pivot (P) and force (F).

The three possible combinations are:

Mechanical advantage is an important quantity that shows how easily one can lift a load using the lever rather than carrying it by hand. It is calculated by the equation

In first and second class levers, mechanical advantage is greater than 1, while in the third class levers mechanical advantage is less than 1. This means that in third class levers we have to use a greater force than the load. However, they are very useful in certain situations.