1 09 quiz problem solving

1.08 problem solving quiz

Get better grades with Learn

82% of students achieve A’s after using Learn

SpringBoard Mathematics Course 3 PreAlgebra

• Create A Quiz
• Relationship
• Personality
• Harry Potter
• Online Exam
• Entertainment
• Training Maker
• Survey Maker
• Brain Games
• ProProfs.com

Problem Solving Quizzes, Questions & Answers

Sort by grade, top trending quizzes.

Popular Topics

Recent quizzes.

• Solve equations and inequalities
• Simplify expressions
• Factor polynomials
• Graph equations and inequalities
• Advanced solvers
• All solvers
• Arithmetics
• Determinant
• Percentages
• Scientific Notation
• Inequalities

What can QuickMath do?

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

• The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
• The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
• The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
• The calculus section will carry out differentiation as well as definite and indefinite integration.
• The matrices section contains commands for the arithmetic manipulation of matrices.
• The graphs section contains commands for plotting equations and inequalities.
• The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.

Math Topics

More solvers.

• Add Fractions
• Simplify Fractions

• Join Mind Tools

How Good Is Your Problem Solving?

© iStockphoto Entienou

Use a systematic approach.

Good problem solving skills are fundamentally important if you're going to be successful in your career.

But problems are something that we don't particularly like.

They're time-consuming.

They muscle their way into already packed schedules.

They force us to think about an uncertain future.

And they never seem to go away!

That's why, when faced with problems, most of us try to eliminate them as quickly as possible. But have you ever chosen the easiest or most obvious solution – and then realized that you have entirely missed a much better solution? Or have you found yourself fixing just the symptoms of a problem, only for the situation to get much worse?

To be an effective problem-solver, you need to be systematic and logical in your approach. This quiz helps you assess your current approach to problem solving. By improving this, you'll make better overall decisions. And as you increase your confidence with solving problems, you'll be less likely to rush to the first solution – which may not necessarily be the best one.

Once you've completed the quiz, we'll direct you to tools and resources that can help you make the most of your problem-solving skills.

How Good Are You at Solving Problems?

Instructions.

For each statement, click the button in the column that best describes you. Please answer questions as you actually are (rather than how you think you should be), and don't worry if some questions seem to score in the 'wrong direction'. When you are finished, please click the 'Calculate My Total' button at the bottom of the test.

Your last quiz results are shown.

You last completed this quiz on , at .

Score Interpretation

Answering these questions should have helped you recognize the key steps associated with effective problem solving.

This quiz is based on Dr Min Basadur's Simplexity Thinking    problem-solving model. This eight-step process follows the circular pattern shown below, within which current problems are solved and new problems are identified on an ongoing basis. This assessment has not been validated and is intended for illustrative purposes only. 

Figure 1 – The Simplexity Thinking Process

Reproduced with permission from Dr Min Basadur from "The Power of Innovation: How to Make Innovation a Part of Life & How to Put Creative Solutions to Work" Copyright ©1995

Below, we outline the tools and strategies you can use for each stage of the problem-solving process. Enjoy exploring these stages!

Step 1: Find the Problem

(Questions 7, 12)

Some problems are very obvious, however others are not so easily identified. As part of an effective problem-solving process, you need to look actively for problems – even when things seem to be running fine. Proactive problem solving helps you avoid emergencies and allows you to be calm and in control when issues arise.

These techniques can help you do this:

• PEST Analysis   helps you pick up changes to your environment that you should be paying attention to. Make sure too that you're watching changes in customer needs and market dynamics, and that you're monitoring trends that are relevant to your industry.
• Risk Analysis   helps you identify significant business risks.
• Failure Modes and Effects Analysis   helps you identify possible points of failure in your business process, so that you can fix these before problems arise.
• After Action Reviews   help you scan recent performance to identify things that can be done better in the future.
• Where you have several problems to solve, our articles on Prioritization   and Pareto Analysis   help you think about which ones you should focus on first.

Step 2: Find the Facts

(Questions 10, 14)

After identifying a potential problem, you need information. What factors contribute to the problem? Who is involved with it? What solutions have been tried before? What do others think about the problem?

If you move forward to find a solution too quickly, you risk relying on imperfect information that's based on assumptions and limited perspectives, so make sure that you research the problem thoroughly.

Step 3: Define the Problem

(Questions 3, 9)

Now that you understand the problem, define it clearly and completely. Writing a clear problem definition forces you to establish specific boundaries for the problem. This keeps the scope from growing too large, and it helps you stay focused on the main issues.

A great tool to use at this stage is CATWOE   . With this process, you analyze potential problems by looking at them from six perspectives, those of its Customers; Actors (people within the organization); the Transformation, or business process; the World-view, or top-down view of what's going on; the Owner; and the wider organizational Environment. By looking at a situation from these perspectives, you can open your mind and come to a much sharper and more comprehensive definition of the problem.

Cause and Effect Analysis   is another good tool to use here, as it helps you think about the many different factors that can contribute to a problem. This helps you separate the symptoms of a problem from its fundamental causes.

Step 4: Find Ideas

(Questions 4, 13)

With a clear problem definition, start generating ideas for a solution. The key here is to be flexible in the way you approach a problem. You want to be able to see it from as many perspectives as possible. Looking for patterns or common elements in different parts of the problem can sometimes help. You can also use metaphors   and analogies to help analyze the problem, discover similarities to other issues, and think of solutions based on those similarities.

Traditional brainstorming   and reverse brainstorming   are very useful here. By taking the time to generate a range of creative solutions to the problem, you'll significantly increase the likelihood that you'll find the best possible solution, not just a semi-adequate one. Where appropriate, involve people with different viewpoints to expand the volume of ideas generated.

Don't evaluate your ideas until step 5. If you do, this will limit your creativity at too early a stage.

Step 5: Select and Evaluate

(Questions 6, 15)

After finding ideas, you'll have many options that must be evaluated. It's tempting at this stage to charge in and start discarding ideas immediately. However, if you do this without first determining the criteria for a good solution, you risk rejecting an alternative that has real potential.

Decide what elements are needed for a realistic and practical solution, and think about the criteria you'll use to choose between potential solutions.

Paired Comparison Analysis   , Decision Matrix Analysis   and Risk Analysis   are useful techniques here, as are many of the specialist resources available within our Decision-Making section . Enjoy exploring these!

Step 6: Plan

(Questions 1, 16)

You might think that choosing a solution is the end of a problem-solving process. In fact, it's simply the start of the next phase in problem solving: implementation. This involves lots of planning and preparation. If you haven't already developed a full Risk Analysis   in the evaluation phase, do so now. It's important to know what to be prepared for as you begin to roll out your proposed solution.

The type of planning that you need to do depends on the size of the implementation project that you need to set up. For small projects, all you'll often need are Action Plans   that outline who will do what, when, and how. Larger projects need more sophisticated approaches – you'll find out more about these in the Mind Tools Project Management section. And for projects that affect many other people, you'll need to think about Change Management   as well.

Here, it can be useful to conduct an Impact Analysis   to help you identify potential resistance as well as alert you to problems you may not have anticipated. Force Field Analysis   will also help you uncover the various pressures for and against your proposed solution. Once you've done the detailed planning, it can also be useful at this stage to make a final Go/No-Go Decision   , making sure that it's actually worth going ahead with the selected option.

Step 7: Sell the Idea

(Questions 5, 8)

As part of the planning process, you must convince other stakeholders that your solution is the best one. You'll likely meet with resistance, so before you try to “sell” your idea, make sure you've considered all the consequences.

As you begin communicating your plan, listen to what people say, and make changes as necessary. The better the overall solution meets everyone's needs, the greater its positive impact will be! For more tips on selling your idea, read our article on Creating a Value Proposition   and use our Sell Your Idea   Bite-Sized Training session.

Step 8: Act

(Questions 2, 11)

Finally, once you've convinced your key stakeholders that your proposed solution is worth running with, you can move on to the implementation stage. This is the exciting and rewarding part of problem solving, which makes the whole process seem worthwhile.

This action stage is an end, but it's also a beginning: once you've completed your implementation, it's time to move into the next cycle of problem solving by returning to the scanning stage. By doing this, you'll continue improving your organization as you move into the future.

Problem solving is an exceptionally important workplace skill.

Being a competent and confident problem solver will create many opportunities for you. By using a well-developed model like Simplexity Thinking for solving problems, you can approach the process systematically, and be comfortable that the decisions you make are solid.

Given the unpredictable nature of problems, it's very reassuring to know that, by following a structured plan, you've done everything you can to resolve the problem to the best of your ability.

This site teaches you the skills you need for a happy and successful career; and this is just one of many tools and resources that you'll find here at Mind Tools. Subscribe to our free newsletter , or join the Mind Tools Club and really supercharge your career!

Rate this resource

The Mind Tools Club gives you exclusive tips and tools to boost your career - plus a friendly community and support from our career coaches! 

Comments (220)

• Over a month ago Sonia_H wrote Hi PANGGA, This is great news! Thanks for sharing your experience. We hope these 8 steps outlined will help you in multiple ways. ~Sonia Mind Tools Coach
• Over a month ago PANGGA wrote Thank you for this mind tool. I got to know my skills in solving problem. It will serve as my guide on facing and solving problem that I might encounter.
• Over a month ago Sarah_H wrote Wow, thanks for your very detailed feedback HardipG. The Mind Tools team will take a look at your feedback and suggestions for improvement. Best wishes, Sarah Mind Tools Coach

Please wait...

Module 1: General Problem Solving

Module 1 quiz — problem solving, module 1 quiz.

Do not open the quiz until you have finished the homework, and are ready to take the quiz.  There is a three-hour time limit for each quiz.  As soon as you click the link for the quiz, the timer starts ticking.  As a result, don’t open the quiz until after you have completed the module material.

• Module 1 Quiz. Provided by : Herkimer College/SUNY. Project : Contemporary Math Course for Achieve the Dream. License : CC BY: Attribution

Convective Heat Transfer over a Flat Plate: Example Problems

Try to solve these problems before watching the solutions in the screencasts.

Example Problem 1

A simplified version of a solar cell consists of a very thin semiconducting silicon layer. A layer of protective glass is glued to the silicon by an adhesive. The solar cell is 0.5 m long and 0.2 m wide. The air temperature is 25°C. It blows over the solar cell at a speed of 5 m/s. Calculate the average heat transfer coefficient,  h̅ . Report your answer in units of W/m 2 -K.

NOTE: In this screencast, the kinematic viscosity is off by an order of magnitude. The number used is 1.7e -6 m 2 /s, but it’s actually more like 1.7e -5 m 2 /s for air. This makes the Reynolds number 10x smaller and makes the actual flow laminar. The general procedure remains the same, but one should select a laminar flow correlation for this problem. The value computed is: h_bar = 38.6 W/m 2 -K, but 12 W/m 2 -K is more realistic.

Example Problem 2

Calculate the surface temperature of a motorcycle cooling fin attached to a motorcycle engine traveling at U ∞ = 40 km/h (25 mph). The ambient air is T ∞ = 27°C (81°F). Model the fin as a flat plate that is L = 5 cm long. To simplify the problem, assume the temperature of the fin is uniform along its length. Start by calculating h̅ using an appropriate correlation. Then calculate q′, which is the heat transferred per unit length of the fin, in units of W/m, which you can use in this expression: q′ = 2h̅L(T s − T ∞ ). The factor of 2 is used because heat is transferred from both sides of the fin.