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• Problem Solving Question Of The Day Compilation Worksheets For Ks3 Maths

KS3 maths worksheets – 100+ problem-solving questions

PDF question and answer booklets

This KS3 maths worksheets booklet from White Rose Maths contains over 100 problem-solving questions. There’s also an answer booklet.

You can also use these questions with GCSE pupils. Some problems are suitable for foundation and higher. Others are suitable for higher tier only.

Example KS3 maths worksheets questions

Max is saving to buy a computer game that costs £26. He saves 5p, 10p and 50p coins in a jar. The ratio of 5p to 10p to 50p coins is 2 : 5 : 1. There are 120 coins in the jar. How much more does he need to save?

You want to cover the floor in carpet titles. The tiles measure 40cm by 40cm. The floor is 3.2m by 2m. Tiles are sold in boxes of 12. How many boxes of tiles will you need to cover the floor?

Richard is doing a survey. He asks people to choose their favourite biscuits. THere are four biscuits: A, B, C or D. Here are the results: A (?); B (20%), C (15%), D (30%). 160 people chose B. How many people chose A?

White Rose Maths provides high-quality, research-driven KS3 and GCSE maths resources to support teaching and learning. Follow on Twitter at  @whiteroseed .

More maths resources

• Maths worksheet packs for Years  7 ,  8  and  9
• GCSE maths games
• KS3 maths questions mega revision PowerPoint
• Key Stage 3 maths worksheets for the whole curriculum

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Ideas and resources for teaching secondary school mathematics

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Problem Solving

• Problem Solving Booklet - Complete Mathematics
• GCSE Mathematics - 90 Problem Solving Questions - AQA (and PowerPoint collated by @EJMaths)
• Additional Mathematics Problem Solving Questions (& Teacher Guide ) - AQA
• GCSE Problem Solving  - MEI
• 55 Problems - MathsBox
• Maths problems, puzzles and ideas - Cubed Maths
• UKMT Problems PowerPoint - collated by Dan Walker
• San Gaku Problems - Dan Walker
• Support for Problem Solving  - OCR
• Badger Maths Problem Solving Samples (Years 1 - 6) - via National Stem Centre
• Daily Maths Puzzles (Key Stage 2) - Sarah Farrell
• Mathematical challenges for able pupils in Key Stages 1 and 2 - DfE
• Problem solving with EYFS, Key Stage 1 and Key Stage 2 children - DfE
• Solve My Maths
• Catriona Agg
• Maths Problem Solving
• MathsChallenge.net
• Brilliant.org
• Underground Mathematics
• Openmiddle.com
• United Kingdom Mathematics Trust
• 1001 Math Problems

Resources you can trust

Rich tasks and maths investigations for KS3

Here you'll find a collection of tried and trusted rich maths tasks and investigations to develop your KS3 students' numeracy skills and understanding. The best investigations are those that encourage curiosity and engage students’ problem-solving skills. Choose from activities that include maths problems in a real-life context, word problems and practical maths tasks to add some fun and creativity to your maths lessons on different shapes, fractions, decimals, and more.

Many of the teaching resources in this collection include lesson plans, PowerPoints or student worksheets. There are a number of resources in this collection that are suitable for learners at both key stages 3 and 4, so can also be used for GCSE practice.

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Category: Practice Questions

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FREE secondary maths resources

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15 Algebra Questions And Practice Problems (KS3 & KS4): Harder GCSE Exam Style Questions Included

Beki Christian

Algebra questions involve using letters or symbols to represent unknown values or values that can change. Here you will find 15 algebra questions to test your knowledge and show you the different ways that algebra can be used to solve a problem to find an unknown value or to make generalisations.

Algebra in KS3 and KS4

There are many topics and techniques within algebra . In KS3 we learn to write and manipulate basic algebraic expressions and linear equations. In KS4 we develop these techniques to allow us to deal with more complicated algebra problems such as ones that involve quadratic equations or a system of equations.

GCSE MATHS 2024: STAY UP TO DATE Join our email list to stay up to date with the latest news, revision lists and resources for GCSE maths 2024. We’re analysing each paper during the course of the 2024 GCSEs in order to identify the key topic areas to focus on for your revision. Thursday 16th May 2024: GCSE Maths Paper 1 2024 Analysis & Revision Topic List Monday 3rd June 2024: GCSE Maths Paper 2 2024 Analysis & Revision Topic List Monday 10th June 2024: GCSE Maths Paper 3 2024 Analysis GCSE 2024 dates GCSE 2024 results GCSE results 2023

How to solve algebraic questions

When you are presented with an algebraic problem it is important to establish what you are being asked to do. Here are some of the key terms along with what they mean:

• Solve the equation – find out the value of the unknown
• Substitute – put the values you have been given into the algebraic expression
• Simplify – collect together like terms to make the expression or equation look simpler
• Expand brackets – multiply out the brackets
• Factorise – put into brackets
• Make x the subject – rewrite the equation in the form x =…..

Remember, when working with algebra, we must still apply BODMAS / BIDMAS. i.e. B rackets, I ndices (powers, exponents, square roots), D ivision, M ultiplication, A ddition, S ubtraction.

When working with algebraic expressions and equations we must consider carefully which operations to deal with first.

Download this 15 Algebra Questions And Practice Problems (KS3 & KS4) Worksheet

Help your students prepare for their Maths GCSE with this free Algebra worksheet of 15 multiple choice questions and answers.

Algebra in KS2

The ideas of writing and simplifying expressions, solving equations and substitution are introduced in KS2. Here are some example KS2 algebra questions:

Algebra questions KS2

1. A chocolate bar costs c pence and a drink costs d pence. Write down an expression for the cost of 2 chocolate bars and 2 drinks.

2 chocolate bars would cost 2 lots of c, or 2c, and 2 drinks would cost 2 lots of d, or 2d.

2. Simplify the expression 4m+5+2m-1

We need to collect together like terms here so 4m + 2m = 6m and 5 – 1 = 4 (watch out for the negative).

Algebra questions KS3

In KS3 we learn a variety of different algebra techniques to answer algebra questions and to practise problem solving with algebra. These include:

• Simplifying algebraic expressions
• Expanding brackets and factoring
• Forming algebraic equations from word problems
• Solving algebraic equations and inequalities
• Substituting into expressions
• Changing the subject of an equation
• Working with real life graphs and straight line graphs

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• Year 6 Maths Test
• Year 7 Maths Test
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Algebra questions KS3: basic algebra

1. In this pyramid, you add two adjacent blocks to find the value of the block above.

What expression will be in the top box?

2.  Brian is a window cleaner. He uses the following formula to calculate the amount to charge his customers:

Charge = £20 + 4n

Where n is the number of windows a house has.

If a house has 7 windows, how much would Brian charge?

In this question, n is 7 so we can substitute 7 into the formula.

Charge = £20 + 4 × 7

Charge = £48

3. The area of a rectangle is 4x-6.

Which of the following pairs could be the length and width of the rectangle?

2x and 2x-3

There are two ways of attempting this question. We know that area \;of \;a \;rectangle = length × width so we could multiply each pair together to see which pair makes 4x − 6.

Alternatively, if we factorise 4x − 6 we get 2(2x − 3) meaning the sides could be 2 and 2x − 3.

4.  The formula for changing degrees Celsius to degrees Fahrenheit is

F=\frac{9C}{5}+32

Rearrange this formula to make C the subject.

Algebra questions KS3: forming and solving equations

5. Work out the size of the smallest angle.

The angles in a triangle add up to 180^{\circ} therefore we can write

Now we have an equation we can solve.

The angles are :

The smallest angle is 34^{\circ} .

6.  Jamie’s dad is 4 times older than Jamie. In 14 years time, Jamie’s dad will be twice the age of Jamie.

What is the sum of Jamie’s age now and Jamie’s dad’s age now?

To solve this we need to write an equation.

Let Jamie’s age now be x . Then Jamie’s dad’s age is 4x .

In 14 years time Jamie’s age will be x + 14 and Jamie’s dad’s age will be 4x + 14 .

Since we know Jamie’s dad’s age will be two times Jamie’s age, we can write

4x+14=2(x+14)

Jamie is currently 7 years old meaning his dad is 28 years old. The sum of their ages is 35 .

Algebra questions KS3: graphs

7.  Which of the following lines passes through the point (2, 5)?

At the point (2, 5), x is 2 and y is 5. We can check which equation works when we substitute in these values:

Algebra questions KS4

Algebra is studied extensively in the GCSE and IGCSE curriculum.

In KS4 we build on the techniques learnt in KS3. Topics include:

• Expanding and factorising polynomials
• Solving quadratic equations
• Solving simultaneous equations
• Inequalities
• Algebraic fractions
• Further work on graphs

Algebra questions KS4: algebraic manipulation

8. Which of the following expressions has the smallest value when a=5 and b=-3?

9. Find an expression in terms of x for the volume of this cuboid

Volume = (5x+1)(2x-3)(3x-1)

Volume = (10x^2+2x-15x-3)(3x-1)

Volume = (10x^2-13x-3)(3x-1)

Volume = 30x^3-39x^2-9x-10x^2+13x+3

Volume = 30x^3-49x^2+4x+3

Algebra questions KS4: forming and solving equations

10. The area of this triangle is 24cm^2 .

Work out the perimeter of the triangle.

The area of a triangle is area = \frac{1}{2} × b × h.

If we fill in what we know we get:

Since x = 3 , the side lengths are 6m, 8cm and 10cm .

The perimeter is 6 + 8 + 10 = 24cm .

11.  Solve the equation x+2-\frac{15}{x}=0

x=-2 or x=15

x=-3 or x=5

x=-5 or x=3

x=-15 or x=2

We can make this a bit easier by getting rid of the fraction involving x. We do this by multiplying each term by x.

12. At a theme park the Jones family purchased 2 adult tickets and 3 child tickets for £48 .  The Evans family purchased 3 adult tickets and 1 child ticket for £44 . 

Calculate the cost of one child ticket.

We can write simultaneous equations to solve this.

2a+3c=48 (Equation 1) 3a+c=44 (Equation 2)

Multiply equation 2 by 3 to make the coefficients of c equal: 9a+3c=132 (Equation 3)

Subtract equation 1 from equation 3: 7a= 84 a=12

Substitute a into equation 3: 3×12+c=44 36+c=44 c=8

The cost of an adult ticket is £12 and a child ticket is £8 .

Algebra questions KS4: graphs

13.  Which of these lines is parallel to the line 2y = x + 7

For two lines to be parallel, their gradient must be equal.

If we rearrange 2y=x+7 to make y the subject we get y=\frac{1}{2}x+\frac{7}{2}.

The gradient is \frac{1}{2}

14. Find the minimum value of the function f(x) = x^2+4x+5 .

To find the minimum value we need to complete the square.

The minimum value is 1. This occurs when (x+2) is 0.

15. The diagram shows the circle x^2+y^2=25 . The line is a tangent to the circle at the point (3,4) . Work out the equation of the line.

To work out the gradient of the line we need to work out the gradient of the normal.

We know that the normal goes through the points (0, 0) and (3, 4) so we can calculate the gradient: \frac{4-0}{3-0}=\frac{4}{3}.

The gradient of the tangent will be \frac{-3}{4}.

We can now use y=mx+c . We know the tangent goes through the point (3, 4) and that it’s gradient is \frac{-3}{4} .

Free GCSE maths revision resources for schools As part of the Third Space Learning offer to schools, the personalised online GCSE maths tuition can be supplemented by hundreds of free GCSE maths revision resources from the secondary maths resources library including: – GCSE maths past papers – GCSE maths predicted papers – GCSE maths worksheets – GCSE maths questions – GCSE maths topic list

Looking for more KS3 and KS4 maths questions?

• 15 Simultaneous equations questions
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Read more: Question Level Analysis Of Edexcel Maths Past Papers (Foundation)

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Mirror Mirror

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The Silent Countdown

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Bridge Build

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Group Size: 6+ Key stages:  KS2, KS3 , KS4, KS5 Team Building Skills: Communication,  Equipment: Pen, Coin and table and chairs  Download Activity PDF This is an indoor team building game played around a table. Ideally even sized teams sit in lines facing each other across a table. Sitting in chairs is

Fruit Salad – Free Team Building Game

For this team building activity everyone is required to stand in a circle. The bigger the group the better – Tricky at the time of print! Go around the circle and give all team members a name – Kiwi, lime, pineapple, banana. These names can be whatever you fancy, although

The Sky Is The Limit aka Newspaper Towers – Free Team Building Exercise

Group Size: Multiple Groups of 4 – 6 Key Stage: KS1, KS2, KS3, KS4, KS5 Team Building Skills: Creativity; Verbal Communication; Decision Making Equipment: Newspapers; Cellotape Download Activity PDF The Sky is the Limit –  AKA: Newspapers Towers,  This activity is a great team building exercise where the equipment of old newspapers and

Free Team Problem Solving Activity – Back To Back aka Sketch It

Back to Back – Sketch it. Students will work in pairs and sit back to back. They will take it in turns to be the describer and the sketcher. The describer will describe a shape without saying the name whilst the sketcher will try to draw the described shape as

Free Team Building Activity – Alphabet Hunt

A great fun yet inexpensive team building activity. All that is required is some scissors a newspaper a piece of A4 paper and a glue stick or cellotape per team. We suggest that this activity is run in teams of 2-6. However larger teams will work. The aim of the

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Problem solving

Problem solving lesson plan

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Problem Solving: Lesson plan

Problem solving: Presentation slides

Demonstrating your skills quick fire activity

Problem solving in practice: Interactive worksheet

Our problem solving content focuses on one of these skills and develops understanding of the six stages of problem solving, as well as identifying different types of situations in which young people might already be using these skills. Furthermore, it encourages them to use an adaptive approach, explaining that different types of problems can be approached in different ways.

The activities on this page support your teaching of these skills through an independent activity, quick activities or a full length, curriculum-linked lesson plan. 

Teaching resources:

• Problem solving: Lesson plan and presentation slides – full lesson plan including icebreaker for use with a group of students in the classroom
• Demonstrating your skills: Quick-fire activity  – 10 minute activity for a group of students in the classroom, can be used as an icebreaker for the lesson plan
• Problem solving in practice: Interactive worksheet – activity for independent learning whether remote or in class

Lesson plan

(60 -75 minutes)

This lesson is designed to equip young people with an adaptable approach to solving problems, large or small. It includes a short film and scenarios that encourage development of practical problem solving skills which can be useful for learning, day to day life, and when in employment.

By the end of the lesson, students will be able to:

• Identify problems of different scales and what is needed to solve them
• Illustrate the use of an adaptable approach to solving problems
• Understand that problem solving is a core transferable skill and identify its usefulness in a work setting
• Work on a problem solving activity in a team

The lesson aims to reinforce students’ understanding of the potential future applications of this skill as they move into the world of work, particularly in an activity differentiated for an older or more able group on creating new opportunities.

Quick-fire activity

(5 - 10 minutes)

The demonstrating your skills quick-fire activity focuses on helping young people understand the key skills that are needed in the workplace, including the importance of problem solving.

Students will be asked to name the skills being demonstrated in a variety of scenarios, and identify ways they’re already using those skills in this short activity.

You might find it useful as a starter or icebreaker activity to begin a lesson, or at the end to allow students to put what they have just learnt in the Problem solving lesson into practice.

Interactive worksheet

(20 - 25 minutes)

Please note that students below the age of 14 cannot sign up for their own LifeSkills account. Any independent tasks must be printed or downloaded and provided digitally for them to complete as they are currently hosted on educator pages.

The Problem solving in practice interactive worksheet introduces some of the themes from the full lesson plan and gives students some practical strategies for problem solving, including introducing the six stages of problem solving. The worksheet can be printed or completed digitally, so can be used flexibly to give students practise putting their problem solving skills into action. You might choose to assign it:

• As homework following the Problem solving lesson
• For independent study
• For remote learning

Looking for more ways to boost self confidence with LifeSkills?

Other lessons that may prove useful for students to build on these activities include the  Adaptability  and  Innovation and idea generation  lessons. Alternatively, consider encouraging them to apply their skills through  Steps to starting a business  or the  Social action toolkit .

Why not build problem solving in as a focus in your students’ wider curriculum? Refer to our  Content guide to find out how this resources can be used as part of your teaching.

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Why not try one of these next?

Staying positive (resilience)

Staying positive and learning through experience are key to succeeding in challenging situations. Try this lesson and help your students succeed at work.

Good leadership styles and effective teamwork can help students excel in their future workplace. Read more about team leader skills in this lesson.

Social action toolkit

Build a comprehensive social action programme and support young people to access enriching experiences that build transferable skills for work.

Problem solving with trigonometry

I can use my knowledge of trigonometry to solve problems.

Lesson details

Key learning points.

• Sometimes there can be more than one valid approach to a problem.
• You should consider all the skills you have.
• Consider multiple approaches and take time to evaluate each.
• Keep the goal in mind throughout, remember what you are trying to find out.

Common misconception

Pupils may struggle to identify a right-angled triangle in the problem.

Encourage pupils to sketch the question out and add any known right angles or perpendicular lines, as this may lead to a right-angled triangle.

Trigonometric ratios - The trigonometric ratios are ratios between each pair of lengths in a right-angled triangle.

This content is © Oak National Academy Limited ( 2024 ), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Starter quiz

6 questions.

NICE’s 1CX Could Be A Game-Changer For Solving Knotty Customer Problems

Imagine that one of your customers is experiencing a problem with a product or service that they have purchased from your company. Wanting to find a fast and easy solution to their problem, they land on your website, but after searching your FAQs and interacting with your chatbot, they realise they won’t be able to find the answer to their problem. It’s a little too complex.

They then decide to call your contact center to seek help. Once they get through to an agent and explain their issue, the agent quickly realises that the customer’s problem is quite complex and not something that they themselves will be able to help with. It will require the assistance of one of their colleagues in the back office. However, rather than asking them to call another team or placing them in another queue, they remember that they helped a customer with a similar issue last week and, in particular, how one of their colleagues in the back office team had been a great help.

Asking the customer to bear with them for a moment, the agent checks their system to see if that colleague is available and quickly messages them to see if they can help. Their colleague quickly responds saying that they can help, and the agent proceeds to loop their colleague into the conversation. Introducing their colleague to the customer and explaining the situation, the agent then takes a back seat in the conversation whilst their colleague helps the customer. This takes a few minutes, so while they wait for the issue to be resolved, the agent catches up with some administrative tasks and answers a few emails from other customers.

Once the customer’s issue is resolved, the agent jumps back into the conversation, thanks their colleague for being able to help and rounds off the interaction by asking the customer if there is anything else that they can help them with today. The customer answers that there is nothing else, and thanks the agent and their colleague for being so helpful. They both bid each other a good day. The call ends.

Customer support agent

I recently played this scenario to Barak Eilam, CEO of NICE , and he explained that the type of connectivity and collaboration described in the scenario is exactly what 1CX , their new product line, aims to facilitate and is something that many of their customers have been asking for for some time now.

1CX is ostensibly a Unified Communications as a Service (UCaaS) product addition to their existing platform, but its launch recognizes a couple of trends that are emerging in the customer service and experience space, namely:

• Digital, automation and self-service technology will mature and improve in scope and effectiveness. This will remove much of the need for agent involvement in the majority of simple and straightforward inquiries from customers.
• As this happens, the nature of the queries that customer service agents will be asked to handle will increase in complexity. Some of these more complex queries will require access to knowledge, systems, and expertise that is often not accessible on the front line but, more often than not, sits in the middle and back offices of large organizations.

Over and above the capability of their new product and what it will allow contact centers to do, particularly when faced with complex customer problems, one of the most interesting things about 1CX is how they are pricing it. Rather than pricing it like a separate UCaaS-lite offering and charging an additional $25 per seat, as is normal with some other systems, existing CXOne clients will only be charged an additional $5 per user per month for this set of enhanced collaboration and communications capabilities.

This is a smart move, particularly given the budget and investment constraints that many contact centers have to operate under, and is likely to prove popular.

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• 29 Aug 2024

Leni Peterson R. (MS/MBA 2023): Solving Big Problems Through Entrepreneurship

Who are you & what are you building?

I am Leni Peterson R. (MS/MBA 2023), CEO and cofounder of Celeste . My background is in Mechanical Engineering and Human Centered Design, product leadership, and innovation consulting. 

I am originally from Mexico City, the largest metropolis in North America with a population of 23 million people. The city simultaneously has every possible water issue including scarcity, flooding, sinking, poor quality, and unequal access. It is here I realized how water touches every aspect of our lives, and how we often fail to appreciate its value until it's gone.

Without water, companies cannot operate. Water is not only a key indicator of climate change, but also a major factor behind supply chain disruptions. Poor water access can exacerbate health and political crises through flooding, scarcity, and fires. Given the macro nature of water crises, individualized strategies are insufficient for managing operational, regulatory, and reputational risks. Collaboration is key to tackling these challenges effectively.

Celeste, through watershed project development, is poised to address the $400 billion water risk and management opportunity. Our goal is to streamline and scale engagement with at-risk suppliers, industry peers, and key stakeholders to stabilize supply chains and enhance water stewardship.

What inspired you to start a company, what resources did you need, and what fears did you face in the process?

From an early age, I was inspired by simple products like the Hippo Roller (a device used to carry drinking water) and insecticidal nets, realizing their potential to significantly improve communities. This revelation shaped my guiding principle: to use design and engineering to solve complex social and environmental issues.

During my time at Mawa Modular – a startup designing modular shelters for refugees in Jordan – I discovered that innovative business models can be as impactful as product design. This experience solidified my desire to join a program that would equip me with the technical skills and business acumen to start my own impact venture. The MS/MBA at Harvard was the perfect fit.

My biggest worries about starting my own venture were, “What if I fail?”, “Where do I even begin?” and “Is entrepreneurship right for me?” For the first question, I have redefined success with every milestone by starting my own company. No job teaches you as much as being your own boss and making tough decisions daily. Even if my company does not achieve the impact I envision, I still gained invaluable experience. So truly, there is no failure in trying. To answer the question “Where do I start?” I recommend finding a problem you can become obsessed with rather than just an idea you thought of in a vacuum. Understanding the problem deeply is the hardest part, but once you do, the idea will come naturally. The world is full of problems, so make a list of profound issues or pain points you have either heard or faced directly.  Focus on problems you are genuinely interested in.  

If you do not know if entrepreneurship is right for you, think about two things: 

1. It is hard but fun. The day to day is not glamorous, but there is nothing quite like it. However, not everyone is meant to be an entrepreneur. 

2. You will not know if it is right until you try it. You need to start to get a sense if you like the autonomy, chaos, impact, and sheer feeling of building something from nothing, and the vivid, heart-pumping, and mind-blowing journey of ups and downs. 

How did the MS/MBA help you build your company?

I knew of product design engineering before coming to Harvard, but it was not until I started the program that I understood how to design a tech company, incentivize people to care and work as a team, and align different plans (financial, engineering, and hiring). The classes that are part of the MS/MBA, such as the Technology Venture Immersion and Launch Lab I/II, guided me to achieve the proper mindset to start my own company. As I saw others fearlessly jump into their own ideas, I realized I really needed three key things to start a company: high levels of optimism in my idea, a dauntless ability to learn new things, and an unapologetic capability to ask for what you need – even if it makes you uncomfortable. The MS/MBA created a perfect environment to test these out in a safe and risk-mitigated way. 

How has the MS/MBA program empowered you as a woman in the start-up space?

The MS/MBA program made entrepreneurship approachable. I came in with this dream, but when I started the program, I realized that it was not far-fetched. It gave me the tools to start. It surrounded me with women and men that were equal parts kind and smart, who knew they could solve a big problem through entrepreneurship. With a community to lean on, a head full of plans, and the learnings to achieve them, there was no way I would not take the jump. And here we are today. 

You Might Want to Read

• The EC Formula: MBA Class of 2024 Looks Back
• It’s Time to Build: Why the MS/MBA Is Right for You!
• HBS Alumna Fighting Cancer with a Novel Cell Therapy

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Solvo - Math Homework Helper 4+

Problem solver & essay writer.

• #144 in Education
• 4.7 • 183 Ratings
• Offers In-App Purchases

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Description.

Solvo is your new superpower in education and beyond Maximize your academic potential with your own personal AI homework helper! Meet Solvo—an AI-powered math, chemistry, biology, physics solver & essay writer that revolutionizes the way you manage study assignments. Simply scan, type, or upload the task in front of you and let the app work its magic! Check out what Solvo can help you with: Scan & Solve • Scan and solve math problems, equations, and more Faced with a boss-level problem (e.g., you need science answers) and don’t know where to start? Snap a picture of it—you’ll see the result and in-depth solution steps. This way, you gain more insights into how to tackle certain tasks and become more confident solving them yourself next time! Math, science answers, and more—you name it, our AI homework helper helps with it in a flash. • Ace any test and quiz Our AI homework helper can answer all sorts of questions typically used in tests and quizzes, including true or false, multiple-choice, and open questions. Biology solver? Chemistry solver? It’s already in your pocket! Simply tap Text-Based Problems, snap a picture of the question, and get your answer in seconds. This feature can also help you test your knowledge and prepare for exams. Streamline Reading & Writing • Write killer essays in a breeze Have excellent ideas for your essay but find it hard to articulate them clearly? No problem—Solvo is an experienced essay writer! Simply tap Create Essay and type your subject. You can go ahead and use the output directly or to get your creative juices flowing. • Improve and reword your writing Solvo isn’t just an essay writer—it’s a great editor! Already prepared a draft of your text and need help with polishing it into something truly A grade-worthy? Just upload your writing to our AI homework helper, and the app will offer suggestions to reword and improve it. This can be a game-changer if you feel stuck with a writing assignment. • Read smarter, not harder Our AI homework helper can be a lifesaver if you need a quick overview of a book. Type the name of the book or its author, or upload the book if you've got a file, and no matter how long or complex, tap Generate Summary. Get the essentials in a breeze! Math solver, physics homework solver, essay writer, biology solver, chemistry solver—Solvo wears many hats! Yes, studies can be challenging, but with our AI homework helper, you're well-equipped to handle them! Get answers to all your problems—including tricky science answers—with prompt assistance for your tasks whenever and wherever you need it and enjoy studying with less anxiety. Be unstoppable in class with Premium! A subscription allows you to: • Remove usage limits • Get more detailed answers • Use text recognition (OCR) • Get instant responses Subscriptions are auto-billed based on the chosen plan. Privacy Policy - https://aiby.mobi/ai_study_ios/privacy Terms of Use - https://aiby.mobi/ai_study_ios/terms

Version 1.30

Get ready for the back-to-school season with Solvo! In this update: — Improved scanning and solving of visual tasks (including graphs, geometry, tables, and more) — Leave feedback after any solution, so we can continue improving task-solving — Copy and share any solution Don’t forget to send feedback to [email protected] and leave your review on the App Store! It helps us make the app even better.

Ratings and Reviews

183 Ratings

A wonderful app

Very helpful app I was needing something to help me with my daughter’s homework my daughter is horrible on taking notes in school. And if I have notes to see the task I’m good at figuring it out how to do the rest so I tried this help because I couldn’t find anything online to help me. So when this can’t up I was like why not. And I was glad I did it tells u how to solve it. And I could figure out the rest by their help. The only thing I would like if they make another app or add on this this one for younger kids. I know a couple of parents that also need help with there kid’s homework (how to help there child I don’t do it for my kids do there homework but I have to explain it to them sometimes and for that I need to refresh my mind as will) and this is a great app for that just hope they for something god younger students grades 2nd to 5th graders would help parents a lot.

Great App / One Major Issue

I love this app. Its saved me multiple times on upcoming tests, and the great thing about it is it thoroughly goes through the topic step-by-step making sure you understand how the AI got to the solution. All that to be said, I really wish there was a feature to edit the text that was scanned in the picture. I think its already an intended design because theres text displayed saying if you’d made typos heres the time to fix it, but it doesn't work. Tapping on the screen doesn't do anything. You can copy and paste the text but theres no way to edit it where the users keyboard opens. This is a 10/10 if I could edit the prompt.

Great academic support

Solvo has truly been a remarkable discovery for me as a busy working mom. My son has been facing difficulties with certain subjects in school, and finding the time and energy to assist him with homework has been a challenge for me. Since we found Solvo, everything has changed for the better. My son doesn’t give up on his assignments when they’re difficult. Solvo gives me peace of mind. I know my son receives the help he needs. The app has empowered my son to become more independent in tackling his academic challenges without unnecessary stress. I highly recommend Solvo to all working parents who want to actively support their children’s education. It’s an invention that has made a significant difference in our lives.

HAPPENING NOW

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The developer, AIBY , indicated that the app’s privacy practices may include handling of data as described below. For more information, see the developer’s privacy policy .

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Can AI Match Human Ingenuity in Creative Problem-Solving?

When ChatGPT and other large language models began entering the mainstream two years ago, it quickly became apparent the technology could excel at certain business functions, yet it was less clear how well artificial intelligence could handle more creative tasks.

Sure, generative AI can summarize the content of an article, identify patterns in data, and produce derivative work—say, a song in the style of Taylor Swift or a poem in the mood of Langston Hughes—but can the technology develop truly innovative ideas?

Specifically, Harvard Business School Assistant Professor Jacqueline Ng Lane was determined to find out “how AI handled open-ended problems that haven’t been solved yet—the kind where you need diverse expertise and perspectives to make progress.”

In a working paper published in the journal Organization Science , Lane and colleagues compare ChatGPT’s creative potential to crowdsourced innovations produced by people. Ultimately, the researchers found that both humans and AI have their strengths—people contribute more novel suggestions while AI creates more practical solutions—yet some of the most promising ideas are the ones people and machines develop together.

Lane cowrote the paper with Léonard Bouissioux, assistant professor at the University of Washington’s Foster School of Business; Miaomiao Zhang, an HBS doctoral student, Karim Lakhani, the Dorothy & Michael Hintze Professor of Business Administration at HBS; and Vladimir Jacimovic, CEO and founder of ContinuumLab.ai and executive fellow at HBS.

Crowdsourcing people for ‘moonshots’

Any innovation process usually starts with brainstorming, says Lane, whose research has long looked at how creative ideas are produced.

“You start with defining the problem, then you generate ideas, then you evaluate them and choose which ones to implement.”

“It’s like a funnel,” she says. “You start with defining the problem, then you generate ideas, then you evaluate them and choose which ones to implement.”

Research has shown that crowdsourcing can be an effective way to generate initial ideas. However, the approach can be time-consuming and expensive. Creative teams typically offer incentives to respondents for their ideas. Then teams often must wait for input and then comb through ideas to come up with the most promising leads.

An off-the-shelf large language model such as ChatGPT, however, is free or low cost for end users, and can generate an infinite number of ideas quickly, Lane says. But are the ideas any good?

To find out, Lane and her fellow researchers asked people to come up with business ideas for the sustainable circular economy, in which products are reused or recycled to make new products. They disseminated a request on an online platform, offering $10 for participating and $1,000 for the best idea. Here’s part of their request:

We would like you to submit your circular economy idea, which can be a unique new idea or an existent idea that is used in the industry.

Here is an example: Car sharing in order to reduce the carbon footprint associated with driving. …

Submit your real-life use cases on how companies can implement the circular economy in their businesses. New ideas are also welcome, even if they are “moonshots.”

Seeking creative ideas from ChatGPT

The researchers asked for ideas that would involve “sharing, leasing, reusing, repairing, refurbishing [or] recycling existing materials and products as long as possible.” Suggestions would be scored for uniqueness, environmental benefits, profit potential, and feasibility.

Some 125 people replied with contributions, offering insights from a variety of industries and professional backgrounds. One, for example, proposed a dynamic pricing algorithm for supermarkets to cut down on food waste, while another suggested a mobile app that could store receipts to reduce paper waste.

At the same time, the research team employed prompt engineering techniques to craft a variety of AI prompts. Using these carefully designed prompts, they generated several hundred additional solutions through ChatGPT. The team strategically modified their prompts to:

• Challenge the model to create more ideas.
• Mimic the perspective of someone from a particular industry, job title, and place—a persona.
• Remind the model to provide ideas that reflect the scoring criteria.

The team then recruited some 300 evaluators well-versed in the circular economy to evaluate a randomized selection of the ideas based on the scoring criteria.

People are creative, but AI ideas are more feasible

The evaluators judged the human solutions as more novel, employing more unique “out of the box” thinking. However, they found the AI-generated ideas to be more valuable and feasible.

For example, one participant from Africa proposed creating interlocking bricks using foundry dust and waste plastic, creating a new construction material and cutting down on air pollution at the same time. “The evaluators said, ‘Wow, this is really innovative, but it would never work,’” Lane says.

“We were surprised at how powerful these technologies were.”

One ChatGPT response, meanwhile, created an idea to convert food waste into biogas, a renewable energy source that could be used for electricity and fertilizer. Not the most novel idea, the researchers noted, but one that could be implemented and might show a clear financial return.

“We were surprised at how powerful these technologies were,” Lane says, “especially in these early stages in the creative process.”

How to reach the best solutions

The “best” ideas, Lane says, may come from those in which humans and AI collaborate, with people engineering prompts and continually working with AI to develop more original ideas.

“We consistently achieved higher quality results when AI would come up with an idea and then we had an instruction that said: Make sure before you create your next idea, it’s different from all the ones before it,” Lane explains.

Additional prompts increased the novelty of the ideas, generating everything from waste-eating African flies to beverage containers tracked by smart chips that instantly pay consumers for recycling them.

Based on the findings, the researchers suggest business leaders keep a few points in mind when implementing AI to develop creative solutions:

• Knowing how to ask the right questions is important. Organizations might want to invest in cultivating an “AI-literate” workforce that can understand the capabilities and limitations of AI to generate the most successful ideas.
• Organizations should resist the temptation to rely excessively on AI. That could “dumb down” the overall level of creative output over time, leading to more incremental improvements than radical breakthroughs, the team says.
• People should view generative AI models as collaborative tools. In a sequential approach, humans could brainstorm solutions, then submit them to AI to refine them and increase their value and feasibility. Alternatively, humans could work more iteratively with AI, constantly shaping and improving the ideas it provides.

The most productive way to use generative AI, the research suggests, is to combine the novelty that people excel at with the practicality of the machine. Says Lane, “We still need to put our minds toward being forward-looking and envisioning new things as we are guiding the outputs of AI to create the best solutions.”

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KS3 Angle pile up problems, 25 questions, Angles in a quadrilateral, triangle

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

27 November 2022

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• Two problems are included
• First problem is repeated 3 times on one sheet for ease of printing
• Second problem is repeated twice to optimise printing
• First problem regards solely angles within a triangle.
• Second problem regards angles within a triangle, quadrilateral and the harder sheet 2 includes alternate angles (the lattter doesn’t have to be included).
• Cheat sheet, which is a good structure for supporting any ability to complete at least the first task.

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A general method for solving differential equations of motion using physics-informed neural networks.

1. Introduction

2. physics-informed neural networks, 2.1. fully connected neural network, 2.2. differential equations, 2.3. training process of neural network, 3. numerical studies, 3.1. two-degree-of-freedom system, 3.1.1. training sample number, 3.1.2. number of hidden layers and neurons, 3.2. four-layer framework structure, 3.2.1. activation function, 3.2.2. the weight coefficients of the loss function, 3.3. cantilever beam, 4. conclusions, author contributions, institutional review board statement, informed consent statement, data availability statement, acknowledgments, conflicts of interest.

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Zhang, W.; Ni, P.; Zhao, M.; Du, X. A General Method for Solving Differential Equations of Motion Using Physics-Informed Neural Networks. Appl. Sci. 2024 , 14 , 7694. https://doi.org/10.3390/app14177694

Zhang W, Ni P, Zhao M, Du X. A General Method for Solving Differential Equations of Motion Using Physics-Informed Neural Networks. Applied Sciences . 2024; 14(17):7694. https://doi.org/10.3390/app14177694

Zhang, Wenhao, Pinghe Ni, Mi Zhao, and Xiuli Du. 2024. "A General Method for Solving Differential Equations of Motion Using Physics-Informed Neural Networks" Applied Sciences 14, no. 17: 7694. https://doi.org/10.3390/app14177694

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