algebra problem solving questions gcse

The resources on this page will hopefully help you teach AO2 and AO3 of the new GCSE specification - problem solving and reasoning.

This brief lesson is designed to lead students into thinking about how to solve mathematical problems. It features ideas of strategies to use, clear steps to follow and plenty of opportunities for discussion.

The PixiMaths problem solving booklets are aimed at "crossover" marks (questions that will be on both higher and foundation) so will be accessed by most students. The booklets are collated Edexcel exam questions; you may well recognise them from elsewhere. Each booklet has 70 marks worth of questions and will probably last two lessons, including time to go through answers with your students. There is one for each area of the new GCSE specification and they are designed to complement the PixiMaths year 11 SOL.

These problem solving starter packs are great to support students with problem solving skills. I've used them this year for two out of four lessons each week, then used Numeracy Ninjas as starters for the other two lessons.  When I first introduced the booklets, I encouraged my students to use scaffolds like those mentioned here , then gradually weaned them off the scaffolds. I give students some time to work independently, then time to discuss with their peers, then we go through it as a class. The levels correspond very roughly to the new GCSE grades.

Some of my favourite websites have plenty of other excellent resources to support you and your students in these assessment objectives.

@TessMaths has written some great stuff for BBC Bitesize.

There are some intersting though-provoking problems at Open Middle.

I'm sure you've seen it before, but if not, check it out now! Nrich is where it's at if your want to provide enrichment and problem solving in your lessons.

MathsBot  by @StudyMaths has everything, and if you scroll to the bottom of the homepage you'll find puzzles and problem solving too.

I may be a little biased because I love Edexcel, but these question packs are really useful.

The UKMT has a mentoring scheme that provides fantastic problem solving resources , all complete with answers.

I have only recently been shown Maths Problem Solving and it is awesome - there are links to problem solving resources for all areas of maths, as well as plenty of general problem solving too. Definitely worth exploring!

We are aware of some issues with pdfs on the website after last night's update. Some should now be fixed and others will be later today.

Edexcel Algebra Questions by Topic

Durham University - BSc Chemistry

Durham University Graduate with 6 years experience.

On this page you can find past paper questions separated by topic and topic tests, for both Foundation and Higher tiers. The first two sets are from past papers and the third one is a set of topic tests. Set 4 comprises the most recent past paper questions spanning from 2017 to 2021. Set 4 is the only set that comes with video solutions .

For notes, worksheets and their solutions, visit the GCSE Algebra Revision page. Full past papers and model solutions can be found on the Paper 1 , Paper 2 and Paper 3 pages.

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• Solving Quadratic Equations (H)

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GCSE algebra practice and questions

Gcse algebra questions.

GCSE algebra questions are mathematical problems that assess students' understanding and application of algebraic concepts and techniques.

Here are three examples of GCSE algebra questions:

Solve the equation 3x + 7 = 16 and express your answer as a whole number.

This question requires students to figure out the value of "x" using their algebra knowledge. In this example students would need to find out which number to multiply 3 by, so that when 7 is add it equals 16. Can your child figure out the answer?

Expand and simplify the expression (2x + 3)(x - 5).

In this question, students need to apply the distributive property to expand the given expression and then simplify it by combining like terms.

Solve the simultaneous equations: 2x + 3y = 10 4x - y = 7

This question involves solving a system of equations, where students need to find the values of x and y that satisfy both equations simultaneously. Various techniques such as substitution or elimination may be used to solve the system.

These examples are just a representation of the types of algebra questions that could appear in GCSE exams. The actual questions can vary in complexity and format, and we recommend regular practice with GCSE algebra to ensure students are ready for their GCSE maths exams .

How to Learn GCSE algebra

GCSE algebra can be a lot for students to get their head around, but keeping these tips in mind while they learn can really help:

Get the basics down: Start by understanding the building blocks of GCSE algebra, like variables, equations, and expressions. Don't forget the order of operations when figuring out algebra equations (ask your child to talk to their teacher about PEMDAS and BODMAS) and how to solve basic linear equations.

Practice, practice, practice: familiarise yourself with GCSE algebra by practicing regularly. Tackle different types of algebra problems to reinforce your skills and become a real problem solver. Use textbooks, online resources, or algebra practice books.

Ask for help: If you're stuck or confused, don't be shy! Reach out to your teacher, join study groups, or let someone in the family know you're struggling. Just getting a little reassurance or chatting to someone that can change your perspective on GCSE algebra can make a huge difference.

Break it down: When faced with a big algebra problem, break it into smaller steps. Take it one piece at a time. Figure out what's given in the equation, what's unknown, and what you need to do to figure out the unknown. Small steps make big problems more manageable.

Get visual: Use your imagination and draw diagrams, graphs, or charts to visualize GCSE algebra concepts. It can help you see connections between variables and equations. Let your creative side shine!

Learn from examples: Check out solved examples and solutions to see how different GCSE algebra problems are tackled. Pay attention to the steps and strategies used. It'll help you build your own problem-solving toolkit.

Flex your mental math: Sharpen those mental math skills! Practice doing calculations in your head, simplify expressions mentally, and show off your speedy math skills. Quick but well-practiced calculations save time in exams.

Tackle word problems: Algebra gets real when it's applied to everyday situations in word problems. Practice turning word problems into algebraic expressions or equations. Break it down, set up the math, and solve for the answer.

Online resources rock: Take advantage of online resources, like video tutorials, interactive quizzes, and educational websites. They've got awesome lessons and practice exercises to boost your algebra game.

Review and reflect: Look back at what you've learned regularly to reinforce your knowledge. Take a moment to think about your mistakes and learn from them. You've got this!

Remember, learning algebra is a journey. Be patient, keep practicing, ask for help when you need it and try to stay positive. With time, effort, and a bit of algebraic magic, you'll conquer GCSE algebra.

GCSE algebra worksheet

This worksheet provides students with the opportunity to hone their grasp of algebra, particularly focusing on simultaneous equations, solving inequalities and word problems. Key learning objectives in Key Stage 3, which is further developed in Key Stage 4.

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Beyond GCSE Revision

Gcse-grade revision from beyond, powered by twinkl, gcse maths problem solving questions with algebra.

Problem solving is a major part of the new GCSE format. The most important point is that, if you see a question that is unlike anything you have seen before, don’t panic or assume that you don’t know how to answer it! You may well know all of the maths content needed to solve the problem but the challenge is working out what you have to use. Join Beyond’s Maths Team as we explore GCSE Maths problem solving questions using Algebra…

First thing’s first: don’t panic!

• Think about what the question has presented to you and if this links in with any of the topics you’ve covered. You may wish to underline the important information in the question, so that you can focus on that and not the irrelevant things.
• Sometimes, a question will give you lots of information in a very roundabout way. Can you think of a better way to present the information, to make it easier to process? Perhaps you could use a two-way table or a Venn diagram.

Sample GCSE Maths problem solving questions

At a party, guests are offered chicken, lasagne or quiche to eat. 7 of the adults choose quiche. There are 100 guests altogether. 16 of the 48 people who choose chicken are children. 28 people eat lasagne and a quarter of these are children. How many children are at the party?

A two-way table really helps with this:

• Using algebra is often a good way to solve problems. If the information in the question suggests a sum, where you have the answer, but not the numbers that go into the sum, using algebra would be a sensible approach.

For example, ‘Aeron is 3 years older than Lily. Heather is 3 times as old as Aeron. The sum of their ages is 67. How old is Lily?’

The calculation that this suggests is: Aeron’s age + Lily’s age + Heather’s age = 67 We don’t know any of the ages but we do know the result of adding them together. Let’s say that Aeron is a years old. In that case, Lily is a – 3 years old and Heather is 3 a years old.

Therefore, the sum of their ages is a + ( a – 3) + 3 a = 67.

Now we can find a by solving the equation and find the ages of the people.

• Coming up with an algebraic expression can be tricky. Say you buy c cartons of juice at x pence each and a hat for £ y ; how much change would you get from £ m ? If you can’t see the answer, make the letters be numbers for a moment and then come up with the sum. Let’s make c be 5, x be 30, y be 2 and m be 20. The cost of the juices would be 5 x 30 pence; with the hat that would be a total cost of (200 + 5 x 30) pence. The change, in pence, from £20 would be 2000 – (200 + 5 x 30). Putting letters back in gives 100 m – (100 y + cx ).
• When a question asks you to ‘show’ something, don’t focus on the final answer; focus on the information that has been given to you, up to that point. Try to build an equation from that information, then try to simplify to give the result.

The perimeter of the shape is 24cm, y = 3 x and z = 2 x , show that x = 2

Perimeter = horizontal sides + vertical sides

( x + y + x + y )+ ( z + z ) = 24

Substituting in y and z in terms of x gives:

x + 3 x + x + 3 x +   2 x + 2 x = 24

• Be comfortable about using methods in reverse. For example, you can use a Venn diagram and prime factors to find the HCF and LCM of two numbers. If you know the HCF and LCM, starting with the Venn Diagram, you can work backwards to find the numbers.

Beyond resources for Maths problem solving questions

GCSE Probability and Statistics Problem Solving Worksheets

GCSE Algebra Problem Solving Worksheets

Long Multiplication Word Problems Differentiated Worksheets

Edexcel Foundation Specimen Papers

You can find our other Maths blogs here – you might find our Maths Mastery Blogs particularly useful! While we’ve got you, don’t forget to  subscribe to Beyond  for access to thousands of secondary teaching resources. You can  sign up for a free account here  and take a look around  at our free resources  before you subscribe too. Happy revising from the Beyond Maths Team.

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GCSE Algebraic Equations Questions and Answers

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GCSE Topics

• Algebraic Expressions (190)
• Factorizing Expressions (14)
• Parallel and Perpendicular Lines (36)
• Function Machine (20)
• Algebraic Formulae (20)
• Simplifying Expressions (128)
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• Factorizing Quadratics (11)
• Formulae (3)
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• Linear Equations (190)
• Gradient of a line (67)
• Transforming Graphs (8)
• Simultaneous Equations (42)
• Equations of Straight Lines (91)
• Areas under curves (17)
• Geometric Sequences (11)
• Quadratics and Fractions (1)
• Quadratic Equations (104)
• Straight Line Graphs (74)
• Algebraic Proof (39)
• Algebraic Equations (308)
• Writing Formulae (1)
• Quadratic Formula (22)
• Real-life Graphs (14)
• Function Notation (26)
• Completing the Square (11)
• Trigonometric Graphs (18)
• Inverse Functions (14)
• Factorising Expressions (30)
• Substitution (59)
• Graphs of inequalities (12)
• Equation of a Circle (22)
• Composite Functions (14)
• Factorising Quadratics (27)
• Speed Distance Time (74)
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• Iterative Methods (16)
• Time Tables (4)
• Expanding Brackets (61)
• Expanding Double Brackets (4)
• Rearranging Formulae (40)
• Ratio & Proportion (248)
• Compound Measures (26)
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The main topics in GCSE Maths are:

• Ratio, Proportion and Rates of Change 
• Geometry and Measures
• Statistics 
• Probability 
• Statistical Measures 
• Data Visualisation 

With regular practice of GCSE Maths topic-wise questions and GCSE Maths past pacers , you can easily score high marks.

Although many people think of GCSE maths as a difficult subject, with the correct training and preparation,you can master it in time. You can practice GCSE Maths  topic-wise questions daily to improve speed, accuracy, and time and to score high marks in the GCSE Maths exam.

A grade of 4 or 5 would be considered "good" because the government has established a 4 as the passing grade; a grade of 5 is seen as a strong pass. Therefore, anything that exceeds this level would be considered good. You can practice GCSE Maths topic-wise questions to score good grades in the GCSE Maths exam.

You can get a high score in GCSE Maths through meticulous practice of GCSE Maths topic-wise questions and GCSE Maths past papers .

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Welcome to the Problem Solving Papers Page

One major difference that I have noticed when comparing the new specification to the old one, is that the amount of problem solving questions has increased dramatically.

It is because of this, that I have decided to create BennettMaths Problem Solving Papers.

The aim is to get students confident enough to attempt these problems through either systematic approaches or even for the lower ability, use a trial and improvement method.

BennettMaths Problem Solving Paper 1          Written Solutions BennettMaths Problem Solving Paper 2          Written Solutions

BennettMaths Problem Solving Paper 3          Written Solutions

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15 Algebra Questions And Practice Problems Worksheet

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

• The Algebra worksheet contains 15 multiple choice questions, with a mix of worded problems and deeper problem solving questions.
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GCSE Problem Solving Questions of the Day - Compilation

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

10 March 2023

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O Level Biology MCQ (PDF) Questions Answers Bank | IGCSE GCSE Biology MCQs e-Book Download

Quiz questions chapter 1-20 & practice tests with answers key | o level biology textbook notes, mcqs & study guide, publisher description.

The e-Book O Level Biology Multiple Choice Questions (MCQ Quiz) with Answers PDF Download (IGCSE GCSE PDF Book): MCQ Questions Chapter 1-20 & Practice Tests with Answers Key (Class 9-10 Biology Questions Bank, MCQs & Notes) includes revision guide for problem solving with hundreds of solved MCQs. O Level Biology MCQ with Answers PDF book covers basic concepts, analytical and practical assessment tests. "O Level Biology MCQ" PDF book helps to practice test questions from exam prep notes. The eBook O Level Biology MCQs with Answers PDF includes revision guide with verbal, quantitative, and analytical past papers, solved MCQs. O Level Biology Multiple Choice Questions and Answers (MCQs) PDF Download , a book covers solved quiz questions and answers on chapters: Biotechnology, co-ordination and response, animal receptor organs, hormones and endocrine glands, nervous system in mammals, drugs, ecology, effects of human activity on ecosystem, excretion, homeostasis, microorganisms and applications in biotechnology, nutrition in general, nutrition in mammals, nutrition in plants, reproduction in plants, respiration, sexual reproduction in animals, transport in mammals, transport of materials in flowering plants, enzymes and what is biology tests for school and college revision guide. O Level Biology Quiz Questions and Answers PDF download, free eBook’s sample covers beginner's solved questions, textbook's study notes to practice tests. The e-Book IGCSE GCSE Biology MCQs Chapter 1-20 PDF includes high school question papers to review practice tests for exams. O Level Biology Multiple Choice Questions (MCQ) with Answers PDF digital edition eBook, a study guide with textbook chapters' tests for IGCSE/NEET/MCAT/MDCAT/SAT/ACT competitive exam. GCSE Biology Practice Tests Chapter 1-20 PDF covers problem solving exam tests from biology textbook and practical eBook chapter-wise as: Chapter 1: Biotechnology MCQ Chapter 2: Animal Receptor Organs MCQ Chapter 3: Hormones and Endocrine Glands MCQ Chapter 4: Nervous System in Mammals MCQ Chapter 5: Drugs MCQ Chapter 6: Ecology MCQ Chapter 7: Effects of Human Activity on Ecosystem MCQ Chapter 8: Excretion MCQ Chapter 9: Homeostasis MCQ Chapter 10: Microorganisms and Applications in Biotechnology MCQ Chapter 11: Nutrition in General MCQ Chapter 12: Nutrition in Mammals MCQ Chapter 13: Nutrition in Plants MCQ Chapter 14: Reproduction in Plants MCQ Chapter 15: Respiration MCQ Chapter 16: Sexual Reproduction in Animals MCQ Chapter 17: Transport in Mammals MCQ Chapter 18: Transport of Materials in Flowering Plants MCQ Chapter 19: Enzymes MCQ Chapter 20: What is Biology MCQ The e-Book "Biotechnology MCQ" PDF, chapter 1 practice test to solve MCQ questions: Branches of biotechnology and introduction to biotechnology. 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