Using Quadratic Formula To Solve Quadratic Equations - Part (III)

*The Quadratic Formula can be used to solve any Quadratic equation. But, students must know how to use it; they must know values of a, b, & c; know their directed numbers; and know how to simplify surds.

Solving Complex Quadratic Equation by Factoring - Part (II)

Take a look at another complex equation where factoring does not work. That's where you MUST use the Quadratic Formula

Factorising and Solving Quadratic Equations - GCSE Basic Algebra Questions

Students often find certain topics like Algebra challenging. I’d like to identify the difference between simple and complex quadratic equations and solve them as examples. The questions are real GCSE (UK/Edexcel) exam questions. 

To solve a quadratic equation (equation of the highest power of 2), one MUST first know how to factorise the equation.

Factorising and solving simple quadratic expressions

Factorising and solving simple quadratic expressions (and equations) like x² – 4 (difference of 2 squares) and x² + 4x + 4 can be easy. 

But such this work, introduced in Grade 9 or 10, often paves way for harder questions in later years. 

See the illustrations below on how to solve quadratic equations. You can relate these examples to the questions your teachers set for you.

Solving Simple Quadratic Equations

Factoring Method or Quadratic Formula (Part I)

The factoring method is introduced early in Year 7 and covered extensively in the later years at secondary schools.

More on Solving Complex Quadratic Equations

Find out either to Factorise and solve or use the Quadratic formula in Part (II)

Download GCSE Maths past papers

You can download the past GCSE exam papers online. Here are some websites that many students prefer to use.

• Maths Genie
• Maths Watch
• Dr Frost maths
• Cobette Maths
• GCSE maths in four weeks

Stationery items you will need for exams are available at Ryman: GCSE maths stationery items

How to Solve Problems involving Fractional Powers

Fractional powers appear past GCSE maths papers. To get the questions right, you must know how to use the Index Law, Surds and rules for solving the algebraic problems. 

This may sound overwhelming, but it is not that hard. See the illustrations (x3 questions) below.

How to Solve Fractional Powers Using Index Laws & Surds

If you need more illustrations like these, check out the free maths resources here.

Let’s have a look at 3 Higher Maths Exam Questions

Top tip:

All you need to do is to pull apart the powers and simplify them.

Check out the past maths questions & study guides here.

Download GCSE Maths past papers

You can download the past GCSE exam papers online. Here are some websites that many students prefer to use.

• Maths Genie
• Maths Watch
• Dr Frost maths
• Cobette Maths
• GCSE maths in four weeks

Stationery items you will need for exams are available here: GCSE maths stationery items

Show your working out clearly and logically. Where there are 3 or more marks, do not only write the answer.

Algebra II - Higher Order Questions Sorted by Topic

If this PDF file does not open, click on 'Open in new window' arrow. (Here ▼)

GCSE Maths 2022 Edexcel Foundation Paper 1 Set Non-calculator

The GCSE maths contents are organised into topics. Teachers set our the termly programs and teach them by topics too. 

So, you should also use the maths questions by topics when revising for the maths exams. Here are some ways to organise your revision notes by topics. More details here, but here is a brief outline.

Here are some GCSE maths tips for acing your exams.

How to organise your GCSE maths revision notes by topics?

The GCSE maths school syllabus has all the outlines that schools/teachers follow when teaching the content. 

All the content should be covered before the exams, but the maths syllabus has lots of things in it. You can be lost in it.

Some suggestions to organise study notes:

Year 7 - 10 Maths Exercise Books

Your exercise books are the best places to find the topics you learn in class. Teachers teach the topics in sequences, so your books will already have the topics in order.

Maths Past Test Papers

The end-of-the-term test papers are fantastic materials to use when looking for maths questions. They are summaries of what you've learnt, condensed.

Maths teachers help

Your maths teacher is the best person to get advice from. S/he knows you well enough to suggest areas you need to improve on. Alternatively, look back at your school report. 

Study group

Take time to have conversations about maths problems and topics that you think you need help with. Talk with friends and family about things that you are struggling with.

Private GCSE maths tuition near you

If you need extra help, get an online/local maths tutor to help you with maths problems.

Download GCSE Maths Questions

There are four GCSE exam boards where you can get the maths past paper Pdf for free AQA, Edexcel, SQA and OCR.

The exam boards also provide the marking schemes, examiner reports, and practice materials.

Check out the resources here for more information on GCSE maths exams, study guides and past papers.

Exam Questions: Solving Quadratics Equations

If this PDF file does not open, click on 'Open in new window' arrow. (Here ▼)

Introduction to Algebra

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GCSE Basic Algebra Questions and Study Guides 2022 Exams

There are four basic parts in GCSE algebra that you should know when revising for the maths papers. They are:

• 1. Substituting
• 2. Expanding
• 3. Factorising
• 4. Solving

GCSE Algebra Questions

Algebra is often regarded by both students and teachers as a tough topic to learn or teach. 

Yet, you will do well if master the four skills. The skills are the same in primary (Years 5, 6, 8) and secondary (Years9, 10, 11, 12).

Basic Algebra Questions

Below you'll find some basic algebra questions (and solutions) addressing the four skills. The questions were adapted from the UK GCSE maths exam papers.

SEE MORE ON GRADE 10 EXAM QUESTIONS HERE

1. Substitution

a. Write down the value of abc when a = 10, b = 2 and c = 0

The answer is 0 (but, many students will write 20) ……………..1 mark

Maths knowledge: any number multiplied by 0 is 0

b. Work out the value of 1/2x - 3y when x= 10 and y= 2

 5 - 6 = - 1 (many students write 1 instead)

Concept tested: Addition and subtraction of -ve and +ve numbers. (Reinforce the differences between 6 - 5 and 5 -6 or ask students to think about the number line, starting at 5 and moving left 6 places)

2 marks

c. Find the value of 3x + 2y when x = 4 and y = 5

 12 - 10 = 2

2 marks

2. Expanding Brackets (note that expanding and factorising are opposites)

 Expand the following expressions

a. 3(2y – 5) =    ……………..1 mark

 6y - 15 ( many student forget to do 3 x - 15)

b. 4(2m + 3n) =    ……………..1 mark

8m + 12n

c. x(x – 10) =    ……………..1 mark

 x^2 - 10x

3. Factorising

Factorise the following expressions  (note that expanding and factorising are opposites)

a. 2a + 10 =                                                   ……………..1 mark

Highest Common Factor (HCF) of 2a and 10 is 2

2(a + 10)

b. 4 + 6x =                                                      ……………..1 mark

HCF = 2

2(2 + 3x)

c. 3x – 9=                                                        ……………..1 mark

3 (x - 3)

d. 2x^2  + 4x

 HCF = 2x

2x (x + 2)

2 marks

4. Solving equation

Solve the following equations to find the value of x

a. 4x = 20                                                       ……………..1 mark

x = 5

b. 3x - 7 = 8                                                   ……………..1 mark

 3x = 8 + 7 ( it is important to get the order 8 + 7 right and not 7 + 8: even the answer is same, the answer may not be the same when - ing, see the example below)

3x = 15

  x = 5

c. 8(x + 12) = 100

 8x + 96 = 100 ..................Expand the brackets

8x = 100 - 96................... (subtract 96 on both sides (remember balancing equations?)

x = 4/8 (Why divide by 8? In order to find the value of x, you must divide LHS and RHS by 8)

x = 1/2 (or 0.5)

2 marks

Check out past algebra questions and maths resources here.

GCSE Foundation Maths Algebra Questions

Solve the following to find the value of y

a. y/3 = 9                         ……………..1 mark

   y = 27 .............multiply 3 x 9 ( now, this is important as you can use this to solve complex equations that have a divisor)

b.  2y/5 = 4                               ……………..1 mark

2y = 20.......... ( 20 = 5 x 4)
y = 10

c.  2y + 3 / 2 = 5

 2y + 3 = 10.......... ( 10 = 2 x 5)

2y = 10 - 3 ...........( subtracting 3 on both sides of the equation)

2y = 7

y = 7/2

y = 3.5

2 marks

Where to get GCSE Maths Questions?

There are four GCSE exam boards where you can get the maths past paper Pdf for free AQA, Edexcel, SQA and OCR.

The exam boards also provide the marking schemes, examiner reports, and practice materials.

Check out the resources here for more information on GCSE maths exams, study guides and past papers.