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.

Division Methods | Long Division and Division by Chunking

These two methods can be very useful. I recommend introducing them together - give the students options to work with.
-------------------------

Method 1 - Long Division

Solve 351divided by 9

 Steps

1. 9 goes into 35, 3 times

2. 9 x 3 - 27

3. 35 - 27 = 8 ......bring the unit, 1, down. That makes 81

4. 9 goes into 81, 9 times.

5. Now, 81 - 81 = 0....no remainder, the answer is 39

 

Note: If there is remainder, your answer will be a mixed number (or a decimal number)

 

Method 2 - Division by Chunking - This is about calculating in parts

Solve 351divided by 9

351
  81        (9 x 9) .....you know that from x9 table
----
270        (9 x 30)

ANSWER 39 ......add 30 and 9 to give you the answer (easy aye :))


YOUTUBE Links
Long Division
Division by Chunking

Multiplication Methods | Long Multiplication, Chunking and Grid

Multiply big numbers by breaking them into parts is the easiest way, especially when working with non calculator papers.

Here, are illustrations on how to make calculations by using Long Multiplication, Multiplication by Chunking and Multiplication by Grid

Work out the value of 135 x 27

Method 1 - Long Multiplication by Chunking

             135
             x22
             -----
             270 .........multiply 2 x 135
         +2700..........put a 0 under 0, then multiply 2 x 135 and add the results
           ------
           2907
         ---------

Method 2 - Multiplication by Chunking

In 135, we have 100 + 30 + 5. Multiply each part by 22

           100 x 22 = 2200
             30 x 22 =   660...easy mental calculation, if 3 x 22 = 66, 30 x 22= 660  
               5 x 22      110
                              ------
                              2970     .......add 2200, 660 and 110 together       ...Happy now? :)
                            ---------

Method 3 - Multiplication by Grid

100   30   5
    0   20   2
---------------
      0      0      0               ....x 0
2000  600  100            ......x20
  200    60    10            ........x2
------------------
2200   660   110          .....add the number down
-------------------
    2970                           .....................Take the grand total (add across)       ......Get it? :( haha!
...............

Teachers' Note - it is important to use simple methods without diverting from traditional ones. However, introducing an optional method can help others students with difficulty in application of the other.

Students' Note - It is better to know two other methods that one.

How to Memorise Multiples of 9

This is the best and easiest technique I learnt in my first year of teaching. Could have been really helpful if I had known in back in Grade 2...

The idea is discovering the pattern in multiples of 9.


Source: PNG Teachers on Facebook

1 x 9 = 09
2 x 9 = 18
3 x 9 = 27
4 x 9 = 36
5 x 9 = 45
6 x 9 = 54

Do you see the pattern developing?
The tens increase from 0, 10, 20, 30, 40, 50....
Units decrease from 9, 8, 7, 6, 5, 4, ....

Now, you can smile :) and complete the rest...

7 x 9 =
8 x 9 =
9 x 9 =
10 x 9 =
11 x 9 =
12 x 9 =
13 x 9 =

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Hope this helps :)