Introduction to Algebra

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

Addition Methods | Adding by Parts

Adding two or more numbers can be fun and easy when done in parts - by parts I mean unit, ten, hundred,....

For example

Work out the value of 5 + 15 + 34 + 58 + 72

add the tens:                      10 + 30 + 50 + 70 = 160  (you see, 70 + 30 give 100, 10 + 50 give 60 )
add the units:               5 +  5  +   4 +   8 +  2 =   24    (5 + 5 = 10, 8 + 2 = 10: that's 20, plus 4 give 24)

Now add 160 and 24

160 + 24 = 184

-----------------------------

Maths is Fun ^o^

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