4 Components of Primary and Secondary Algebra and Related Questions

1. Substituting
2. Expanding
3. Factorising
4. Solving
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Algebra is often regarded by both students and teachers as a tough topic to learn or teach. I think the important thing (and from experience) is to know the general outline forehand  makes it easier. Regardless, of primary (Yr 5, 6, 8) or secondary (Yr 9, 10, 11, 12), the layout is similar. Here, you will see sample questions (and solutions) I used in tuition groups at both primary and secondary levels to introduce Algebra. Questions adapted from UK GCSE maths exam papers, 2010 - 2012.


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 multiply 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 that differences between 6 - 5 and 5 -6 or ask students to think about 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 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

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

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