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Mathematics

Grade 8

The number system

(natural and whole numbers)

Module 3

Algebra

ALGEBRA

CLASS ASSIGNMENT 1

  • Discover ALGEBRA step by step...
  • In Algebra, we make use of letters in the place of unknowns (numbers that we do not know).
  • Letters represent variables (values that may vary) and numbers are the constants (the values remain the same).

Look at the polynomial, for example

From the above, you will be able to recognise the following:

  • The number of terms (terms are separated by + and - signs): 3 terms
  • Coefficient of x size 12{x} {} ² (the number immediately before x size 12{x} {} ²): 3
  • Coefficient of x size 12{x} {} (the number immediately before x size 12{x} {} ): - 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {}
  • Constant: 5
  • The degree of expression (highest power of x size 12{x} {} ): 2
  • The expression is arranged in descending powers of x size 12{x} {} .
  • 3 x size 12{x} {} ² means 3 x x size 12{x} {} ² (3 multiplied by x size 12{x} {} ²)
  • x size 12{x} {} ² means ( x size 12{x} {} ) x ( x size 12{x} {} ) ( x size 12{x} {} multiplied by x size 12{x} {} )
  • What happens to ( + )and ( - ) signs during multiplication and division?

Here you have it:

  • ( + ) x of ÷ ( + ) = ( + )
  • ( - ) x of ÷ ( - ) = ( + )
  • ( + ) x of ÷ ( - ) = ( - )

1. Study the following in your groups and supply the answers:

( 1 4 x 2 x ) 4 + 6 size 12{ { { \( { { size 8{1} } over { size 8{4} } } x rSup { size 8{2} } ` - `x \) } over {4} } `+`6} {}

  • Indicate the following:

1.1 number of terms

1.2 coefficient of x size 12{x} {}

1.3 constant

1.4 degree of the expression

2. Now we can use variables to define the following with the magical language of mathematics --- i.e. algebraic expressions.

See if you can define these in the form of algebraic expressions:

Given Algebraic Expression

2.1 The sum of a number and 9

2.2 A number multiplied by 7

2.3 The difference between a and b

2.4 6 less than a number reduced by 7

2.5 The product of a number and b

2.6 Quotient of a number and 7

2.7 Square of a

2.8 Square root of a

2.9 Subtract the difference between a and b from their product

3. The following are referred to as flow diagrams – They consist ofa) inputb) formula in which the input number is substitutedc) output

Complete (a), (b) and (c)

4. See if you can determine a formula for the following and complete the table.

x size 12{x} {} 2 5 8 10 15 47
y 7 11 17

formula: y =

HOMEWORK ASSIGNMENT 1

1. Determine a formula for each of the following and complete the table.

1.1 formula: y = ……………………………………………………

x size 12{x} {} 2 5 8 9 12 20
y 10 16 22

1.2 formula: y = ……………………………………………………

x size 12{x} {} 3 7 10 9 12 20
y 12 32 47

1.3 formula: y = ……………………………………………………

x size 12{x} {} 1 3 4 9 12 20
y 1 9 16

1.4 formula: y = ……………………………………………………

x size 12{x} {} 1 2 3 6 7 10
y 1 8 27

1.5 formula: y = ……………………………………………………

x size 12{x} {} 1 2 4 9 12 20
y 2 5 17

2. The sketch shows matches arranged to form squares and combinations of squares.

2.1 Make a sketch to show four squares and indicate how many matches were used.

Matches? …………………………

2.2 Can you determine a formula that will provide a quick way for determining how many matches you will need to form ( x size 12{x} {} ) number of squares?

y = ………………………………… (with y representing the number of matches)

2.3 Now make use of your formula to determine how many matches you will need to form 110 squares.

2.4 Determine how many squares you will be able to form with 2 005 matches.

3. Examine the following expression and answer the questions that follow:

1 4 a + a 2 5 + 7 + 3a 3 size 12{ - { {1} over {4} } a``+`` { {a rSup { size 8{2} } } over {5`} } ``+`7`+3a rSup { size 8{3} } } {}

3.1 Arrange the expression in ascending powers of a.

3.2 Determine:

3.2.1 number of terms

3.2.2 coefficient of a ²

3.2.3 degree of the expression

3.2.4 constant term

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Source:  OpenStax, Mathematics grade 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11034/1.1
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