Algebra

Algebra

By Ala Tamimi

Algebra uses letters to represent unknown values.

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Usually we use x, y to represent the variables, or any other letters.

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When we multiply the variable by a number we don't use the multiplication sign to write it, for example:

2 × y = 2y

3 × z = 3z​

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The same when we multiply two different variables:

y × z = yz​

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TERM

A number or letter on its own, or numbers and letters multiplied together.

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An expression is a string of terms combined using the operations +, – .​

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An expression is a string of terms combined using the operations +, – .​

Algebraic terms that have the same letters are called like terms.

Multiple Choice

Which of these terms are like terms?

• 2y, 2x

• 3z, -7z

• 4x, 2xy

• 3xy, 3y

Only like terms can be added or subtracted.

When like terms are added and subtracted, it is called simplifying.

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Multiple Choice

Simplify 5y + 6y

• 5y + 6y = 11y²

• 5y + 6y = 56y²

• 5y + 6y = 11y

Write variable expressions for the following operations:

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u multiplied by 8

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t divides by 9

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r multiplied by the sum of y and x​

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Multiple Choice

James' Family wants to visit the museum, Suppose that x is the cost of a child admission & y is the cost of an adult admission.

Their family consists of two adults and three children.

The term that represent the cost of their children tickets is:

• x

• y

• 2y

• 3x

Multiple Choice

(x is the cost of a child admission & y is the cost of an adult admission)

The term that represent the cost of the parents' tickets is:

• x

• y

• 2y

• 3x

Multiple Choice

(x is the cost of a child admission & y is the cost of an adult admission)

The expression that represents the total cost of the family's tickets is:

• x + y

• 5xy

• 2y + 3x

• 3y + 2x

Multiple Choice

(x is the cost of a child admission & y is the cost of an adult admission)

If the ticket of a child costs £2, How much will they pay for their children

• £4

• £6

Simplify :

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3x + 7y + 10x - 2y =​

Multiple Choice

Simplify

2x + 6y - x + 4y =

• 8xy + 3xy

• x + 10y

• 3x + 10y

• x + 10y

Multiple Choice

Simplify

3xy - y + 2xy =

• 5xy - y

• 4xy

• xy - y

Multiple Choice

If x = -3, what's the value of the term 2x ?

• 6

• 5

• -1

• -6

Multiple Choice

If y = 1, and x = 2, calculate:

3y + 5x

• 13

• 11

• 8

Multiple Choice

2x and 5x² are like terms.

• TRUE

• FALSE

Multiple Choice

x + x² = 3x²

• TRUE

• FALSE

Multiply Terms:

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Multiple Choice

y × y =

• 2y

• y²

• 2y²

• y

Multiple Choice

2z × 5y =

• 7zy

• 10zy

• 10z

• 10y

Multiple Choice

2xy × -12y² =

• -24xy³

• -10xy

• -10xy²

• -24xy

Multiple Choice

y² × y³ =

• 5y

• y⁶

• y⁵

• 6y

Expanding brackets:

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​Brackets are used in algebra to show a repeated calculation, without having to write the same calculation out several times.

Expanding brackets:

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Multiple Choice

Multiplying brackets (Expanding)

2(x + 1) =

• 2x + 1

• 2x + x

• 2 + x

• 3x

Multiple Choice

Expand

x ( y + 2 ) =

• 2xy

• xy + 2

• y + 2x

• xy + 2x

Multiple Choice

Expand

xy ( y + x - 2)

• xy²+x²y-2xy

• x²y² - 2xy