What you need to know

Things to remember:

  • Substitute (replace) the letter values with the number they are equal to.
  • We use BIDMAS to evaluate the expression

Before we start, we just need to recall three bits of terminology:

  • Evaluate means to find the value of, or to calculate, something.
  • Non-linear means that there are powers and square roots.
  • Expressions are mathematical phrases that include variables, numbers, and operators.

 

So, this topic is to do with finding the value of expressions that have powers and square roots. We will start with a linear first expression though.

Evaluate 5x+2 when x=3?

This question is telling us that we need to find the value of 5x+2 when x=3, so the first step in our 2 step program is to substitute this value in.

Step 1: Substitute the variable values into the expression.

5x+2=5\times3+2\text{ when } x=3

Step 2: Evaluate the expression using BIDMAS.

Brackets

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Indices (Powers)

None

 

Divisions

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Multiplications

5\times3+2=15+2

Additions and Subtractions

15+2=17

5x+2=17\text{ when } x=3

We follow these exact same steps when we have a non-linear expression.

Evaluate 3x^2-\sqrt{x}\div2 when x=4?

Step 1: Substitute the variable value into the expression.

3x^2-\sqrt{x}\div2=3\times4^2-\sqrt{4}\div2\text{ when } x=4

Step 2: Evaluate the expression using BIDMAS.

Brackets

None

 

Indices (Powers)

3\times4^2-\sqrt{4}\div2=3\times16-2\div2

Note: Square rooting is actually a power of \dfrac{1}{2}, so we do them at the same time as whole number powers.

 

Divisions

3\times16-2\div2=3\times16-1

 

Multiplications

3\times16-1 =48-1

Additions and Subtractions

48-1=47

3x^2-\sqrt{x}\div2=47 \text{ when } x=16

Example Questions

Question 1: Evaluate x^3-x^2 when x=5?

Answer

Step 1: Substitute the variable values into the expression.

 

x^3-x^2=5^3-5^2 \text{ when } x=5

 

Step 2: Evaluate the expression using BIDMAS.

 

Brackets

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Indices (Powers)

 

5^3-5^2 = 125-25

 

 

Divisions

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Multiplications

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Additions and Subtractions

 

125-25 = 100 \text{ when } x=5

 

x^3-x^2  = 100 \text{ when } x=5

Question 2: Evaluate 3x- \sqrt{x}\times4 when x=49?

Answer

Step 1: Substitute the variable values into the expression.

 

3x- \sqrt{x}\times4 =3\times49- \sqrt{49}\times4 \text{ when } x=49

 

Step 2: Evaluate the expression using BIDMAS.

 

Brackets

None

 

Indices (Powers)

 

3\times49- \sqrt{49}\times4 =3\times49-7\times4

 

 

Divisions

None

Multiplications

3\times49-7\times4=147-28

 

Additions and Subtractions

 

147-28=119

 

3x- \sqrt{x}\times4 = 119 \text{ when } x=49