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Introduction

Definition of Evaluation in Mathematics

In mathematics, evaluation refers to the process of finding the numerical value of an expression or equation. This involves substituting the given values of variables into the expression or equation and simplifying it to obtain the final answer. For example, if we have an expression 2x + 3y and we are given the values of x and y, say x=4 and y=5, we can evaluate the expression by substituting these values into the expression as follows:

2(4) + 3(5) = 8 + 15 = 23

Hence, the value of the expression 2x + 3y when x=4 and y=5 is 23.

Body Paragraphs with Examples

To better understand evaluation in mathematics, let’s consider the following examples:

Example 1:

Evaluate the expression 3x + 2y when x=2 and y=3.

Solution:

Substitute the given values of x and y into the expression as follows:

3(2) + 2(3) = 6 + 6 = 12

Hence, the value of the expression 3x + 2y when x=2 and y=3 is 12.

Example 2:

Evaluate the expression 4x – 5y when x=-3 and y=2.

Solution:

Substitute the given values of x and y into the expression as follows:

4(-3) – 5(2) = -12 – 10 = -22

Hence, the value of the expression 4x – 5y when x=-3 and y=2 is -22.

Example 3:

Evaluate the expression 2(x + y) – 3(2x – y) when x=1 and y=2.

Solution:

Substitute the given values of x and y into the expression as follows:

2(1 + 2) – 3(2(1) – 2) = 2(3) – 3(0) = 6

Hence, the value of the expression 2(x + y) – 3(2x – y) when x=1 and y=2 is 6.

Example 4:

Evaluate the expression 5a² – 2b³ when a=2 and b=-3.

Solution:

Substitute the given values of a and b into the expression as follows:

5(2)² – 2(-3)³ = 5(4) – 2(-27) = 20 + 54 = 74

Hence, the value of the expression 5a² – 2b³ when a=2 and b=-3 is 74.

Example 5:

Evaluate the expression 6x – 3y + 2z when x=2, y=-1, and z=4.

Solution:

Substitute the given values of x, y, and z into the expression as follows:

6(2) – 3(-1) + 2(4) = 12 + 3 + 8 = 23

Hence, the value of the expression 6x – 3y + 2z when x=2, y=-1, and z=4

Example 6:

Evaluate the expression (a + b)² – (a – b)² when a=3 and b=2.

Solution:

Substitute the given values of a and b into the expression as follows:

(3 + 2)² – (3 – 2)² = 5² – 1² = 24

Hence, the value of the expression (a + b)² – (a – b)² when a=3 and b=2 is 24.

Example 7:

Evaluate the expression 2x³ – 5x² + 4x – 3 when x=1.

Solution:

Substitute the given value of x into the expression as follows:

2(1)³ – 5(1)² + 4(1) – 3 = 2 – 5 + 4 – 3 = -2

Hence, the value of the expression 2x³ – 5x² + 4x – 3 when x=1 is -2.

Example 8:

Evaluate the expression (x² + y²) / (x + y) when x=3 and y=2.

Solution:

Substitute the given values of x and y into the expression as follows:

(3² + 2²) / (3 + 2) = 13 / 5

Hence, the value of the expression (x² + y²) / (x + y) when x=3 and y=2 is 13/5.

Example 9:

Evaluate the expression ?(a² + b²) when a=3 and b=4.

Solution:

Substitute the given values of a and b into the expression as follows:

?(3² + 4²) = ?(9 + 16) = ?25 = 5

Hence, the value of the expression ?(a² + b²) when a=3 and b=4 is 5.

Example 10:

Evaluate the expression log?27.

Solution:

The expression log?27 can be evaluated by asking the question, “What power must 3 be raised to get 27?” The answer is 3, since 3³=27. Therefore, log?27=3.

FAQ Section

Q: What is the difference between simplification and evaluation in mathematics? A: Simplification refers to the process of reducing an expression to its simplest form, while evaluation refers to finding the numerical value of an expression.

Q: What is the importance of evaluation in mathematics? A: Evaluation is important in mathematics as it helps students understand mathematical concepts better, solve complex problems, and verify the correctness of their answers.

Q: Can an expression be evaluated without substituting values for variables? A: Yes, some expressions can be evaluated using algebraic manipulations without substituting values for variables. For example, 2x + 3x can be evaluated as 5x.

Q: Can an equation be evaluated? A: No, an equation cannot be evaluated as it is a statement of equality between two expressions. However, an equation can be solved to find the value of the variable that makes the equation true.

Quiz

1. Evaluate the expression 4x + 2y when x=5 and y=3.
2. Evaluate the expression 3a – 2b + 5c when a=2, b=1, and c=4.
3. Evaluate the expression 2(x² – y) + 3(x – y²) when x=3 and y=2.
4. Evaluate the expression ?(16 + 25).
5. Evaluate the expression 3cos(?/3) – 2sin(?/6).
6. Evaluate the expression (2a – 3b)² – (a + b)² when a=4 and b=2.
7. Evaluate the expression (x – y) / (x + y) when x=7 and y=2.
8. Evaluate the expression log?16.
9. Evaluate the expression 2x² – 5x + 1 when x=0.
10. Evaluate the expression ?(2² + 3²).

Answers:

1. 28
2. 17
3. 9
4. 5
5. 0
6. 9
7. 5/9
8. 2
9. 1
10. ?13

Conclusion