Olympiad Test: Algebraic Expressions - Class 7 MCQ

The constant term in the expression 1 + x² + x is 1.

A constant has a fixed value, such as 4, 100, or -17. In algebraic expressions, we combine variables and constants using operations like addition, subtraction, multiplication, and division.

For example:

• The expression 4x + 5 is formed by multiplying the variable x by the constant 4 and then adding 5.
• The expression 10y - 20 is created by multiplying y by 10 and then subtracting 20.

We can also create expressions by combining variables with themselves or with other variables. For instance:

• x² is obtained by multiplying x by itself.
• 2y² is formed by multiplying y by itself and then multiplying by 2.
• 3x² - 5 involves first obtaining x², multiplying it by 3, and then subtracting 5.

In summary, the constant term in the expression is clearly defined as 1.

Coefficient refers to the numerical value associated with a variable in an expression. In the expression y - y³ + y², we can identify the coefficient of y³ as follows:

• The term involving y³ is -y³.
• The coefficient is the number in front of y³, which is -1.

Therefore, the coefficient of y³ in the expression is -1.

Subtraction of z from y is expressed algebraically as y−z. 

- To find the value of  x + 4 for x = 2, substitute 2 into the expression:
x + 4 = 2 + 4
- Calculate the result:
2 + 4 = 6 
- The correct answer is option A: 6.

- When terms have the same algebraic factor, they are called like terms.
- Like terms have identical variables raised to the same powers, but they may have different coefficients.
- For example, in the expression 3x² + 5x - 2x², the terms 3x² and -2x² are like terms.

- An expression containing two unlike terms is called a binomial.
- Binomial comes from the prefix "bi-" meaning two, and "nomial" meaning terms.
- A binomial is part of polynomial expressions, which can have multiple terms.
- Examples of a binomial include expressions like 3x + 2 or a - b.
- Monomial refers to a single term, and trinomial refers to three terms.
- Thus, the correct answer is A: binomial.

- A variable is a symbol that represents a quantity which can change or take different values.

- In both mathematics and programming, variables act as placeholders for data that can vary.

- Examples of variables include x and y in algebra, which can represent any number.

- Unlike constants, which have a fixed value (e.g., 4, 100, -17), variables are flexible and adaptable.

- We create algebraic expressions by combining variables with constants using operations such as addition, subtraction, multiplication, and division.

• For example, the expression 4x + 5 is formed by multiplying x by the constant 4 and then adding 5.
• Similarly, 10y - 20 is obtained by multiplying y by 10 and then subtracting 20.

- Expressions can also be formed by combining variables with themselves or with other variables.

• The expression x² is created by multiplying x by itself.
• Other examples include 2y², 3x² - 5, and xy.

- In summary, variables are essential in forming algebraic expressions, allowing for a wide range of mathematical operations and representations.

Solution:

To simplify the expression 3x - 5a - x² + 9b with the values:

• x = 3
• a = -1
• b = -2

We substitute the values into the expression:

3(3) - 5(-1) - (3)² + 9(-2)

• Calculate each term:
• 3(3) = 9
• -5(-1) = 5
• (3)² = 9
• 9(-2) = -18

Now, combine the results:

9 + 5 - 9 - 18

Calculating step-by-step:

• 9 + 5 = 14
• 14 - 9 = 5
• 5 - 18 = -13

The final value is -13.

Solution:

To simplify the expression 2b - 8x + 4x² + 4a, we substitute the values:

• Let x = 3, a = -1, and b = -2.

Now, substituting these values into the expression:

• 2b 2(-2) = -4
• -8x: -8(3) = -24
• 4x²: 4(3²) = 4(9) = 36
• 4a: 4(-1) = -4