Important Questions Test: Algebra - Class 6 MCQ

• Pattern of "V": The pattern of "V" requires two lines coming together at an angle to form a V shape.


• Number of matchsticks: To create a V shape, we need 2 matchsticks for the two lines and 1 matchstick for the point where they meet.


• Total matchsticks: Therefore, the total number of matchsticks required to make a pattern of "V" is 2 + 1 = 3.

• Step 1: To create a pattern of "Z", you need to draw two diagonal lines meeting at a right angle.


• Step 2: Each diagonal line requires 2 matchsticks.


• Step 3: The right angle where the two lines meet will require an additional matchstick.


• Step 4: Therefore, the total number of matchsticks required to make a pattern of "Z" is 2 + 2 + 1 = 5.

So, the correct answer is 5 matchsticks.

Number of matchsticks required to make a pattern of “A” is 5.

(3a + 2b - 4c)(4z) + (3a + 2b - 4c)
(3a + 2b - 4c)(4z + 1)

• Definition: An equilateral triangle is a triangle in which all three sides are equal in length.


• Given: Each side of the equilateral triangle is 'x' units.


• Perimeter Formula: The perimeter of any polygon is the sum of the lengths of its sides. For an equilateral triangle, the perimeter is the sum of all three sides.

• Since the given triangle is equilateral, all three sides are of equal length, which is 'x' units.


• Therefore, the perimeter P of the equilateral triangle is P = x + x + x = 3x units.


• Hence, the correct answer is 3x.

• Equation A: This is an equation with a variable (x). It can be solved for x.


• Equation B, C, and D are not equations as they do not have an equals sign and a variable that can be solved for.

The value of the variable in an equation which satisfies the equation is called a Solution to the Equation. So for example we take the equation 2n=10, If n = 1, the number of matchsticks is 2. Clearly, the condition is not satisfied, because 2 is not 10.

• LHS: The Left Hand Side (LHS) of an equation consists of the terms on the left side of the equals sign.


• RHS: The Right Hand Side (RHS) of an equation consists of the terms on the right side of the equals sign.


• Equal: The equation states that the LHS is equal to the RHS.


• Definite value: For a particular value of the variable in the equation, the LHS is equal to the RHS.


• Conclusion: The LHS of an equation is equal to its RHS only for a definite value of the variable in the equation.

• Substitute the given values into the equation:


• x + 4 = 2


• x + 4 - 4 = 2 - 4


• x = -2


• Therefore, the solution to the equation is x = -2

• Variables: Variables are letters used to represent unknown values in mathematical expressions.


• Expression: An expression is a combination of variables, constants, and operators that represents a value.


• 2x: In the expression 2x, 'x' is a variable representing an unknown value.


• 3y: In the expression 3y, 'y' is a variable representing another unknown value.


• 5: The number 5 in the expression is a constant, not a variable.

• 2: There are 2 variables used in the expression 2x + 3y + 5.

• The expression 2x + 3y + 5 contains 2 variables, 'x' and 'y'.


• Therefore, the correct answer is 2.

• Given expression: y multiplied by 10 and then 7 added to product


• Translation: 10y + 7


• Therefore, the correct expression is: 10y + 7

• Step 1: Multiply 'y' by 5


• Step 2: Add 3 to the result obtained in Step 1

• Step 1: 5 times of 'y' is represented as 5y


• Step 2: Adding 3 to 5y gives the expression 5y + 3

• Therefore, the correct expression for "5 times of 'y' to which 3 is added" is 5y + 3

• Expression: 2y - 9


• Given Statement: 9 subtracted from 2y

• When we have the expression 2y - 9, it means we have 2 times y with 9 subtracted from it.


• We can interpret this as taking 9 away from the value of 2y.


• Therefore, the correct statement for the expression 2y - 9 is "9 subtracted from 2y."


• So, option B: "9 subtracted from 2y" is the correct choice.

• Equation: An equation is a mathematical statement that shows the equality of two expressions, typically separated by an equal sign.


• A: 2x + 3 = 5 is an equation as it contains an equal sign, indicating equality between two expressions.


• B, C, D: These options contain inequality signs (<, >, ≤), which represent inequalities, not equations.

• 2x + 3 = 5: This equation can be solved to find the value of x that satisfies the equality.


• Step 1: Subtract 3 from both sides to isolate the term with x: 2x = 2.


• Step 2: Divide by 2 on both sides to solve for x: x = 1.


• Final The value of x that satisfies the equation 2x + 3 = 5 is x = 1.

• Among the given options, A (2x + 3 = 5) is the only equation, while B, C, D are inequalities.


• An equation represents an equality relationship between two expressions, making it distinct from inequalities.

The correct option is Option A.

If we break the factor 16p, it can be written as p multiplied with 16 (16 × p)

If we break the factor 16 - p, it can be written as p subtracted from 16 (16 - p)

If we break the factor 16 + p, it can be written as p added to 16 (16 + p) 

• Perimeter of an equilateral triangle: In an equilateral triangle, all sides are equal in length. Therefore, the perimeter is equal to 3 times the length of one side.

• An equilateral triangle is a type of triangle in which all three sides are equal in length.


• Since all sides are equal, the perimeter of an equilateral triangle is the sum of the lengths of all three sides, which is equal to 3 times the length of one side.


• This property is unique to equilateral triangles and does not apply to isosceles or right-angled triangles.


• Therefore, the correct answer is option A: equilateral triangle.

• Given Equation: p - 5 = 5


• Values given in bracket: (0, 10, 5 - 5)


• We need to find the value of p.


• To find the value of p, we need to isolate p in the equation.


• Adding 5 to both sides of the equation, we get: p = 5 + 5 = 10


• Therefore, the solution is p = 10.

• Variable: In mathematics, a variable is a symbol or letter representing a value that is not yet known.


• Condition: A condition on a variable restricts the possible values that the variable can take.


• Equation: An equation is a statement that two mathematical expressions are equal.


• Answer: In this context, an equation is used to set a condition on a variable, defining the relationship between different expressions involving the variable.


• Example: If we have an equation like "2x + 5 = 11", the condition on the variable x is that it must satisfy the equation by taking a specific value.

• Definition of 'Variable': A variable is a symbol used to represent any member of a set of numbers or other objects, which can vary or change in value.


• Example: In the equation y = 2x + 3, x is a variable because its value can change, leading to different values of y.


• Characteristics: Variables are used in mathematics, science, and computer programming to represent unknown or changing quantities.


• Functions: Variables play a crucial role in mathematical equations, scientific experiments, and computer algorithms by allowing for flexibility and adaptability.


• Importance: Understanding variables is essential in problem-solving and critical thinking, as they enable us to analyze, predict, and control changes in various situations.

• Given: Meena's present age is y years.


• To find: What will be her age 5 years from now?

• Meena's age 5 years from now will be her present age (y) plus 5 years.


• Therefore, her age 5 years from now is represented as y+5.

• The correct answer is y+5.