Mathematics Class Concepts

What should the remainder be for (x - a) to be a factor of the polynomial?

What is the qualifying sum of money for Radha's recurring deposit of ₹400 per month for 18 months?

What is the area of the shaded portion QPBC if the area of ∆APQ is 18 cm²?

What is the value of x in the given scenario?

What is the length of PR in the given measurement?

Which of the following statements about the volume and surface area of a sphere and two hemispheres is valid?

What is the mean of the squares of the first seven natural numbers, given their sum is 140?

What is the probability of drawing a black marble from a bag containing 3 red and 2 blue marbles?

Polynomial Factors

A polynomial in 'x' will have (𝑥 − 𝑎) as a factor if the remainder is 0 when divided by (𝑥 − 𝑎).

Recurring Deposits

The qualifying sum of money for interest calculation in a recurring deposit is the total amount deposited, calculated as monthly deposit multiplied by the number of months.

Area of a Circle

In a circle, a diameter divides the circle into two semicircles.

Tangent and Radius

The tangent to a circle is perpendicular to the radius at the point of contact.

Trigonometry and Right Angled Triangles

In a right-angled triangle, the trigonometric ratios can be used to find the lengths of sides.

Surface Area and Volume of Spheres

Cutting a sphere into two hemispheres does not change the total volume.
The total surface area of two hemispheres is greater than the surface area of the original sphere.

Mean

The mean of a set of numbers is the sum of the numbers divided by the number of numbers.
The sum of the squares of the first seven natural numbers can be used to find their mean.

Probability

The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes.
If there are no black marbles in the bag, the probability of drawing a black marble is 0.

This quiz covers key concepts in mathematics including polynomial factors, area of a circle, and properties of trigonometric ratios. Dive into topics such as recurring deposits, surface area and volume of spheres, and calculating means. Perfect for reinforcing essential mathematical knowledge.