Class 9 Mathematics | ICSE Board Board | Mixed Level Practice Test - 40 Questions (2026)

If $(x + 2)$ is a factor of the polynomial $p(x) = 2x^3 - x^2 + kx + 2$, find the value of $k$.

In the given figure, if $AB \parallel CD$, $\angle APQ = 50^\circ$ and $\angle PRD = 127^\circ$, find the value of $x$ and $y$ where $x = \angle PQR$ and $y = \angle QPR$.

If the mean of 6, 8, 5, $x$, 4 is 7, then find the value of $x$.

A shopkeeper marks an article at ₹200. What discount percent should he offer to sell it for ₹160?

If $a + b + c = 0$, find the value of $\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}$.

If the radius of a sphere is doubled, then what is the ratio of the new volume to the original volume?

The points A(2, -2) and B(-7, 4) are given. Find the coordinates of the point which divides the line segment AB in the ratio 1:2 internally.

Simplify: $\frac{(a^2 - b^2)^3 + (b^2 - c^2)^3 + (c^2 - a^2)^3}{(a - b)^3 + (b - c)^3 + (c - a)^3}$

A rectangular field is 20 m long and 14 m wide. There is a path of 1 m width around the outside of the field. Find the area of the path.

If $\sqrt{5}=2.236$ approximately, find the value of $\frac{1}{\sqrt{5}}$ to three decimal places.

If $(x + 2)$ is a factor of the polynomial $p(x) = 2x^3 + 5x^2 - kx - 18$, then the value of $k$ is:

In the given figure, $O$ is the center of the circle. If $\angle BAC = 40^\circ$, then $\angle BOC$ is equal to:

If the mean of the observations $x, x+2, x+4, x+6, x+8$ is 11, then the value of $x$ is:

A die is thrown once. The probability of getting a number greater than 4 is:

The value of $\sqrt{5 - 2\sqrt{6}}$ is:

If the surface area of a sphere is $144\pi$ cm$^2$, then its volume is:

The solution set for the inequation $2x - 3 < x + 2$, where $x \in W$ (Whole Numbers), is:

If $a + b + c = 0$, then the value of $a^3 + b^3 + c^3$ is equal to:

A shopkeeper sells an article at a discount of 20%. If the marked price of the article is ₹500, then the selling price is:

If the coordinates of a point are $(-2, 3)$, then its perpendicular distance from x-axis is:

If $x + \frac{1}{x} = 5$, then find the value of $x^2 + \frac{1}{x^2}$.

The angles of a quadrilateral are in the ratio 3:5:9:13. Find the measure of the largest angle.

If $(x+2)$ is a factor of the polynomial $2x^3 + 5x^2 - x - k$, find the value of $k$.

In the given figure, if $AB || CD$, $\angle APQ = 50°$ and $\angle PRD = 127°$, find the values of $x$ and $y$ respectively.

The area of a rhombus is $240 cm^2$ and one of the diagonals is $16 cm$. Find the length of the other diagonal.

If the mean of 6, 8, 5, x, and 4 is 7, then find the value of x.

A bag contains 5 red balls and 3 blue balls. A ball is drawn at random. What is the probability that the ball drawn is blue?

Find the area of an equilateral triangle whose side is 'a' cm.

What is the value of $(2^0 + 3^0 + 4^0)$?

Find the value of $\sqrt[3]{27} + \sqrt{25}$.

If the mean of the observations $x, x+2, x+4, x+6, x+8$ is 11, find the value of $x$.

In the given figure, $O$ is the center of the circle and $\\angle AOB = 110^{\\circ}$. Find the measure of $\\angle ACB$.

Factorize the expression: $4x^2 - 9y^2$.

If $a + b + c = 0$, find the value of $a^3 + b^3 + c^3$.

The coordinates of a point which lies on y-axis and is at a distance of 4 units from x-axis are:

What is the probability of getting a sum of 9 when two dice are thrown simultaneously?

Find the area of an equilateral triangle whose side is $2a$.

If $x = 2$ and $y = -1$, find the value of $x^3 + y^3 + 3xy(x+y)$.

A cuboid has dimensions 6 cm $\times$ 4 cm $\times$ 2 cm. Find its total surface area.

If $P(x) = x^2 - 2\\sqrt{2}x + 1$, then $P(2\\sqrt{2})$ is equal to: