"Othello" written by William Shakespeare play explores themes of jealousy, manipulation, betrayal

Worksheet for Class: 9 (Mathematics)

Question 1- Express the rational number 0.45¯ in the form pq, where p and q are natural number.

Question 2- Find the remainder, when the polynomial 2x4+x3+4x2−3x−2 is divided by x−3(without applying long division).

Question 3- Find the value of k if (x-1) is a factor of 4x3+3x2−4x+k.

Question 4- In which quadrant or on which axis each of the given points lie?

(i) (-2,4)

(ii) (-8,0)

(iii) (1,-7)

(iv) (-7,-2)

Question 5- If a point C lies between two points A and B such that AC=BC, then prove that AC = 1/2 AB.

Question 6- If xab=1, and b≠0, then find the value  of ‘a’.

Question 7- Represent 5–√ on a number line.

Question 8- Find the value of ‘a’ such that x = 1  and y = 1 is a solution of the linear equation

9ax + 12ay = 63

Question 9 Evaluate (104)3 using suitable identity.

Question 10- Expand (1x+y3)3

Example 11- Simplify (8116)−34[(259)−32÷(52)−3]

Example 12- Simplify the following by rationalising the denominator 

73√–52√48√+18√

Example 13- If a2+b2+c2=250 and ab+bc+ca=3, then find the value of a+b+c.

Example 14 – If x+1x=7, then find the value of x3+1x3.

Example 15- Find the square root of 9.5 geometrically.

Example 16- The sides of a triangle are in the ratio 12:17:25 and its perimeter is 540 cm. Find the area of the triangle.

Example 17- Factorise: 

(i) 3x3+3–√x−2

(ii) 2–√x2+3x+2–√

Example 18- If p2+4q2+9r2=2pq+6qr+3pr, then prove that p3+8q3+27r3=18pqr.

Example 19- If (3x-2) is a factor of 3x3+x2–20x+12, find the other factors.

Example 20- Find the volume of the largest right circular cone that can be fitted in a cube whose edge is 21 cm.

Example 21- A plastic box 1.5m long, 1.25m wide and 65 cm deep is to be made. It is to be open at the top. Ignoring the thickness of the plastic sheet, determine:

(i) the area of the sheet required for making the box.

(ii) the cost of sheet for it, if a sheet measuring 1m2 cost Rs. 20.

Example 22- A hemisphere dome of a building needs to be painted. If the circumference of the base of 

the dome is 17.6 m, find the cost of painting it, given the cost of painting is Rs. 5 per 100 sq cm.