CUBES AND CUBE ROOTS

1) Find the cubes of the following
a) 35 b) 402 c) 98 d) 11/12 e) 23 8/9 f) 0.01 g) 5.17

2) Examine if the following are perfect cubes
a) 392 b) 106480 c) 1728 d) 400

3) Find the cube root of
a) 91125 b) 531441 c ) - 571787 d) 343/1131
e) -13824 g) 0.008 h) 0.000064 i) 9261/42875

4) What is the smallest number by which 625 must be divided so that the quotient is a perfect cube.Also find the cube root of the quotient.

5) Find the smallest number which when multiplied by 3600 will make the product a perfect cube.Find the cube root of the product.

6) Multiply 137592 by the smallest number so that the product is a perfect square.Also find the cube root of the product.

SQUARES AND SQUARE ROOTS

1) Find the square of
a) 17 b) 431 c) 13/14 d) 8 3/7 e) 0.03 f) 1.02

2) Find the square root by prime factorisation
a) 729 b) 7056 c) 5929 d) 38416

3) Find the square root of
a) 34 15/49 b) 21 2797/3364 c) 2116/15129

4) Find the square root of
a) 37.0881 b) 0.000529 c) 42.25 d) 84.8241

5) Find the square root upto 3 places of decimals of
a) 66 b) 2 1/12 c) 7.234 d) 11 2/3 e) 1

6) What must be added to 452664 to make it a perfect square?

7) Find the least number that should be subtracted from 2361 to make it a perfect square. Also find the square root of the number obtained.

8) 2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows.find the number of rows and plants in the garden.

9) Find the smallest number by which 3645 should be divided so as to get a perfect square. Also find the square root of the number obtained.

10) Simplify
( √81 + √0.81 + √0.0081) × √10000

POLYNOMIALS

1) Divide
a) – 20 x⁴ by 10 x
b) 3y ³ by √3 y
c) 4a⁴ by - 2 √2 a²
d) y⁴ - 3y ³ + ½ y² by 3y
e) -4p³ + 4p²+p+4 by 2p

2) Divide by taking factors
a) x²+6x + 8 by x+4
b) y²- y -12 by y – 4
c) x² + 7x +10 by x + 5
d) x⁴+3x²+2 by x² + 2 (Hint: Take x² = y)

3) Divide using by long division method
a) 3y⁴ - y³ + 12 y² + 2 by 3y² - 1
b) 6y – 6 y²+ 5y³ - 1 5y - 1
c) 8q³ - 6q² + 4q – 1 by 2 + 4q
d) a⁴ + a³ + a² by a + 1
e) x( x² - x +1) – ( 9 + 4 x⁴) by 4x - 1

CONSTRUCTION OF QUADRILATERALS

1) Construct a rhombus with side 4.5 cm and one diagonal 6 cm.
2) Construct a parallelogram ABCD in which AB = 3.5 cm ,BC = 4 cm and AC = 6.5 cm.
3) Construct a quadrilateral ABCD in which AB = AD = 3 cm, BC = 2.5 cm, AC = 4 cm and BD = 5 cm.
4) Construct a quadrilateral ABCD in which AC = AD = 6 cm, BC = 7.5 cm, CD = 5 cm and BD = 10 cm.
5) Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 6.5 cm, and its 3 angles
A =75 degrees, B = 105 degrees and C = 120 .
6) Construct a quadrilateral PQRS in which PQ = 3.5 cm, QR = 6.5 cm, and 3 angles P = 100 degrees, R = 110 degrees and S = 75 degrees.
7) Construct a rectangle with sides 4.5 cm and 6 cm.
8) Construct a parallelogram whose 2 sides and one angle are 4 cm, 5.5 cm and 70 degrees respectively.
9) Construct a PQRS in which PQ = 3.5 cm, QR = 2.5 cm , RS = 4 cm, angles Q = 75 degrees and R = 120 degrees
10) Construct a trapezium ABCD in which AB CD, AB = 8 cm ,BC = 6 cm, CD = 4 cm and
angle B = 60 degrees.( Hint : Find angle C by using the fact that AB CD)

SPECIAL TYPES OF QUADRILATERALS

1) The angles P,Q,R,S of a quadrilateral are in the ratio 1:3:7:9
a) find the measure of each angle.
b) Is PQRS a trapezium? Why?
c) Is PQRS a parallelogram? Why?

2) State True or False
a) Every rectangle is a parallelogram.
b) Every parallelogram is a rhombus.
c) Every rhombus is a parallelogram.
d) Every rectangle is a square.
e) Every square is a rectangle.
f) Every square is a rhombus.
g) Every parallelogram is a rectangle.
h) Every parallelogram is a square.

3) 2 adjacent angles of a parallelogram are equal.Find the measure of each angle of the parallelogram.

4) The ratio of 2 adjacent sides of a parallelogram are in the ratio 2:3.If its perimeter is 48 cm,find the sides of the parallelogram.

5) The diagnols of a quadrilateral are of lengths 10 cm and 24 cm. If the diagnols bisect each other at right angles, find the length of each side of the quadrilateral. What special name will you give to the quadrilateral?