INTERNATIONAL INDIAN SCHOOL, RIYADH CLASS: IX SUB: MATHEMATICS HERONS FORMULA 1. The sides of a triangle are in the ratio 5 : 12 : 13 & its perimeter is 150 cm. Find the area of triangle (75sqcm) 2. The sides of a triangle are in the ratio 3 : 4 : 5 & its perimeter is 144 cm. Find the area of triangle (864 sqcm) 3. Find the area of isosceles triangle each of whose equal sides is 13cm and whose base is 24cm (60 sq cm) 4. Find the area of triangle two sides of which are 8cm and 11cm and the perimeter is 32 cm (8√30sqcm) 5. The lengths of two adjacent sides of a parallelogram are 51cm and 37cm and one of its diagonal is 20 cm.

Find its area (612sqcm) 6. One of the diagonals of a rhombus of perimeter 140 m is 60 m. Find its area (1081.5 cm2) 7. Find the cost of laying grass in a triangular field of sides 50m, 65m and 65m at the rate of Rs 7/m2

(area = 1500 m2 , cost = Rs 10, 500) 8. A floor design is made on a floor of a room by joining four triangular tiles of dimensions 12cm, 20cm & 24cm

each. Find the cost of the tiles at the rate of ₨ √14 per cm2 (₨ 1792) 9. Using Herons formula find the area of equilateral triangle whose perimeter is 24 cm (16√3 cm2 ) 10. Find the area of a quadrilateral ABCD in which AB = 3cm, BC = 4cm, CD = 6cm & AD = 5cm & diagonal AC =

5cm (18 cm2) 11. Find the area of a quadrilateral ABCD in which AB = 9cm, BC = 40cm, CD = 28cm and AD = 15cm and angle

ABC = 90° (306 cm2 ) 12. A park in the shape of a quadrilateral ABCD has ∟C = 90°, AB = 9m, BC = 12m, CD = 5cm, and AD = 8 m. How much area does it occupy (65.5m2 ) 13. A field is in the shape of a trapezium whose parallel sides are 25cm and 10 cm, the non-parallel sides are 14m

and 13m. Find the area of the field. (area of ∆ = 84m2, h = 56/5m, area = 196m2) 14. Two parallel sides of a trapezium are 120cm and 154cm and other sides are 50cm and 52cm. Find its area 15. Two parallel sides of a trapezium are 60m and 77m and other sides are 26m and 25m. Find its area (1644m2) 16. Find the area of a triangle whose perimeter is 180cm and two of its sides are 80cm and 18cm (720cm2) 16. The base of an isosceles triangle is 16 cm and its area is 48sqcm. Find the perimeter of a ∆ (36cm) 17. If the area of an equilateral ∆ 36√3 cm2, find its perimeter (36 cm)

INTERNATIONAL INDIAN SCHOOL, RIYADH CLASS: IX SUB: MATHEMATICS NUMBER SYSTEMS 1. Represent √9.3 on the number line 2. Find two irrational numbers between 2/5 and ¾ 3. If x = 3 + 2√2, find the value of x2 + 1/x2 (34) 4. If a and b are rational numbers, find a and b

√5 – 1 + √5 + 1 = a + b√5 (a = 3, b = 0) √5 + 1 √5 – 1

5. Simplify: 1 + 1 + 1 (1) 1 + √2 √2 + √3 √3 + √4 6. If x = √3 + √2 and y = √3 - √2 , then find the value of x2 + y2 (98) √3 - √2 √3 + √2 7. If x = 3 + 2 √2, find the value of √x - 1/√x (2) 8. given that √3 = 1,732 & √5 = 2.236, find the value of 6 (11. 904) √5 - √3 9. Find the value x, if 5x -3 x 3 2x – 8 = 225 (x = 5) 10. Which is the greatest among: √2, 3√4, 4√3? 11. Evaluate: 125 -1/3 x 271/3 (62 + 82)1/2 (6)

12. Give an example of two irrational numbers whose: (a) Sum is rational (b) Product is rational (c) Quotient is rational (d) Difference is a rational number 13. Simplify: 4 - 1 (80) (216) – 2/3 (256) – 3/4

14. Simplify: 8 2/3 - √9 (10)0 + (1/144) – ½ (13) 15. Find the value of (81)0.16 x (81)0.09 (3) -------------------------------------------------------------------------------------------------------------------------------

CLASS: IX 2019-20 SUB: MATHEMATICS POLYNOMIALS 1. Find the value of a if (x – 1) is a factor of the polynomial a2x3 – 4ax + 4a - 1 (a =±1) 2. Find the value of k if 2x – 3 is a factor of 2x3 + kx2 + x + 12 (k = - 9) 3. Without actual division prove that x4 + 2x3 – 2x2 + 2x – 3 is exactly divisible by x2 + 2x – 3 4. If p(x) = x2 – 5x + 7, evaluate p(2) – p(- 1) + p(1/3) (- 59/9) 5. The polynomial ky3 + 3y2 – 3 and 2y3 – 5y + k when divided by (y – 5) leave the same

remainder in each case. Find the value of k (k =153/124) 6. The polynomials ax3 – 3x2 + 4 and 2x3 – 5x + a when divided by (x – 2) leave the remainder p

and q respectively. If p – 2q = 4, find a (p = 24,q = 10, a = 4) 7. If the polynomial x3 + mx2 + nx + 6 has (x -2) as a factor and leaves remainder 3 when divided By (x – 3), find the value of m and n (m = - 3, n = - 1)

8. Factorise : i) p4 – 81q4 (p + 3q) (p - 3q) (p2 + pq2)

ii) 8x3 – 27 (2x – 3) (4x2 + 6x + 9) iii) 3 – 12(a – b)2 3[ 1 + 2a – 2b] [ 1 – 2a + 2b] 9. Without calculating the cubes find the value of (- ¾)3 + (- 5/8)3 + (11/8)3 (495/256) 10. If a + b + c = 9 and a2 + b2 + c2 = 35, find the value of a3 + b3 + c3 – 3abc (108) 11. If x + y = 12 and xy = 27, then find the value of x3 + y3 (756) 12. If x + 1/x = 7, then show that x3 + 1/x3 = 322 13. Simplify: (2x – 5y)3 – (2x + 5y)3 (– 120x2y – 250y3) 14. Find the value of : (2.3)3 - 0.027 (2) (2.3)2 + 0.69 + 0.09 15. Find the value of 853 + 153 (100)

852 + 152 – 85 x 15 16. Simplify: x3 – 4 – x + 4x2 x2 + 3x - 4 (x + 1)