2008 ICSE ICSE Sample Papers : Mathematics : Class:IX Question paper
Sample Paper – 2008 Class – IX Subject – Mathematics
SECTION – I (40 marks) [Time – Two hours and a half] Note : This section is compulsory. Answer all the questions from this section. Question – 1. [2 + 2 + 2 + 2 + 2] (a) Insert one rational number between 5/7 and 4/9 and arrange them in descending order. (b) Round the number correct to 4 significant figures : 546.86. (c) Express as decimal : 35%. (d) A watch is sold for Rs.405 at a loss of 10%. Find the cost price of the watch. (e) Expand using standard formula : (x + 3)2. Question – 2. [2 + 2 + 2+ 2 + 2] (a) Factorize : 8x3 + y3. (b) v = u + at. Make ‘a’ as a subject and write the formula. (c) Solve : x/2 = 3 + x/3. (d) Solve the simultaneous linear equation : 3/x + 4y = 7 5/x + 6y = 13 (e) Simplify the following : (xm/xn)l(xn/xl)m(xl/xm)n. Question – 3. [2 + 2 + 2 + 2 + 2] (a) In the given figure, AOB is a straight line. Find L AOC and L BOD. Fig. (b) In the given figure, find the value of x, y, z and p. Fig. (c) In the figure given below, X and Y are midpoints of AB and AC respectively. If BC = 6 cm, AB = 5.4 cm and AC = 5 cm, calculate the perimeter of trapezium XYCB. Fig. (d)In the figure given below, DE is parallel to BC, AD = 3 cm, BD = 4 cm and BC = 5 cm, find AE : EC. Fig. (e) Find the number of sides of a regular polygon if each of its interior angles is 108º. Question – 4. [3 + 4 + 3] (a) Calculate the area of a triangle whose sides are 13 cm, 5 cm and 12 cm. (b) The volume of a rectangular solid is 3600 cm3. If it is 20 cm long and 9 cm high, find its total surface area. (c) If 5 tan? = 4, find the value of (5 sin? – 3 cos?)/(5 sin? + 2 cos?). SECTION – II (40 Marks) Answer ANY FOUR questions from this section. Question – 5. [2 + 2 + 3 + 3] (a) Prove that v2 is an irrational number. Hence show that 3 – v2 is an irrational number. (b) Three candidates in a school election got 108, 132 and 260 votes each. What percentage of the votes did the winner receive ? (c) A trader buys goods at 19% off the list price. He wants to get a profit of 20% after allowing a discount of 10%. At what percent above the list price should he mark the goods ? (d) Two equal sums of money were lent at 10% and 13% p.a. on simple interest. At the end of 3 years the total interest received is Rs6900. Find the total sum lent. Question – 6. [ 3 + 2 + 2 + 3] (a) If (x + 1/x)2 = 3, find the value of x3 + 1/x3. (b) Factorize : x2 + 1/x2 – 11. (c) If A = P (1 + rt/100), find t. If A = 460, P = 400 and r = 5, find t. (d) If x = p + 1, find the value of p from the equation 1/2(5x – 30) – 1/3(1 + 7p) = 1/4. Question – 7. [ 3 + 2 + 2 + 3] (a) Solve the following simultaneous equation graphically : 4x – y = 5, 5y – 4x = 7. (b) Six years hence a man’s age will be three times his son’s age, and three years ago he was nine times as old as his son. Find their present ages. (c) If 2x = 3y = 6–z, prove that 1/x + 1/y + 1/z = 0. (d) Use log table to evaluate the following : (7.09×0.2531)/(23.46×0.57). Question – 8. [ 4 + 3 + 3] (a) Draw a straight line AB = 4.4 cm. Mark a point P outside AB and draw a perpendicular from P to AB. (b) In a triangle ABC, 6LA = 4LB = 3LC. Find the angles of triangle ABC. (c) In the figure given below, ABC is an equilateral triangle. Base BC is produced to E, such that BC = CE. Calculate LACE and LAEC. Q.7(a)/page 229 Question – 9. [ 3 + 3 + 4] (a) O is any point in the interior of a triangle ABC. Prove that OB + OC < AB + AC. (b) In a rhombus ABCD, prove that AC2 + BD2 = 4AB2. (c) Construct a quadrilateral ABCD in which, AB = 2.7 cm, BC = 1.9 cm, AD = 3.6 cm, AC = 3.5 cm and BD = 5.3 cm. Question – 10. [ 2 + 4 + 4] (a) Prove that a median divides a triangle into two triangles of equal area. (b) Calculate the area of quadrilateral ABCD in which, LA = 90º, AB = 32 cm, AD = 24 cm and BC = CD = 25 cm. (c) Find the value of : (cos 0º + sin 45º + sin 30º)(sin 90º – cos 45º + cos 60º). Question – 11. [4 + 2 + 4] (a) Three cubes each of side 6 cm are joined together sidebyside to form a cuboid . Find the volume and the surface area of the cuboid. (b) Find the slope and yintercept of the line 3x – 4y + 2 = 0 (c) Draw a histogram to represent the following data and then draw frequency polygon on the same graph paper : Class interval 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 Frequency 3 5 12 9 4
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