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 :
Question – 3. [2 + 2 + 2 + 2 + 2]
(a) In the given figure, AOB is a straight line. Find L AOC and L BOD.
(b) In the given figure, find the value of x, y, z and p.
(c) In the figure given below, X and Y are mid-points of AB and AC respectively. If BC = 6 cm, AB = 5.4 cm and AC = 5 cm, calculate the perimeter of trapezium XYCB.
(d)In the figure given below, DE is parallel to BC, AD = 3 cm, BD = 4 cm and BC = 5 cm, find AE : EC.
(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 :
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.
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 side-by-side to form a cuboid . Find the volume and the surface area of the cuboid.
(b) Find the slope and y-intercept 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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