# ICSE (IX) GUESS PAPER IN MATHS FOR 2012.

**ICSE (IX) Guess Paper in Maths for 2012.**

**Time 2 ½ hrs] Maths [Max. Marks = 80.**

**Section – I (40 Mark)**

**Answer ALL questions.**

Q.1.

(a) Arrange the fractions 2/3, – 4/9, – 5/8, 7/12 in ascending order. [3]

(b) Insert two rational numbers between 1/3 and 1/4 and arrange in ascending order. [3]

(c) Insert two irrational numbers between √2 and √7. [4]

Q.2.

(a) Rationalise the denominator of : 2/(3 – √5). [3]

(b) Construct *L*60º using ruler and compass only. [3]

(c) How much percent more than the cost price should a shopkeeper mark his goods, so that after allowing a discount of 12.5%, he should have a gain of 5% on his outlay? [4]

Q.3.

(a) Find the amount and the compound interest on Rs8000 for 1 ½ years at 10% per annum, the interest being compounded half-yearly. [4]

(b) Expand the following using standard formulae :

(2x + 7y)^{2}. [3]

(c) Factorise the following:

3x^{2} + 14x + 8. [3]

Q.4.

(a) In a right angled Δ ABC, *L*A = 90º. If AB = 5 cm and CA = 12 cm, find the hyponuse. [3]

(b) BD is a diagonal of the quadrilateral ABCD. AM and CN are perpendicular from A and C respectively on BD. Prove that area of quadrilateral ABCD = 1/2BD×(AM + CN). [4]

(c) Find the value of :

cos2 45º + sin2 60º + sin2 30º. [3]

**Section – II (40 Marks) **

**Answer ANY FOUR questions. **

Q.5.

(a) Prove that 5 + √2 is an irrational number. [3]

(b) A shopkeeper bought locks at the rate of 8 locks for Rs34 and sold them at the rate of 12 locks for Rs57. Calculate :

(i) his gain percent and

(ii) the number of locks he should sell to earn a profit of Rs45. [3]

(c) A trader sold 20% of his articles at 10% profit and 50% of the remaining articles at 10% loss. What should be the rate of profit for sale of the left articles in order that the trader may make an overall profit of 15%? [4]

Q.6.

(a) A man borrowed a sum of money and agrees to pay off by paying Rs3150 at the end of first year and Rs4410 at the end of second year. If the rate of compound interest is 5% per annum, find the sum borrowed. [3]

(b) If x + y – z = 4 and x^{2} + y^{2} + z^{2} = 38, then find the value of xy – yz – zx. [3]

(c) Factorize the following :

(i) 64a^{6} – b^{6} and

(ii) 27x^{4} – 8x. [4]

Q.7.

(a) Rearrange the formula p = 4√(x – 1) + 1 so that x becomes the new subject. Find the value of x when p = 13. [3]

(b) Solve the equation : (2x – 3)/(2x – 1) = (3x – 1)/(3x + 1). [3]

(c) Solve the following simultaneous equations :

83x – 67y = 383

67x – 83y = 367. [4]

Q.8.

(a) If a^{x} = b^{y} = c^{z} and b^{2} = ac, prove that y = 2xz/(z + x). [3]

(b) If log 7 – log 2 + log 16 – 2 log 3 – log (7/45) = 1 + log n, find n. [3]

(c) Use logarithm table to evaluate (0.7634)^{1/3}/√(272.3 + 15.2) [4]

Q.9.

(a) In a Δ ABC, *L*B – *L*C = 22º and *L*C – *L*A = 7º. Find all the angles of the triangle. [3]

(b) Using ruler and compass only, construct *L*75º. [3]

(c) Using ruler and compass only, divide the line segment of length 6.2 cm into 5 equal parts. [4]

Q.10.

(a) If XY || QR, PX = 1 cm, QX = 3 cm, YR = 4.5 cm and QR = 9 cm, find PY and XY. [3]

(b) Find the number of sides of a regular polygon if each of its interior angle is:

(i) 160º and (ii) 120º. [3]

(c) Construct a quadrilateral ABCD, in which AB = 3.6 cm, BC = 3.1 cm, CD = 2.4 cm, DA = 3 cm and BD = 3.4 cm. [4]

Q.11.

(a) Find the area of a triangle whose sides are: 29 cm, 20 cm and 21 cm. [3]

(b) The length and breadth of a rectangular solid are respectively 25 cm and 20 cm. If the volume is 7000 cm^{3}, find its height. [3]

(c) If the volume of a cylinder of height 7 cm is 448π cm^{3}, find its lateral surface area and total surface area. [4]

Q.12.

(a) If tan θ = 5/12, find sec θ and sec θ + cosec θ, where θ is acute. [3]

(b) Find the slope and the y-intercept of the line :

5x – 3y – 6 = 0. [3]

(c) Draw a histogram for the following frequency distribution : [4]

Marks | Below 15 | Below 30 | Below 45 | Below 60 | Below 75 | Below 90 |

Frequency | 15 | 27 | 54 | 72 | 81 | 87 |

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