Subject

Mathematics

Class

ICSE Class 10

Pre Boards

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Sample Papers

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ICSE Class 10 Mathematics Solved Question Paper 2012

Short Answer Type

If A = $[\begin{matrix} 3 & 1 \\ - 1 & 2 \end{matrix}]$ and B = $[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$ , Find A² - 5A + 7I

The monthly pocket money of Ravi and Sanjeev are in the ratio 5:7. Their expenditures are in the ratio 3:5. If each saves Rs. 80 every month, find their monthly pocket money

3.
Using the Remainder Theorem factorise completely the following polynomial.
3x³ + 2x² – 19x + 6

Given equation is, 3x³ + 2x²- 19x + 6

Let p(x) = 3x³ + 2x² – 19x + 6

By hit and trial method,

P(–1) = 3(–1)³ + 2(–1)² – 19(–1) + 6 = –3 + 2 + 19 + 6 = 24 ≠ 0

P(1) = 3(1)³ + 2(1)² – 19(1) + 6 = 3 + 2 – 19 + 6 = –8 ≠ 0

p(2) = 3(2)³ + 2(2)² – 19(2) + 6 = 24 + 8 – 38 + 6 = 0

Thus, (x – 2) is a factor of p(x).

Now,

Therefore, 3x³ + 2x² – 19x + 6 = (x - 2)(3x² + 8x - 3)

= (x - 2)(3x² + 9x - x - 3)

= (x - 2)[3x(x + 3) - 1(x + 3)]

= (x - 2)(x + 3)(3x - 1)

Thus, x = 2, -3, 1/3

On what sum of money will the difference between the compound interest and simple interest for 2 years be equal to Rs. 25 if the rate of interest charged for both is 5% p.a.?

ABC is an isosceles right angled triangle with ∠ABC = 90 $°$ . A semi-circle is drawn with AC as the diameter. If AB = BC = 7 cm, find the area of the shaded region.
Take ( $π = \frac{22}{7}$ )

Given a line segment AB joining the points A(– 4, 6) and B(8, – 3). Find

(i) The ratio in which AB is divided by y-axis.

(ii) Find the coordinates of the point of intersection.

(iii) The length of AB.

In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC = 7.5 cm. Calculate the radius of circle.

Evaluate without using trigonometric tables:

$\cos^{2} (26 °) + \cos (64 °) \sin (26 °) + \frac{\tan (36 °)}{\cot (54 °)}$

Marks obtained by 40 students in a short assessment is given below, where a and b are two missing data.

Marks 5 6 7 8 9

Number of Students 6 a 16 13 b

If the mean of the distribution is 7.2, find a and b.

10.

Kiran deposited Rs. 200 per month for 36 months in a bank’s recurring deposit account. If the bank pays interest at the rate of 11% per annum, find the amount she gets on maturity.