ICSE Class 10 - CISCE Important Questions for Mathematics

In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region.

If the quadratic equation px² − 2√5px + 15 = 0 has two equal roots then find the value of p.

In the following figure, in ΔPQR, seg RS is the bisector of ∠PRQ. If PS = 6, SQ = 8, PR = 15, find QR.

In the given figure, if A(P-ABC) = 154 cm²  radius of the circle is 14 cm, find

(1) `∠APC` 

(2) l ( arc ABC) .

In the given figure, if A(P-ABC) = 154 cm²  radius of the circle is 14 cm, find

(1) `∠APC` 

(2) l ( arc ABC) .

Jaya borrowed Rs. 50,000 for 2 years. The rates of interest for two successive years are 12% and 15% respectively. She repays 33,000 at the end of the first year. Find the amount she must pay at the end of the second year to clear her debt.

P(1, -2) is a point on the line segment A(3, -6) and B(x, y) such that AP : PB is equal to 2 : 3. Find the coordinates of B.

Mr Lalit invested Rs. 5000 at a certain rate of interest, compounded annually for two years. At the end of the first year, it amounts to Rs. 5325. Calculate

1) The rate of interest

2) The amount at the end of the second year, to the nearest rupee.

In what time will Rs. 1500 yield Rs. 496.50 as compound interest at 10% per annum compounded annually?

Use ruler and compasses only for the following questions. All constructions lines and arcs must be clearly shown.

Construct the locus of points at a distance of 3.5 cm from A.

Use ruler and compasses only for the following questions. All constructions lines and arcs must be clearly shown

Construct the locus of points equidistant from AC and BC.

Use ruler and compasses only for the following questions. All constructions lines and arcs must be clearly shown

Mark 2 points X and Y which are a distance of 3.5 cm from A and also equidistant from AC and BC. Measure XY.

The present population of the town is 2,00,000. The population is increased by 10% in the first year and 15% in the second year. Find the population of the town at the end of two years.

If a, b, c are in continued proportion, prove that (a + b + c) (a – b + c) = a² + b² + c²

Construct a triangle ABC with AB = 5.5 cm, AC = 6 cm and ∠BAC = 105°

Hence:

1) Construct the locus of points equidistant from BA and BC

2) Construct the locus of points equidistant from B and C.

3) Mark the point which satisfies the above two loci as P. Measure and write the length of PC.

Ranbir borrows Rs. 20,000 at 12% per annum compound interest. If he repays Rs. 8400 at the end of the first year and Rs. 9680 at the end of the second year, find the amount of loan outstanding at the beginning of the third year.

The value of 'a' for which of the following points A(a, 3), B (2, 1) and C(5, a) a collinear. Hence find the equation of the line.

The compound interest, calculated yearly, on a certain sum of money for the second year is Rs. 1320 and for the third year is Rs. 1452. Calculate the rate of interest and the original sum of money

At what rate % p.a. will a sum of Rs. 4000 yield Rs. 1324 as compound interest in 3 years?

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.?