(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

Without using trigonometric identity , show that :

`cos^2 25^circ + cos^2 65^circ = 1`

Without using trigonometric identity , show that :

`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`

Use graph paper for this question.

(Take 2 cm = 1 unit along both x-axis and y-axis.)

Plot the points O(0, 0), A(–4, 4), B(–3, 0) and C(0, –3).

1. Reflect points A and B on the y-axis and name them A' and B' respectively. Write down their co-ordinates.
2. Name the figure OABCB'A'.
3. State the line of symmetry of this figure.

Use a graph paper for this question.

(Take 2 cm = 1 unit on both x and y axes)

1. Plot the following points: A(0, 4), B(2, 3), C(1, 1) and D(2, 0).
2. Reflect points B, C, D on the y-axis and write down their coordinates. Name the images as B', C', D' respectively.
3. Join the points A, B, C, D, D', C', B' and A in order, so as to form a closed figure. Write down the equation to the line about which if this closed figure obtained is folded, the two parts of the figure exactly coincide.

Construct a triangle BPC given BC = 5 cm, BP = 4 cm and .

i) complete the rectangle ABCD such that:
a) P is equidistant from AB and BCV
b) P is equidistant from C and D.
ii) Measure and record the length of AB.

Use ruler and compass only for the following question. All construction lines and arcs must be clearly shown.

1. Construct a ΔABC in which BC = 6.5 cm, ∠ABC = 60°, AB = 5 cm.
2. Construct the locus of points at a distance of 3.5 cm from A.
3. Construct the locus of points equidistant from AC and BC.
4. Mark 2 points X and Y which are at a distance of 3.5 cm from A and also equidistant from AC and BC. Measure XY.

Evaluate:

sin² 34° + sin² 56° + 2 tan 18° tan 72° – cot² 30°

Prove that:

tan (55° + x) = cot (35° – x)

Prove that:

`(cot A - 1)/(2 - sec^2 A) = cot A/(1 + tan A)` 

Prove that (sin θ + cosec θ)² + (cos θ + sec θ)² = 7 + tan² θ + cot² θ. 

If the interest is compounded half yearly, calculate the amount when the Principal is Rs. 7,400, the rate of interest is 5% per annum and the duration is one year.

In how many years will Rs. 15,625 amount to Rs. 17,576 at 4% p.a., compound interest?

The population of a city is 1,25,000. If the annual birth rate and death rate are 5.5% and 3.5% respectively. Calculate the population of the city after 3 years.

The cost of a machine depreciates by 10% every year. If its present worth is Rs.18,000; what will be its value after three years?

The S.I. and C.I. on a sum of money for 2 years is Rs. 200 and 210 respectively. If the rate of interest is the same. Find the sum and rate.

Which in better investment: 7% Rs. 100 shares at Rs.120 or 8% Rs. 10 shares at Rs. 13.50.

Mamta invested Rs. 10,846 in buying the shares of a company at Rs. 17 each. If the face value of each share be? 10 and company paid 15% dividend at the end of the year, find the dividend earned by her.

Ajay owns 560 shares of a company. The face value of each share is Rs. 25. The company declares a dividend of 9%.

Calculate:

1. The dividend that Ajay will get.
2. The rate of interest on his investment, if Ajay had paid Rs. 30 for each share.

Points (3, 0) and (−1, 0) are invarient points under reflection in the line L₁; point (0, −3) and (0, 1) are invarient points on reflection in line L₂.

1. Write the equation of the line L₁ and L₂.
2. Write down the images of points P(3, 4) and Q(−5, −2) on reflection in L₁. Name the images as P' and Q' respectively.
3. Write down the images of P and Q on reflection in L₂. Name the image as P'' and Q'' respectively.

Use remainder theorem and find the remainder when the polynomial g(x) = x³ + x² – 2x + 1 is divided by x – 3.