If x2 + y2x2 - y2 = 178 t

Subject

Mathematics

Class

ICSE Class 10

Pre Boards

Practice to excel and get familiar with the paper pattern and the type of questions. Check you answers with answer keys provided.

Sample Papers

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 Multiple Choice QuestionsShort Answer Type

1.

A die has 6 faces marked by the given numbers as shown below:


The die is thrown once. What is the probability of getting
(i) a positive integer.
(ii) an integer greater than - 3.
(iii) the smallest integer.


2.

Find x, y if -2031- 12x + 3- 21 = 2y3.


3.

Shahrukh opened a ‘Recurring Deposit’ account in a bank and deposited Rs. 800 per month for 1½ years. If he received Rs. 15,084 at the time of maturity, find the rate of interest per annum.


4.

Without using trigonometric tables, evaluate

sin234° + sin256° + 2tan18°tan72° - cot230°


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5.

Using the Remainder and Factor Theorem, factorise the following polynomial:
x3 + 10x2 - 37x + 26


6.

The numbers 6, 8, 10, 12, 13 and x are arranged in an ascending order.
If the mean of the observations is equal to the median, find the value of x.


7.

In the figure, m∠DBC = 58°. BD is the diameter of the circle. Calculate:

(i) m∠BDC

(ii) m∠BEC

(iii) m∠BAC


8.

Use graph paper to answer the following questions. (Take 2 cm = 1 unit on both axes)
(i) Plot the points A( - 4, 2) and B(2, 4)
(ii) A' is the image of A when reflected at the y-axis. Plot it on the graph paper and write
the co-ordinates of A'.
(iii) B' is the image of B when reflected on the line AA'. Write the co-ordinates of B'.
(iv) Write the geometric name of the figure ABA'B'.
(v) Name a line of symmetry of the figure formed.


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9.

A shopkeeper bought a washing machine at a discount of 20% from a wholesaler, the printed price of the washing machine being Rs. 18,000. The shopkeeper sells it to a consumer at a discount of 10% on the printed price. If the rate of sales tax is 8%, find:
(i) the VAT paid by the shopkeeper.
(ii) the total amount that the consumer pays for the washing machine.


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10.

If x2 + y2x2 - y2 = 178 then find the value of :

(i) x:y

(ii) x3 + y3x3 - y3


(i) As given,

x2 + y2x2 - y2 = 178

By applying componendo-dividendo, we get

x2 + y2 + x2 - y2x2 + y2 - x2 + y2 = 17 + 817 - 8

 2x22y2 = 259

 x2y2 = 259

 xy = 53

 x : y = 5 : 3

(ii) As we get xy = 53,

x3y3 = 12527

By applying componendo - dividendo,we get

x3 + y3x3 - y3 = 125 + 27125 - 27

 x3 + y3x3 - y3 = 15298

 x3 + y3x3 - y3 = 7649


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