**MATHEMATICS (ICSE 2014)**

**Two and Half Hour**. *Answers to this Paper must be written on the paper provided separately. **You will not be allowed to write during the first 15 minutes. *

*This time is to be spent in reading the question paper.*

*The time given at the head of this Paper is the time allowed for writing the answers. **Attempt all questions form Section A and any four questions from Section B. *

*All working, including rough work, must be clearly shown and must be done*

*on the same sheet as the rest of the Answer. Omission of essential working*

*will result in the loss of marks**.*

*The intended marks for questions or parts of questions are given in brackets ***[ ]***.*

*Mathematical tables are provided.*

**SECTION A [40 Marks]**

*(Answer all questions from this Section.)*

**Question 1.**

**(a)** Ranbir borrows at per annum compound interest. If he repays at the end of the first year and at the end of the second year, find the amount of loan outstanding at the beginning of the third year. ** [3]**

**(b)** Find the value of , which satisfy the in equation . Graph the solution set on the number line. **[3]**

**(c)** 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

(iii) The smallest integer **[4]**

**Answer.**

**(a)** Given: Principal for the first year

We known that *[Reference Link]*

Amount after the 1st year

Money repaid at the end of 1st year

Principle for the 2nd year

Amount after 2nd year

Money repaid at the end of the second year

The loan amount outstanding at the beginning of the third year

**(b)** Given

Multiplying throughout by 6

Therefore

Hence the solution set is

Therefore the values of are

The graph of the solution set is shown by dots on the number line.

**(c)** No. of sample space

A positive integer

No. of favorable cases

Probability

An integer greater than

No. of favorable cases

Probability

Smallest integer

Probability of smallest integer

**Question 2:**

**(a)** Find if **[3]**

**(b) **Sharukh opened a Recurring Deposit Account in a bank and deposited Rs. 800 per month for years. If he received Rs. 15,084 at the time of maturity. Find the rate of interest per annum. **[3]**

**(c)** Calculate the ratio in which the line joining is divided by point Also find (i) (ii) Length of . **[4] **

**Answer:**

**(a) **Given

**(b)** Here, = money deposited per month

Time for which the money is deposited =

Let the rate of interest be per annum, then

*[Reference Link]*

Total money deposited

Since money deposited +Interest = Maturity value

Hence rate of interest

**(c)** Let divide the line segment joining the points and in the ratio

Coordinate of is: *[Reference Link]*

But Coordinate of

The required ratio is , (Divides Internally)

(i) Therefore

Substituting

(ii) Coordinate of is

Length of

**Question 3:**

**(a)** Without using trigonometric tables, evaluate

**[3]**

**(b) **Using the remainder and factor theorem, factor the following polynomial: **[3]**

**(c)** In the figure given below is a rectangle . From the rectangle a quarter circle and a semicircle are removed Calculate the area of the remaining piece of the rectangle (Take ) **[4]**

**Answers:**

**(a) **Given

**(b)** Let

Putting , we get

By factor theorem is actor of

On dividing by , we get as the quotient and remainder

Therefore the other factor of are the factor of

Now,

Hence

**(c) **Area of rectangle

Area of quarter circle

Area of semicircle

Area of remaining piece of rectangle

**Question 4: **

**(a)** The number and are arranged in an ascending order. If the mean of the observations is equal to the median, find the value of ** [3]**

**(b)** In the figure, is a diameter of the circle. Calculate: **[3]**

(i)

(ii)

(iii)

**(c)** Using graph Paper to answer the following questions. (Take unit on both axis)

(i) Plot the points and

(ii) is the image of when reflected in the . Plot it on the graph paper and write the coordinates of

(iii) is the image of when reflected in the line write the coordinates of

(iv) Write the geometric name of the figure

(v) Name a line of symmetry of the figure formed. **[4]**

**Answers:**

**(a)** Arrange numbers in ascending order are

Mean

No. of terms

Median

Median

According to given condition

or

**(b)** In

(i) (angle in the semi circle)

(ii) (cyclic quadrilateral)

(iii) (angles in the same segment)

(c) As shown in the graph below:

(i) Coordinate of

(ii) Coordinate of

(iii) Geometric name

(iv) is the symmetric line.

**SECTION B [40 Marks]**

*(Answer any four questions in this Section.)*

**Question 5:**

**(a)** A shopkeeper bought a washing machine at a discount of from a wholesaler, the printed price of the washing machine being . The shopkeeper sells it to a consumer at a discount of on the printed price. If the rate of sales tax is find:

(i) the VAT paid by the shopkeeper

(ii) the total amount that the consumer pays for the washing machine. ** [3]**

**(b)** If , then find the value of

(i)

(ii) **[3]**

**(c)** In

(i) Prove that is similar to

(ii) Find

(iii) Find area of ** [4]**

**Answers:**

**(a) **Given: Printed price of washing machine

Rate of discount

(i) Amount of discount to shopkeeper

Shopkeeper’s Price

Sales Tax paid by shopkeeper

Discount for consumer

*This post first appeared on Icse Mathematics « MATHEMATICS MADE EASY FOR STUDENTS, please read the originial post: here*