Other Solved Mathematics Board Papers

**MATHEMATICS (ICSE – Class X Board Paper 2018)**

**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) Find the value of and if

** [3]**

(b) Sonia had a recurring deposit in a bank and deposited Rs. 600 per month for years. If the rate of interest was per annum, find the maturity value of this account. ** [3]**

(c) Cards bearing numbers are kept in a bag. A card is drawn at random from this bag. Find a probability of getting a card which is:

(i) a prime number

(ii) a number divisible by

(iii) a number that is multiple of

(iv) an odd number ** [4]**

Answers:

(a)

and

Hence,

(b) Monthly investments

,

Maturity value

(c) Cards:

(i) Prime numbers:

Probability (a prime number)

(ii) Numbers divisible by

Probability (a prime number)

(iii) Numbers multiple of

Probability (a prime number)

(iv) Odd numbers: None

Probability (a prime number)

**Question 2:**

(a) The circumference of the base of a cylindrical vessel is and its height is . Find the

(i) radius of the cylinder

(ii) volume of the cylinder (use )** [3]**

(b) If and are three consecutive terms of an A.P., find the value of .** [3]**

(c) is a cyclic quadrilateral. Given that and , calculate

(i)

(ii)

(iii) ** [4]**

Answers:

(a) Circumference

Height

Circumference

Volume

(b) and are in AP

Therefore the terms are and the common difference is

(c) Join

(i)

(opposite angles of a cyclic quadrilateral)

(ii)

(iii) (angles in the same segment)

Therefore

**Question 3:**

(a) If ) and are factors of , find the values of and .** [3]**

(b) Prove that ** [3]**

(c) Using a graph paper draw a histogram for the given distribution showing the number of runs scored by 50 batsman. Estimate the mode of the data.** [4]**

Runs Scored | 3000-4000 | 4000-5000 | 5000-6000 | 6000-7000 | 7000-8000 | 8000-9000 | 9000-10000 |

No. of Batsman | 4 | 18 | 9 | 6 | 7 | 2 | 4 |

Answers:

(a)

Factors:

… … … … … (i)

… … … … … (ii)

Solving (i) and (ii)

Substituting in (ii)

(b)

. Hence proved.

(c)

Mode

**Question 4:**

(a) Solve the following inequation, write down the solution set and represent it on a real number line.

** [3]**

(b) If the straight lines and are perpendicular to one another, find the value of .** [3]**

(c) Solve and give your answer correct to two decimal places.** [4]**

Answers:

(a)

First equation:

Second equation:

Hence the solution set

(b) Two equations are:

Since the two lines are perpendicular to each other

(c)

Therefore

or

**SECTION B [40 Marks]**

*(Attempt any four questions from this Section.)*

**Question 5:**

(a) The term of a G.P is and the term is . Find the first term and the common ratio of the series.** [3]**

(b) A man invests Rs. 22500 in Rs. 50 shares available at discount. If the dividend paid by the company is , calculate:

(i) The number of shares purchased

(ii) The annual dividend received

(iii) The rate of return he gets on his investment. Give your answer correct to the nearest whole number.** [3]**

(c) Use graph paper for this question (Take 2 cm = 1 unit along both and ). is a quadrilateral whose vertices are and .

(i) Reflect quadrilateral on the y-axis and name it as

(ii) Write down the coordinate of and

(iii) Name two points which are invariant under the above reflection

(iv) Name the polygon ** [4]**

Answers:

(a)

Therefore

Therefore

(b) Face Value , Discount

Market Value

Total Investment

(i) Number of shares bought

(ii) Annual dividend received

(iii) Rate of return

(c)

(i) Refer to the graph

(ii) and

(iii) and are irrelevant to the reflection

(iv) is a trapezium

**Question 6:**

(a) Using the properties of proportion, solve for . Given that is positive

** [3]**

(b) If , and , find .** [3]**

(c) Prove that ** [4]**

Answers:

(a)

Applying Componendo and Dividendo

(b)

(c)

Hence Proved

**Question 7:**

(a) Find the value of for which the following equation has equal roots.

** [3]**

(b) On a map drawn to a scale of , a rectangular plot of land has the following dimensions. ; and all angles are right angles. Find :

(i) the actual length of the diagonal of the plot in km

(ii) the actual area of the plot in sq. km** [3]**

(c) and are the vertices of the triangle , is a point on such that . Find the coordinates of . Hence find the equation of the line passing through the point and .** [4]**

Answers:

(a) Given

Therefore

For equal roots,

(b) Scale is

(i)

Let the length of be on the ground

Therefore

(ii) on the ground

on the ground

Therefore Area of

(c) and and

Let

Hence

Slope of

Therefore equation of

**Question 8:**

(a) Rs. 7500 was divided equally among a certain number of children. Had there been 20 less children each would have received Rs.100 more. Find the original number of students.** [3]**

(b) If the mean of the following distribution is 24, find the value of . ** [3]**

Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |

No. of Students | 7 | 8 | 10 | 5 |

(c) Using ruler and compass only, construct a such that and and

(i) Construct a semi-circle of

(ii) Construct a cyclic quadrilateral , such that is equidistant from and .** [4]**

Answers:

(a) Let the number of children be

Therefore if children received

Then 1 child received

Let the number of children be

Therefore if children received

Then 1 child received

Given

Therefore the number of children be

(b)

Marks | Mid Term | No. of Students | |

0-10 | 5 | 7 | 35 |

10-20 | 15 | ||

20-30 | 25 | 8 | 200 |

30-40 | 35 | 10 | 350 |

40-50 | 45 | 5 | 225 |

Mean

(c)

**Question 9:**

(a) Priyanka has a recurring deposit account of Rs. 1000 per month at per annum. If she gets Rs. 5550 as interest at the time of maturity, find the total time for which the account was held.** [3]**

(b) In , is parallel to and

(i) Find

(ii) Prove that and are similar

(iii) Find, ** [3]**

(c) The following figure represents a solid consisting of a right circular cylinder with a hemisphere at one end and a cone at the other. Their common radius is . The height of the cylinder and cone is each . Find the volume of the solid.** [4]**

Answers:

(a) Monthly Income

(negative number is not possible)

Therefore

Therefore total time line months or years

(b) (i) In and

is common

SInce

and (alternate angles)

Therefore (by AAA Postulate)

Given

(ii) Consider &

Since

(alternate angles)

(alternate angles)

Therefore (AAA Postulate)

(iii)

(c) Radius , Height of Cylinder Height of Cone

Volume of total solid = Volume of Cone + Volume of Cylinder + Volume of Hemisphere

**Question 10:**

(a) Use remainder theorem to factorize the following polynomial.

** [3]**

(b) In the figure given below is the center of the circle. If and . Find the value of giving reasons.** [3]**

(c) The angle of elevation from a point of the top of the tower , high is and that the tower from the point is . Find the height of the tower , correct to the nearest meter.** [4]**

Answers:

(a)

Let be a factor

Therefore is a factor

Now dividing:

(b) Radius

(given)

Therefore

In since (Isosceles triangle)

Since is Isosceles triangle,

Therefore

Therefore (straight line)

(c) From

From

**Question 11:**

(a) The term of an A.P. is 22 and term is 66. Find the first term and the common difference. Hence find the sum of the series to 8 terms. ** [4]**

(b) Use graph paper for this question

A survey regarding height (in cm) of 60 boys belonging to Class 10 of a school was conducted. The following data was recorded:

Taking 2 cm = height of 10 cm along one axis and 2 cm = 10 boys along the other axis draw an ogive of the above distribution. Use the graph to estimate the following:

Height in cm | 135-140 | 140-145 | 145-150 | 150-155 | 155-160 | 160-165 | 165-170 |

No of boys | 4 | 8 | 20 | 14 | 7 | 6 | 1 |

(i) the median

(ii) the lower quartile

(iii) if above 158 cm is considered as a tall boy in a class, find the number of boys who are tall in the class. ** [6]**

Answers:

(a)

… … … … … (i)

… … … … … (ii)

Solving (i) and (ii)

Substituting in (i)

(b)

Wages | No. workers | Cumulative Frequency (c.f) |

On the graph paper, we plot the following points:

(i) Median

From the graph

(ii) Lower quartile

From the graph

(iii) The number of boys students