## Maths 2015 Solved Question Paper Previous Year ICSE

Maths 2015 Solved Question Paper Previous Year ICSE for practice so that student of class 10th ICSE can achieve their goals in next exam of council. Sample paper for Maths for 2020 exam  also given . Hence by better practice and Solved Question Paper of Previous Year including 2015 is very helpful for ICSE student. By the practice of Maths 2015 Solved Question Paper ICSE Previous Year you can get the idea of solving. Try Also other year except Maths 2015 Solved Question Paper ICSE Previous Year for practice. Because only Maths 2015 Solved Question Paper ICSE Previous Year is not enough for preparation of council exam.

### Maths 2015 Solved Question Paper Previous Year ICSE

(Two hours and a half)

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 from 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.

### Maths 2015 Solved Question Paper Previous Year ICSE

SECTION A [40 Marks] (Answer all questions from this Section.)

Question 1

(a) A shopkeeper bought an article for Rs. 3,450. He marks the price of the article 16% above the cost price. The rate of sales tax charged on the article is 10%. Find the :
(i) marked price of the article.
(ii) price paid by a customer who buys the article. 

(b) Solve the following inequation and write the solution set:
13x – 5 < 15x + 4 < 7x + 12, x ε R
Represent the solution on a real number line. 

(c) Without using trigonometric tables evaluate: (a) (b) (c) Question 2

(a) If A = $\begin{bmatrix} 3 & x \\ 0 & 1 \end{bmatrix}$ and $\begin{bmatrix} 9 & 16 \\ 0 & -y \end{bmatrix}$, , find x and y when A= B.
(b) The present population of a town is 2,00,000. Its population increases by 10% in the first year and 15% in the second year. Find the population of the town at the end of the two years. 
(c) Three vertices of a parallelogram ABCD taken in order are A(3, 6), B(5, 10) and C(3, 2) find:
(i) the coordinates of the fourth vertex D.
(ii) length of diagonal BD.
(iii) equation of side AB of the parallelogram ABCD. 

(a) (b) (c) Let the coordinate of D be (x, y). In a parallelogram, mid point of diagonal AC co-incides with the mid-point of diagonal BD.  Question 3

(a) In the given figure, ABCD is a square of side 21 cm. AC and BD are two diagonals of the square. Two semi circles are drawn with AD and BC as diameters. Find the areq of the shaded region. (Take π = $\frac { 22 }{ 7 }$ ). 
(b) The marks obtained by 30 students in a class assessment of 5 martks is given below:  

 Marks 0 1 2 3 4 5 No. of Students 1 3 6 10 5 5

Calculate the mean, median and mode of the above distribution.
(c) In the figure given below, O is the centre of the circle and SP is a tangent. If ∠SRT = 65°, find the value of x, y and z. Answer 3

(a) Given : Side = 21 cm,
Let Diagonal of the square = √2 (side) (b) Mode = 3 marks (as highest frequency is 10)
(c) In ∆ OSP,
50° + 90° +z = 180°
∴ z = 40°

Question 4

(a) Katrina opened a recurring deposit account with a Nationalised Bank for a period of 2 years. If the hank pays interest at the rate of 6% per annum and the monthly installment is 1,000, find the:
(i) interest earned in 2 years.
(ii) matured value. 
(b) Find the value of ‘K’ for which x = 3 is a solution of the quadratic equation, (K + 2) x2 – Kx + 6 = 0.
Thus find the other root of the equation. 
(c) Construct a regular hexagon of side 5 cm. Construct a circle circumscribing the hexagon. All traces of construction must be clearly shown. 

(a) (b)  (c) Steps of Construction: (i) Using the given data, construct the regular hexagon ABCDEF with each side equal to 5 cm.
(ii) Draw the perpendicular bisectors of sides AB and AF which intersect each other at point O.
(iii) With O as centre and OA as radius draw a circle which will pass through all the vertices of the regular hexagon ABCDEF.

### Maths 2015 Solved Question Paper Previous Year

SECTION B [40 Marks] Answer any four Questions in this Section.

Question 5

(a) Use a graph paper for this question taking 1 cm = 1 unit along both the x and y axis :
(i) Plot the points A(0, 5), B(2, 5), C(5, 2), D(5, -2), E(2, -5) and F(0, -5).
(ii) Reflect the points B, C, D and E on the y-axis and name them respectively as B’, C’, D’and E’
(iii) Write the coordinates of B’, C’, D’and E’.
(iv) Name the figure formed by BCDE E’D’CR’.
(v) Name a line of symmetry for the figure formed. 

(b) Virat opened a Saving Bank account in a bank on 16th April 2010. His pass book shows the following entries:

 Date Particulars Withdrawal (Rs) Deposit (Rs) Balance (Rs) April 16, 2010 By cash — 2500 2500 April 28th By cheque — 3000 5500 May 9th To cheque 850 — 4650 May 15th By cash — 1600 6250 May 24th To cash 1000 — 5250 June 4th To cash 500 — 4750 June 30th By cheque — 2400 7150 July 3rd By cash — 1800 8950

Calculate the interest Virat earned at the end of 31st July, 2010 at 4% per annum interest. What sum of money will he receive if he closes the account on 1st August, 2010 ? 

(a) (i) See diagram below. (ii) Coordinates:
B’ (-2, 5), C’ (-5, 2),
D’ (-5, -2), E’ (-2, -5)
(iii) Octagon
(iv) x-axis or y-axis.

(b) Question 6

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

(b) In the given figure ABC is a triangle and BC is parallel to the y-axis. AB and AC intersects the y-axis at P and Q respectively. (i) Write the coordinates of A.
(ii) Find the length of AB and AC.
(iii) Find the ratio in which Q divides AC.
(iv) Find the equation of the line AC. 

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