## Maths 2014 Solved Question Paper Previous Year ICSE

Maths 2014 Solved Question Paper Previous Year ICSE for practice so that student of class 10th ICSE can achieve their goals in next exam of council. Even Sample paper for Maths for 2020 exam  also given . Hence by better practice and Solved Question Paper of Previous Year including 2014 is very helpful for ICSE student. By the practice of Maths 2014 Solved Question Paper ICSE Previous Year you can not only get the idea of solving but enhance your skill. Try Also other year except Maths 2014 Solved Question Paper ICSE Previous Year for practice. Because only Maths 2014 Solved Question Paper ICSE Previous Year is not enough for preparation of council exam

Maths 2014 Solved Question Paper Previous Year

(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 2014 Solved Question Paper Previous Year

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

Question 1

(a) Ranbir borrows Rs. 20,000 at 12% per annum compound interest. If he repays Rs. 8400 at the end of the first year and Rs. 9680 at the end of the second year, find the amount of loan outstanding at the beginning of the third year. [3]

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. [4]

Question 2

(b) Shahrukh opened a Recurring Deposit Account in a hank and deposited Rs. 800 per month for if 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 A (-4, 2) and B(3, 6) is divided by point P(x, 3). Also find (i) x (ii) Length of AP. [4]

Hence, rate of interest = 6% p.a.
(c) Let P(x, 3) divide the line segment joining the points A (-4, 2) and B (3, 6) in the ratio k : 1

Question 3

(a) Without using trigonometric tables, evaluate sin2 34° + sin2 56°+ 2 tan 18° tan 72°- cot2 30° [3]
(b) Using the Remainder and Factor Theorem, factorise the following polynomial: x3 + 10x2 – 37x + 26. [3]
(c) In the figure given below, ABCD is a rectangle. AB = 14 cm, BC = 7 cm. From the rectangle, a quarter circle BFEC and a semicircle DGE are removed.
Calculate the area of the remaining piece of the rectangle. (Take π = $\frac { 22 }{ 7 }$[4]

On dividing x3 + 10x2 – 37x + 26 by x – 1, we get x2 + 11x – 26 as the quotient and remainder = 0.

Question 4

(a) 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. [3]
(b) In the figure, ∠DBC = 58°. BD is a diameter of the circle. Calculate :
(i) ∠BDC         (ii) ∠BEC            (iii) ∠BAC
(c) Using graph paper to answer the following questions. (Take 2 cm – 1 unit on both axis)
(i) Plot the points A (- 4, 2) and B (2, 4)
(ii) A’ is the image of A when reflected in the y-axis. Plot it on the graph paper and write the coordinates of A’.
(iii) B’ is the image of B when reflected in the line AA’. Write the coordinates of B’.
(iv) Write the geometric name of the figure ABAB’.
(v) Name a line of symmetry of the figure formed. [4]

(b) In ∆ BCD; ∠DBC = 58°
(i) ∠BCD = 90° (Angle in the semicircle as BD is diameter)
∴ ∠DBC + ∠BCD + ∠BDC = 180°
⇒ 58°+ 90° +∠BDC = 180°
⇒ ∠BDC = 180° – (90° + 58°)
= 180°-148°
= 32° Ans.

(ii) ∠BEC + ∠BDC = 180° ( ∵BECD is a cyclic quadrilateral)

∠BEC = 180°- ∠BDC = 180°-32°
∠BEC = 148°

(iii) ∠BAC = ∠BDC (Angle of same segment are equal)
∠BAC = 32°

(c) (i) See Graph.

(ii) Coordinate of A’ = (4, 2)
(iii) Coordinate of B’ = (2, 0)
(iv) Geometric name = Kite.
(v) AA’ is the symmetric line.

### Maths 2014 Solved Question Paper Previous Year

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

Question 5

(a) 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. [3]

(c) In ∆ABC, ∠ABC = ∠DAC, AB = 8 cm, AC = 4 cm, AD = 5 cm.
(i) Prove that ∆ACD is similar to ∆BCA.
(ii) Find BC and CD
(iii) Find area of ∆ACD : area of ∆ABC. [4]

(a) Given: Printed price of washing machine = Rs. 18,000, Rate of discount = 20%.

Question 6

(a) Find the value of ‘a’ for which the following points A (a, 3), B (2, 1) and C (5, a) are collinear. Hence find the equation of the line. [3]
(b) Salman invests a sum of money in Rs. 50 shares, paying 15% dividend quoted at 20% premium. If his annual dividend is Rs. 600, calculate:
(i) the number of shares he bought.
(ii) his total investment.
(iii) the rate of return on his investment. [3]
(c) The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate :
(i) the radius of the sphere.
(ii) the number of cones recast. (Take π = $\frac { 22 }{ 7 }$) [4]

Question 7

(a) Calculate the mean of the distribution given below using the short cut method.

 Marks 11-20 21-30 31-40 41-50 51-60 61-70 71-80 No. of students 2 6 10 12 9 7 4

(b) In the figure given below, diameter AB and CD of a circle meet at P. PT is a tangent to the circle at T. CD=7.8 cm, PD=5 cm, PD=4 cm.
Find:
(i) AB.
(ii) the length of tangent PT. [3]
(c) Let A = $\begin{bmatrix} 2 & 1 \\ 0 & -2 \end{bmatrix}$, B = $\begin{bmatrix} 4 & 1 \\ -3 & -2 \end{bmatrix}$ and C = $\begin{bmatrix} -3 & 2 \\ -1 & 4 \end{bmatrix}$ . Find A2 + AC-5B.

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