# Maths 2016 Solved Question Paper Previous Year ICSE

**Maths 2016 Solved Question Paper Previous Year ICSE**

**Maths 2016 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 **2016** is very helpful for** ICSE** student. By the practice of **Maths 2019 Solved Question Paper ICSE Previous Year **you can get the idea of solving. Try Also other year except** Maths 2016 Solved Question Paper ICSE Previous Year** for practice. Because only **Maths 2016 Solved Question Paper ICSE Previous Year** is not enough for preparation of council exam.

**Solved Question Paper Previous Year ****Maths 2016 **

## (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.

**Solved Question Paper Previous Year ****Maths 2016 **

**SECTION A [40 Marks]**

*(Answer all questions from this Section.)*

**Question 1**

**(a)** Using remainder theorem, find the value ofk if on dividing 2x^{3} + 3x^{2 }– kx + 5 by x-2, leaves a remainder 7. **[3]**

**(b)** Given A = and I = and A^{2}=9A+mI. Find m. **[4]**

**(c)** The mean of following numbers is 68. Find the value of ‘x’: 45, 52, 60, x, 69, 70, 26, 81 and 94. Hence estimate the median. **[3]**

**Answer 1**

**(a)**

**(b)**

**(c)**

**Question 2**

**(a)** The slope of a line joining P(6, k) and Q(1 – 3k, 3) is . Find : **[3]**

(i) k

(ii) Midpoint of PQ, using the value of ‘k’ found in (i).

**(b)** Without using trigonometrical tables, evaluate :

cosec^{2} 57° – tan^{2} 33° + cos 44° cosec 46° – √2 cos 45° – tan^{2} 60° **[4]**

**(c)** A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones. **[3]**

**Answer 2**

**(a) (i)**

**(ii)**

**(b)**

**(c)**

**Question 3**

**(a)** Solve the following inequation, write the solution set and represent it on the number line.** [3]**

**(b)** In the given figure below, AD is a diameter. O is the centre of the circle. AD is parallel to BC and ∠CBD = 32°.

Find :

(i) ∠OBD

(ii) ∠AOB

(iii) ∠BED **[4]**

**(c)** If (3a + 2b) : (5a + 3b) = 18 : 29. Find a : b. ** [3]**

**Answer 3**

**(a)**

**(b)**

**(c)**

**Question 4**

**(a)** A game of number has cards marked with 11, 12, 13, 40. A card is drawn at random. Find the Probability that the number on the card drawn is :

(i) A perfect square

(ii) Divisible by 7. **[3]**

**(b)** Use graph paper for this question.

(Take 2 cm = 1 unit along both x and y axis).

Plot the point O (0, 0), A (-4, 4), B (-3, 0) and C (0, -3).

(i) Reflect points A and B on the y axis and name them A’and B’respectively. Write down their coordinates.

(ii) Name the figure OABCB’A’.

(iii) State the line of symmetry of this figure. **[4]**

**(c)** Mr. Lalit invested Rs. 5,000 at a certain rate of interest, compounded annually for two years. At the end of first year it amounts to Rs. 5,325. Calculate :

(i) The rate of interest.

(ii) The amount at the end of second year, to the nearest rupee. **[3]**

**Answer 4**

**(a)** Total number of all possible outcomes = 30.

**(b)** (i) A'(4,4) and B'(3, 0)

(ii) Arrow Head

(iii) y-axis is the line of symmetry.

**(c)** Given : Principal = Rs. 5,000, Time = 2 years, After one year amount = Rs. 5,325

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

**Question 5**

**(a)** Solve the quadratic equation x^{2} – 3(x + 3) = 0; Give your answer correct to two significant figures. **[3]**

**(b)** A page from the saving bank account of Mrs. Ravi is given below :

She closed the account on 30th September, 2006. Calculate the interest Mrs. Ravi earned at the end of 30th September, 2006 at 4.5% per annum interest. Hence find the amount she receives on closing the account.** [4]**

**(c)** In what time will Rs. 1500 yield Rs. 1996.50 as compound interest at 15% per annum compounded annually ?** [3]**

**Answer 5**

**(a)** Given:

x^{2} – 3 (x +3) = 0

x^{2} – 3x – 9 = 0

**(b)** For interest as per the entries of the pasbook, we have

Month |
Minimum balance between 10th day and the last day (in Rs.) |

April | 8,300 |

May | 7,600 |

June | 10,300 |

July | 10,300 |

August | 3,900 |

Total _{%} |
40,400 |

**(c)**

**Question 6**

**(a)** Construct a regular hexagon of side 5 cm. Hence construct all its lines of symmetry and name them. **[3]**

**(b)** In the given figure PQRS is a cyclic quadrilateral PQ and SR produced meet at T. **[4]**

(i) Prove ∆ TPS ~ ∆ TRQ.

(ii) Find SP if TP = 18 cm, RQ = 4 cm and TR = 6 cm.

(iii) Find area of quadrilateral PQRS if area of ∆ PTS = 27cm^{2}.

**Answer 6**

**(a)** **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, BC, CD, DE, EF and FA which intersect AB at V, BC at X, CD at Y, DE at U, EF at W and FA at Z.

(iii) Join the mid points of opposite sides i.e., UV, WX and YZ and the diagonals passing through the centres i.e., AD, BE and CF.

Hence A regular hexagon has six lines of symmetry – UV, WX, YZ, AD, BE, CF.

**(b)**

**(c)**

**Question 7**

**(a)** An aeroplane at an altitude of 1500 metres finds that two ships are sailing towards it in the same direction. The angles of depression as observed from the aeroplane are 45° and 30° respectively. Find the distance between the two ships. **[4]**

**(b)** The table shows the distribution of the scores obtained by 160 shooters in a shooting competition. Use a graph sheet and draw an ogive for the distribution.

(Take 2 cm = 10 scores on the X axis and 2 cm = 20 shooters on the Y-axis).

Scores |
0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |

No. of shooters |
9 | 13 | 20 | 26 | 30 | 22 | 15 | 10 | 8 | 7 |

**Use your graph to estimate the following:**

(i) The median.

(ii) The inter quartile range.

(iii) The number of shooters who obtained a score of more than 85%.** [6]**

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