ICSE Class 10CISCE
Share
Notifications

View all notifications

Mathematics 2015-2016 ICSE Class 10 Question Paper Solution

Login
Create free account


      Forgot password?
Mathematics
Marks: 80Date: 2016-03-14
Duration: 2h30m

Question 1 to Question 4 is Compulsory

Attempt any four questions from Question 5 to Question 11


[10]1
[3]1.1

Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 - kx + 5 by x - 2, leaves a remainder 7

Concept: Remainder Theorem
Chapter: [0.0203] Factorization
[4]1.2

Given A = `[(2,0),(-1,7)]` and I = `[(1,0),(0,1)]` and `A^2 = 9A+ ml`. Find m

Concept: Matrices Examples
Chapter: [0.0208] Matrices
[3]1.3

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.

Concept: Median of Grouped Data
Chapter: [0.06] Statistics
[10]2
[3]2.1

The slope of a line joining P(6, k) and Q (1-3k, 3) is `1/2` Find

1) k

2) A midpoint of PQ, using the value of ‘k’ found in (1).

Concept: Slope of a Line
Chapter: [0.021] Co-ordinate Geometry Equation of a Line
[4]2.2

Without using trigonometrical tables, evaluate:

`cosec^2 57^@ - tan^2 33^@ + cos 44^@ cosec 46^@ - sqrt2 cos 45^@ -  tan^2 60^@`

Concept: Trigonometry Problems and Solutions
Chapter: [0.05] Trigonometry
[3]2.3

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.

Concept: Area and Volume of Solids - Sphere
Chapter: [0.04] Mensuration
[10]3
[3]3.1

Solve the following inequation, write the solution set and represent it on the number line.

`-3(x - 7) >= 15 - 7x > (x+1)/3`, x ∉ R

Concept: Representation of Solution on the Number Line
Chapter: [0.020499999999999997] Linear Inequations
[4]3.2

In the figure given below, an AD is a diameter. O is the centre of the circle AD is parallel to BC and `angle CBD` = 32°. Find  `angle OBD`

Concept: Number of Tangents from a Point on a Circle
Chapter: [0.032] Circles
[3]3.3

If (3a + 2b) : (5a + 3b) = 18 : 29. Find a : b

Concept: Ratio and Proportion Example
Chapter: [0.0204] Ratio and Proportion
[10]4
[3]4.1

A game of numbers 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 :

1) A perfect square

2) Divisible by 7

Concept: Simple Problems on Single Events
Chapter: [0.07] Probability
[4]4.2

Use graph paper for this question. (Take 2 cm = 1 unit along both x and y-axis.) Plot the points O(0, 0), A(-4, 4), B(-3, 0) and C(0, -3)

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

2) Name the figure OABCB’A’.

3) State the line of symmetry of this figure

Concept: Lines of Symmetry
Chapter: [0.034] Symmetry
[3]4.3

Mr Lalit invested Rs. 5000 at a certain rate of interest, compounded annually for two years. At the end of the first year, it amounts to Rs. 5325. Calculate

1) The rate of interest

2) The amount at the end of the second year, to the nearest rupee.

Concept: Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years
Chapter: [0.011000000000000001] Compound Interest
[10]5
[3]5.1

Solve the quadratic equation x2 -  3(x + 3) = 0; Give your answer correct two significant figures

Concept: Quadratic Equations
Chapter: [0.0202] Quadratic Equations
[4]5.2

A page from the savings bank account of Mrs Ravi is given below.

Date Particulars Withdrawal
(Rs.)
Deposit (Rs.) Balance (Rs.)
April 3rd 2006 B/F     6000
April 7th By cash   2300 8300
April 15th By cheque   3500 11800
May 20th To self 4200   7600
June 10th By cash   5800 13400
June 15th To self 3100   10300
August 13th By cheque   1000 11300
August 25th To self 7400   3900
September 6th
2006
By cash   2000 5900

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.

Concept: Types of Accounts
Chapter: [0.013000000000000001] Banking
[3]5.3

In what time will Rs. 1500 yield Rs. 496.50 as compound interest at 10% per annum compounded annually?

Concept: Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years
Chapter: [0.011000000000000001] Compound Interest
[10]6
[3]6.1

Construct a regular hexagon of side 5 cm. Hence construct all its lines of symmetry and name them.

Concept: Circumscribing and Inscribing a Circle on a Triangle
Chapter: [0.033] Constructions
[4]6.2

In the given figure PQRS is a cyclic quadrilateral PQ and SR produced meet at T

1) Prove ΔTPS ~ ΔTRQ.

2) Find SP if TP = 18 cm, RQ = 4 cm and TR = 6 cm

3) Find the area of quadrilateral PQRS if the area of ΔPTS = 27 cm2.

Concept: Cyclic Properties
Chapter: [0.032] Circles
[3]6.3

Given matrix A = `[(4sin30^@, cos0^@),(cos0^@, 4sin30^@)]`and B = `[(4),(5)]` 

if AX = B

1) Write the order of matrix X.

2) Find the matrix ‘X’.

Concept: Matrices Examples
Chapter: [0.0208] Matrices
[10]7
[4]7.1

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

Concept: Heights and Distances - Solving 2-D Problems Involving Angles of Elevation and Depression Using Trigonometric Tables
Chapter: [0.05] Trigonometry
[6]7.2

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:

1) The median

2) The interquartile range.

3) The number of shooters who obtained a score of more than 85%.

Concept: Median from the Ogive
Chapter: [0.06] Statistics
[10]8
[3]8.1

If `x/a=y/b = z/c` show that `x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`

Concept: Trigonometric Identities
Chapter: [0.05] Trigonometry
[4]8.2

Draw a line AB = 5 cm. Mark a point C on AB such that AC = 3 cm. Using a ruler and a compass only, construct :

1) A circle of radius 2.5 cm, passing through A and C.

2) Construct two tangents to the circle from the external point B. Measure and record the length of the tangents.

Concept: Construction of Tangents to a Circle
Chapter: [0.033] Constructions
[3]8.3

A line AB meets X – axis at A and Y –axis at B. P (4, -1) divides AB in the ratio 1 : 2.

1) Find the coordinates of A and B.

2) Find the equation of the line through P and perpendicular to AB.

Concept: Equation of a Line
Chapter: [0.021] Co-ordinate Geometry Equation of a Line
[10]9
[3]9.1

A dealer buys an article at a discount of 30% from the wholesaler, the marked price being Rs. 6000. The dealer sells it to a shopkeeper at a discount of 10% on the marked price. If the rate of the VAT is 6%, find

1) The price paid by the shopkeeper including the tax.

2) The VAT paid by the dealer

Concept: Introduction to Sales Tax and Value Added Tax
Chapter: [0.013999999999999999] Gst (Goods and Services Tax)
[4]9.2

The given figure represents a kite with a circular and a semicircular motifs stuck on it.
The radius of a circle is 2.5 cm and the semicircle is 2 cm. If diagonals AC and BD are
of lengths 12 cm and 8 cm respectively, find the area of the:

1) Shaded part. Give your answer correct to the nearest whole number.

2) Unshaded part

Concept: Simple Applications of All Co-ordinate Geometry.
Chapter: [0.021] Co-ordinate Geometry Equation of a Line
[3]9.3

A model of a ship is made to a scale 1: 300

1) The length of the model of the ship is 2 m. Calculate the lengths of the ship.

2) The area of the deck ship is 180,000 m2. Calculate the area of the deck of the model.

3) The volume of the model in 6.5 m3. Calculate the volume of the ship.

Concept: Area and Volume of Solids - Sphere
Chapter: [0.04] Mensuration
[10]10
[3]10.1

Mohan has a recurring deposit account in a bank for 2 years at 6% p.a. simple interest. If he gets Rs. 1200 as interest at the time of maturity find:

1) the monthly instalment

2) the amount of maturity

Concept: Types of Accounts
Chapter: [0.013000000000000001] Banking
[4]10.2

The histogram below represents the scores obtained by 25 students in a mathematics mental test. Use the data to :

1) Frame a frequency distribution table

2) To calculate mean

3) To determine the Modal class

Concept: Graphical Representation of Histograms
Chapter: [0.06] Statistics
[3]10.3

A bus covers a distance of 240 km at a uniform speed. Due to heavy rain, its speed gets reduced by 10 km/h and as such it takes two hrs longer to cover the total distance. Assuming the uniform speed to be ‘x’ km/h, form an equation and solve it to evaluate ‘x’.

Concept: Heights and Distances - Solving 2-D Problems Involving Angles of Elevation and Depression Using Trigonometric Tables
Chapter: [0.05] Trigonometry
[10]11
[3]11.1

Prove that `cosA/(1+sinA) + tan A =  secA`

Concept: Trigonometric Identities
Chapter: [0.05] Trigonometry
[4]11.2

Use ruler and compasses only for the following questions. All constructions lines and arcs must be clearly shown

Construct a  ABC in which BC = 6.5 cm,  ABC = 60°, AB = 5 cm.

Concept: Circumscribing and Inscribing a Circle on a Triangle
Chapter: [0.033] Constructions

Use ruler and compasses only for the following questions. All constructions lines and arcs must be clearly shown.

Construct the locus of points at a distance of 3.5 cm from A.

Concept: Loci Examples
Chapter: [0.031] Loci

Use ruler and compasses only for the following questions. All constructions lines and arcs must be clearly shown

Construct the locus of points equidistant from AC and BC.

Concept: Loci Examples
Chapter: [0.031] Loci

Use ruler and compasses only for the following questions. All constructions lines and arcs must be clearly shown

Mark 2 points X and Y which are a distance of 3.5 cm from A and also equidistant from AC and BC. Measure XY.

Concept: Loci Examples
Chapter: [0.031] Loci
[3]11.3

Ashok invested Rs. 26,400 on 12%, Rs. 25 shares of a company. If he receives a dividend of Rs. 2,475. Find the :

1) number of shares he bought

2) The market value of each share

Concept: Shares and Dividends
Chapter: [0.012] Shares and Dividends

Request Question Paper

If you dont find a question paper, kindly write to us





      View All Requests

Submit Question Paper

Help us maintain new question papers on Shaalaa.com, so we can continue to help students




only jpg, png and pdf files

CISCE previous year question papers Class 10 Mathematics with solutions 2015 - 2016

     CISCE Class 10 Maths question paper solution is key to score more marks in final exams. Students who have used our past year paper solution have significantly improved in speed and boosted their confidence to solve any question in the examination. Our CISCE Class 10 Maths question paper 2016 serve as a catalyst to prepare for your Mathematics board examination.
     Previous year Question paper for CISCE Class 10 Maths-2016 is solved by experts. Solved question papers gives you the chance to check yourself after your mock test.
     By referring the question paper Solutions for Mathematics, you can scale your preparation level and work on your weak areas. It will also help the candidates in developing the time-management skills. Practice makes perfect, and there is no better way to practice than to attempt previous year question paper solutions of CISCE Class 10.

How CISCE Class 10 Question Paper solutions Help Students ?
• Question paper solutions for Mathematics will helps students to prepare for exam.
• Question paper with answer will boost students confidence in exam time and also give you an idea About the important questions and topics to be prepared for the board exam.
• For finding solution of question papers no need to refer so multiple sources like textbook or guides.
S
View in app×