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Mathematics Set 1 2017-2018 ICSE Class 10 Question Paper Solution

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Mathematics [Set 1]
Marks: 80Academic Year: 2017-2018
Date: March 2018

Question 1 to Question 4 is compulsory

Attempt any four questions fromQuestion 5 to Question 11


Find the value of and 'y' if:

`2[(x,y),(9 , (y - 5))] + [(6,4),(-7,5)] = [(10,7),(22,15)]`

Concept: Matrices Examples
Chapter: [0.0208] Matrices

Sonia had a recurring deposit account in a bank and deposited Rs. 600 per month for 2 1/2 years. If the rate of interest was 10% p.a., find the maturity value of this account.

Concept: Bank
Chapter: [0.013000000000000001] Banking

Cards bearing numbers 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card which is:

1) a prime number

2) a number divisible by 4.

3) a number that is a multiple of 6.

4) an odd number.

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

The circumference of the base of the cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? (1000 cm3 = 1l)

`["Assume "pi=22/7]`

Concept: Volume of a Cylinder
Chapter: [0.04] Mensuration

If (k – 3), (2k + l) and (4k + 3) are three consecutive terms of an A.P., find the value of k.

Concept: Nature of Roots
Chapter: [0.0202] Quadratic Equations

PQRS is a cyclic quadrilateral. Given ∠QPS = 73°, ∠PQS = 55° and ∠PSR = 82°, calculate:

1) ∠QRS

2) ∠RQS

3) ∠PRQ

Concept: Cyclic Properties
Chapter: [0.032] Circles

If (x + 2) and (x + 3) are factors of x3 + ax + b, find the values of 'a' and `b'.

Concept: Factor Theorem
Chapter: [0.0203] Factorization

Prove that `sqrt(sec^2 theta + cosec^2 theta) = tan theta + cot theta`

Concept: Trigonometric Identities
Chapter: [0.05] Trigonometry

Using a graph paper draw a histogram of the given distribution showing the number of runs scored by 50 batsmen. Estimate the mode of the data:

No. of
4 18 9 6 7 2 4
Concept: Concept of Median
Chapter: [0.06] Statistics

Solve the following inequation, write down the solution set and represent it on the real number line:

–2 + 10x ≤ 13x + 10 < 24 + 10x, x 𝜖 Z

Concept: Representation of Solution on the Number Line
Chapter: [0.020499999999999997] Linear Inequations
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If the straight lines 3x – 5y = 7 and 4x + ay + 9 = 0 are perpendicular to one another, find the value of a.

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

Solve x2 + 7x = 7 and give your answer correct to two decimal places

Concept: Quadratic Equations
Chapter: [0.0202] Quadratic Equations

The 4th term of a G.P. is 16 and the 7th term is 128. Find the first term and common ratio of the series

Concept: Concept of Ratio
Chapter: [0.0204] Ratio and Proportion [0.0204] Ratio and Proportion

A man invests Rs. 22,500 in Rs. 50 shares available at 10% discount. If the dividend paid by the company is 12%, calculate:

1) The number of shares purchased

2) The annual dividend received.

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

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

Use graph paper for this question (Take 2 cm = 1 unit along both x and y-axis). ABCD is a quadrilateral whose vertices are A(2, 2), B(2, –2), C(0, –1) and D(0, 1).

1) Reflect quadrilateral ABCD on the y-axis and name it as A'B'CD

2) Write down the coordinates of A' and B'.

3) Name two points which are invariant under the above reflection

4) Name the polygon A'B'CD

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

Using properties of proportion, solve for x. Given that x is positive:

`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`

Concept: Concept of Proportion
Chapter: [0.0204] Ratio and Proportion

if A = `[(2,3),(5,7)]`, B = `[(0,4),(-1,7)]` and c = `[(1,0),(-1, 4)]`, find AC + B2 – 10C.

Concept: Matrices Examples
Chapter: [0.0208] Matrices

Prove that (1 + cot θ – cosec θ)(1+ tan θ + sec θ) = 2

Concept: Trigonometric Identities
Chapter: [0.05] Trigonometry

Find the value of k for which the following equation has equal roots.

x2 + 4kx + (k2 – k + 2) = 0

Concept: Nature of Roots
Chapter: [0.0202] Quadratic Equations

On a map drawn to a scale of 1: 50,000, a rectangular plot of land ABCD has the following dimensions. AB = 6 cm; BC = 8 cm and all angles are right angles. Find:

1) the actual length of the diagonal distance AC of the plot in km.

2) the actual area of the plot in sq. km.

Concept: Surface Area of a Sphere
Chapter: [0.04] Mensuration [0.04] Mensuration

A(2, 5), B(–1, 2) and C(5, 8) are the vertices of a triangle ABC, `M' is a point on AB such that AM: MB = 1: 2. Find the coordinates of 'M'. Hence find the equation of the line passing through the points C and M

Concept: Equation of a Line
Chapter: [0.021] Co-ordinate Geometry Equation of a Line
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Rs. 7500 were 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 children.

Concept: Quadratic Equations
Chapter: [0.0202] Quadratic Equations

If the mean of the following distribution is 24, find the value of 'a '.

Marks 0-10 10-20 20-30 30-40 40-50
Number of
7 a 8 10 5
Concept: Concept of Median
Chapter: [0.06] Statistics

Using ruler and compass only, construct a ΔABC such that BC = 5 cm and AB = 6.5
cm and ∠ABC = 120°

1) Construct a circum-circle of ΔABC

2) Construct a cyclic quadrilateral ABCD, such that D is equidistant from AB and BC.

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

Priyanka has a recurring deposit account of Rs. 1000 per month at 10% per annum. If she gets Rs. 5550 as interest at the time of maturity, find the total time for which the account was held.

Concept: Computation of Interest
Chapter: [0.013000000000000001] Banking

In ΔPQR, MN is parallel to QR and `(PM)/(MQ) = 2/3`

1) Find `(MN)/(QR)`

2) Prove that ΔOMN and ΔORQ are similar.

3) Find, Area of ΔOMN : Area of ΔORQ

Concept: Similarity of Triangles
Chapter: [0.035] Similarity

The following figure represents a solid consisting of a right circular cylinder with a hemisphere at one end and a cone at the other. This common radius is 7 cm. The height of the cylinder and cone are each of 4 cm. Find the volume of the solid.

Concept: Surface Area of a Right Circular Cone
Chapter: [0.04] Mensuration [0.04] Mensuration

Use Remainder theorem to factorize the following polynomial:

`2x^3 + 3x^2 - 9x - 10`

Concept: Remainder Theorem
Chapter: [0.0203] Factorization

In the figure given below 'O' is the centre of the circle. If QR = OP and ∠ORP = 20°. Find the value of 'x' giving reasons

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

The angle of elevation from a point P of the top of a tower QR, 50 m high is 60o and that of the tower PT from a point Q is 30°. Find the height of the tower PT, correct to the nearest metre

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

The 4th term of an A.P. is 22 and the 15th term is 66. Find the first terns and the common
difference. Hence find the sum of the series to 8 terms.

Concept: Nature of Roots
Chapter: [0.0202] Quadratic Equations
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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:

Height in
135-140 140-145 145-150 150-155 155-160 160-165 165-170
No. of
4 8 20 14 7 6 1

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:

1) the median

2) lower Quartile

3) if above 158 cm is considered as the tall boys of the class. Find the number of boys in the class who are tall.

Concept: Finding the Mode from the Lower Quartile
Chapter: [0.06] Statistics
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