Maths 2018 Solved Question Previous Year Paper ICSE

  Previous Year Question Paper ICSE Maths 2018 Solved

Maths 2018 Solved Question Previous Year Paper 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 2018 is very helpful for ICSE student. By the practice of Maths 2018 Solved Question Paper ICSE Previous Year you can get the idea of solving. Try Also other year except Maths 2018 Solved Question Paper ICSE Previous Year for practice. Because only Maths 2018 Solved Question Paper ICSE Previous Year is not enough for preparation of council exam.

Maths 2018 Solved Question Previous Year Paper ICSE

General Instructions :

  • 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.

  Previous Year Question Paper ICSE Maths 2018 Solved

Section A [40 marks]

(Answer all questions from this Section.)

Question 1

(a) Find the value of x’ and y’ if : [3]
ICSE Maths Question Paper 2018 Solved for Class 10 1
(b) Sonia had a recurring deposit account in a bank and deposited 3600 per month for 244 years. If the rate of interest was 10% p.a., find the maturity value of this account. [3]
(c) 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 : [4]
(i) a prime number.
(ii) a number divisible by 4.
(iii) a number that is a multiple of 6.
(iv) an odd number.

Answer 1

ICSE Maths Question Paper 2018 Solved for Class 10 2
⇒ 2 JC + 6 = 10 ⇒ 2x = 4 ⇒ x = 2
And 2y – 5 = 15 ⇒ 2y = 20 ⇒ y = 10
Hence, the values of x and y are x = 2 and y = 1

(b) Here, amount deposited per month = ₹ 600
Number of months = 2 x 12 + 6 = 30  [∵ v T = 2 \frac{1}{2} years]
Rate of interest = 10% p.a.
ICSE Maths Question Paper 2018 Solved for Class 10 3
Hence, the amount received by Sonia on maturity is ₹ 20325.

(c)Total number of cards in the bag = 10

(i) Total prime numbers = 1 i.e., 2
∴ Required Probability = \frac{1}{10}
(ii) Total numbers divisible by 4 = 5 (i.e., 4, 8, 12, 16, 20]
Required Probability = \frac{5}{10} = \frac{1}{2}
(iii) Total numbers divisible by 6 or multiple of 6 = 3 [i.e., 6, 12, 18]
∴ Required Probability = \frac{3}{10}
(iv) Total odd number = 0
∴ Required Probability = \frac{0}{10} = 0.

Question 2

(a)The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. Find the :
(i) radius of the cylinder
(ii) volume of cylinder, (use π = \frac{22}{7}[3]
(b) If (k – 3), (2k + 1) and (4k + 3) are three consecutive terms of an A.P., find the value of k.
(c) PQRS is a cyclic quadrilateral. Given ∠QPS = 73°, ∠PQS = 55° and ∠PSR = 82 °, calculate: [4]
(i) ∠QRS
(ii) ∠RQS
(iii) ∠PRQ
ICSE Maths Question Paper 2018 Solved for Class 10 4
Answer 2

(a) Let r be the radius of the base of cylindrical vessel and ft = 25 cm be its height.
Now, circumference of the base = 132 cm
2πr = 132
ICSE Maths Question Paper 2018 Solved for Class 10 5
Hence, the radius of the cylinder is 21 cm and volume of the cylinder is 34650 cm3

(b) Here, ft – 3, 2k + 1 and 4k + 3 are three consecutive terms of an A.P.
∴ 2k + 1 – (k – 3) = 4k + 3 – (2k + 1)
⇒ 2k + 1 – k + 3 = 4k + 3 – 2k – 1
⇒ k + 4 = 2k + 2
⇒ 2k – k =4 – 2
⇒ k = 2
Hence, the value of ft is 2.

(c) (i) Since PQRS is a cyclic quadrilateral
∠QPS + ∠QRS – 180°
⇒ 73° + ∠QRS = 180°
⇒ ∠QRS = 180° – 73°
∠QRS = 107°
(ii) Again, ∠PQR + ∠PSR = 180°
∠PQS + ∠RQS + ∠PSR = 180°
55° – ∠RQS + 82° = 180°
∠RQS = 180° – 82° – 55° = 43°
(iii) In ∆PQS, by using angles sum property of a ∆.
∠PSQ + ∠SQP + ∠QPS = 180°
∠PSQ + 55° + 73° = 180°
∠PSQ = 180° – 55° – 73°
∠PSQ = 52°
Now, ∠PRQ = ∠PSQ = 52° [Oop. ∠s of the same segment]
Hence, ∠QRS = 107°, ∠RQS = 43° and
∠PRQ = 52°

Question 3

(a) If (x + 2) and (x + 3) are factors of x3 + ax + b, find the values of ‘a’ and ‘b’. [3]

(b) Prove that ICSE Maths Question Paper 2018 Solved for Class 10 6 [3]
(c) Using a graph paper draw a histogram for the given distribution showing the number of runs scored by 50 batsmen. Estimate the mode of the data : [4]
ICSE Maths Question Paper 2018 Solved for Class 10 7

Answer 3

(a) Given that (x + 2) and (x + 3) are factors of p(x) = x3 + ax + b.
∴ p(- 2) = (- 2)+ o(- 2) + b = 0
⇒ – 8 – 2a + b = 0 => – 2a + b = 8 …….(i)
And p(- 3) = (- 3)3 + a(- 3) + b = 0
⇒ – 27 – 3a + b = 0 => – 3a + b = 27 ……..(ii)
Subtracting (i) from (ii), we obtain
(- 3a 4 – b) – (- 2a + b) = 27 – 8
– 3a + b + 2a – b = 19
-a = 19
⇒ a = 19
From (i), we obtain
– 2(19) + b = 8
– 38 + b = 8
⇒ b = 8 + 38
⇒ b = 46
Hence, the values of a and b are a = 19 and b = 46.
ICSE Maths Question Paper 2018 Solved for Class 10 9
ICSE Maths Question Paper 2018 Solved for Class 10 10

Question 4

(a) Solve the following in equation, write down the solution set and represent it on the real number line: [3]
– 2 + 10x ≤ 13x + 10 < 24 + 10x, x ∈ Z
(b) If the straight lines 3x – 5y = 7 and 4x + ay + 9 = O are perpendicular to one another, find the value of a. [3]
(c) Solve x2 + 7x = 7 and give your answer correct to two decimal places. [4]

Answer 4

(a) Given that :

ICSE Maths Question Paper 2018 Solved for Class 10 11
Thus, the required solution set is :
ICSE Maths Question Paper 2018 Solved for Class 10 12
Using number line, we have
ICSE Maths Question Paper 2018 Solved for Class 10 13

(b) Given lines are
3x – 5y = 1 ……….(i) and 4x + ay + 9 = 0  …………(ii)
Slope of line (i) (m1) =  -\left(\frac{3}{-5}\right)=\frac{3}{5}
Slope of line (ii) (m2) = -\left(\frac{4}{a}\right)

Also, given that two lines are perpendicular to one and another
∴ (m1) (m2) = – 1
⇒ ICSE Maths Question Paper 2018 Solved for Class 10 15
Hence, the value of a = \frac{12}{5} .

(c) Here, x2 + 7x = 7
⇒ x2 + 7x – 7 = 0
ICSE Maths Question Paper 2018 Solved for Class 10 16
ICSE Maths Question Paper 2018 Solved for Class 10 17

Solved Previous Year Question Paper ICSE Maths 2018 

SECTION – B [40 MARKS]

(Attempt any four questions)

Question 5

(a) The 4th term of a G. P. is 16 and the 7h term is 128. Find the first term and common ratio of the series. [3]
(h) A man invests ₹ 22,500 in ₹ 50 shares available at 10% discount. If the dividend paid by the company is 12%c, calculate : [3]
(i) The number of shares purchased.
(ii) The annual dividend received.
(iii) The rate of return he gets on his investment. Give your answer correct to the nearest whole number.
(c) 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). [4]
(i) Reflect quadrilateral ABCD on the y-axis and name it as A’B’CD.
(ii) Write down the coordinates of A’ and B’.
(iii) Name two points which are invariant under the above reflection.
(iv) Name the polygon A’B’CD.

Answer 5

(a) Let a and r be the first term and common ratio of given G.P.
∴ a= 16
⇒ ar3 = 16
and a7 = 128
⇒ a6 = 128
Dividing (ii) and (i), we obtain
ICSE Maths Question Paper 2018 Solved for Class 10 18
a3 = 3
a3 = 23
a = 2

From (i), we have
2(r3) = 16
r3 = 8
r3 = 23
⇒ r = 2
Hence, the first term and common ratio of the given series is 2 and 2.

(b) Total investment = ₹ 22,500
Face value of a share = ₹ 50
Market value of a share = ₹ (50 – 10% of 50) = ₹ (50 – 5) = ₹ 45
∴ No. of shares purchased = \frac{22500}{45} = 500
Annual dividend per share = 12 % of 50
\frac{12}{100} \times 50 = ₹ 6
Total annual dividend = ₹ 6 × 500 = ₹ 3000
Rate of return =\frac{3000}{22500} × 100
= 13.3 %
= 13% (Nearest whole number)
Hence, number of shares purchased are 500, total annual dividend is ₹ 3000 and rate of return on investment is nearly 13 % p. a.
(c) Scale used is : 2 cm = 1 unit along both x and y axis.
(i) Here, vertices of the quadrilateral ABCD are A(2, 2), B(2, -2), C(0, -1) and D(0, 1)
ICSE Maths Question Paper 2018 Solved for Class 10 19
(iii) Two points which are invariant are C and D.
(iv) A’B’CD is a trapezium.

Question 6

(a) Using properties of proportion, solve for x. Given that x is positive : [3]
ICSE Maths Question Paper 2018 Solved for Class 10 20 [3]
(b) ICSE Maths Question Paper 2018 Solved for Class 10 21,ICSE Maths Question Paper 2018 Solved for Class 10 22andICSE Maths Question Paper 2018 Solved for Class 10 23, find AC + B2 – 10C. [3]
(c) Prove that (1 + cot θ – cosec θ) (1 + tan θ + sec θ) = 2 [4]

 

Answer 6

ICSE Maths Question Paper 2018 Solved for Class 10 24
By componendo and Dividendo, we have
ICSE Maths Question Paper 2018 Solved for Class 10 25
Squaring both sides, we have
ICSE Maths Question Paper 2018 Solved for Class 10 26
Hence the value of x is \frac{5}{8}

(b) Given that
ICSE Maths Question Paper 2018 Solved for Class 10 27

(c) L.H.S. = (1 +cot θ – cosec θ) (1 + tan θ + sec θ)
ICSE Maths Question Paper 2018 Solved for Class 10 28

Question 7

(a) Find the value of kfor which the following equation has equal roots. [3]
x2 + 4kx + (k– k + 2) =0
(b) On a map drawn to a scale of 1 : 50,000, a rectangular plot of land ABCD has the following daimentions AB = 6 cm;BC = 8 cm and all angles are right angles. Find :
(i) the actual length of the diagonal distance AC of the plot in km.
(ii) the actual area of the plot in sq. km.
(c) 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 co-ordinates of M’. Hence find the equation of the line passing through the points C and M. [4]

 

Answer 7

(a) Given quadratic equation is :
x2 + 4kx + (k2 – k + 2) = 0
For equal roots, we have
b2 – 4 ac = 0
⇒ (4k)2 – 4(1) (k2-k + 2) = 0
⇒ 16k2 – 4k2 + 4k – 8 = 0
⇒ 12k2 + 4k – 8 = 0
or 3k2 + k – 2 = 0
⇒ 3k2 + 3k – 2k -2 = 0
⇒ 3k(k + 1) – 2(k + 1) = 0
⇒ (k + 1)(3k – 2) = 0
⇒ k + 1=0 or 3k – 2 = 0
k = – 1 or k = \frac{2}{3}

(b) Scale used on the map is 1 : 50,000
Dimensions of a rectangular plot ABCD are AB = 6 cm, BC = 8 cm Since each angle is right angle
∴ By using Pythagoras theorem, we have
ICSE Maths Question Paper 2018 Solved for Class 10 29
(i) Actual length of the diagonal AC = 10 × 50000 cm
\frac{500000}{100000} km
= 5 km
(ii) Area of the rectangular field ABCD on map
= 6 × 8 = 48 cm2
Actual area of the field = 48 × 500000 × 500000
= 12(10)10 sq. cm.
= 12 sq. km.

(c) Coordinates of the vertices of a ∆ ABC are A(2, 5), B(- 1, 2) and C (5, 8). Since M is a point on AB such that AM : MB = 1 : 2
ICSE Maths Question Paper 2018 Solved for Class 10 31

ICSE Maths Question Paper 2018 Solved for Class 10 30
Coordinates M are
ICSE Maths Question Paper 2018 Solved for Class 10 32

Now, equation of the line CM is given as :
ICSE Maths Question Paper 2018 Solved for Class 10 33

Question 8

(a) ₹ 7500 were divided equally among a certain number of children. Had there been 20 less children, each would have received ₹ 100 more. Find the original number of children. [3]
(b) If the mean of the following distribution is 24, find the value of ‘a’. [3]
ICSE Maths Question Paper 2018 Solved for Class 10 34
(i) Using ruler and compass only, construct a ∆ABC such that BC = 5 cm and AB = 6.5 cm and ∠ABC = 120°. [4]
(ii) Construct a circum-circle of ∆ABC.
(iii) Construct a cyclic quadrilateral ABCD, such that D is equidistant from AB and BC.

Answer 8

(a) Total amount = ₹ 7500
Let the number of children be x
∴ Share of each child = ₹ \frac{7500}{x}
According to the statement
ICSE Maths Question Paper 2018 Solved for Class 10 35
(x – 20) (7500 + 100a) = 7500 x
7500x + 100x2 – 150000 – 2000x – 7500x = 0
100x– 200x – 150000 = 0
x– 20a – 1500 = 0
x– 50x + 30x – 1500 = 0
x(x – 50) + 30(x – 50) = 0
(x – 50) (a + 30) = 0
⇒ a = 50 or a = – 30
Rejecting -ve value, because number of children cannot be negative.
∴ x = 50

Hence, the original number of children is 50.
ICSE Maths Question Paper 2018 Solved for Class 10 36
Mean = 24 (given)
∴ \frac{15 a+810}{30+a} = 24
15a + 810 = 720 + 24a
⇒ 24a – 15a = 810 – 720
⇒ 9a = 90
⇒ a = 10
Hence, the value of a is 10.
ICSE Maths Question Paper 2018 Solved for Class 10 37
Steps of Construction :

  1. Draw a line segment AB = 6.5 cm.
  2. At B, construct an angle of 120° and cut off BC = 5 cm.
  3. Join AC, to have ∆ABC.
  4. Draw the perpendicular bisectors of line segments AB and BC.
  5. Let they intersect each other in 0.
  6. With 0 as centre and radius OA or OB or OC, draw the circumcircle of ∆ABC.
  7. Produce perpendicular bisector of line segment AB and let it intersect the circumcircle of ∆ABC at D.
  8. Join AD and CD.
    Thus, quad. ABCD is the required quadrilateral.

Question 9

(a) Priyanka has a recurring deposit account of ₹ 1000 per month at 10% per annum. If she gets ₹ 5550 as interest at the time of maturity, find the total time for which account has held. [3]
(b) In ∆ PQR, MN is parallel to QR and \frac{P M}{M Q} = \frac{2}{3} [3]
ICSE Maths Question Paper 2018 Solved for Class 10 38
(i) Find \frac{M N}{Q R}
(ii) Prove that ∆OMN and ∆ORQ are similar.
(iii) Find, Area of ∆OMN: Area of ∆ORQ
(c) The following figure represents a solid consisting of a right circular cylinder with a hemisphere at one end and a cone at the other. Their common radius is 7 The height of the cylinder and cone are each of 4 cm. Find the volume of the solid. [4]
ICSE Maths Question Paper 2018 Solved for Class 10 39

Answer 9

Amount deposited per month = ₹ 1000

Rate of interest = 10% p.a.
Interest = ₹ 5550
ICSE Maths Question Paper 2018 Solved for Class 10 40
n2 + n = 1332
n2 + n – 1332 = 0
n2 + 37n – 36n – 1332 = 0
n(n + 37) – 36(n + 37) = 0
(n – 36) (n + 37) = 0
n = 36 or n = – 37
Rejecting – ve value of n, we have n = 36
Hence, the total time for which the account was held, was 36 month or 3 years.

(c) Given that:
ICSE Maths Question Paper 2018 Solved for Class 10 41
In ∆PQR, MN is parallel to QR
∴ By using Basic Proportionality theorem, we have
ICSE Maths Question Paper 2018 Solved for Class 10 43
(c) Here, radius of cone = radius of cylinder = radius of hemisphere = 7 cm
Height of cone = 4 cm
Height of cylinder = 4 cm
ICSE Maths Question Paper 2018 Solved for Class 10 44

Question 10

(a) Use Remainder theorem to factorize the following polynomial: [3]
2x3 + 3x– 9x – 10.
(b) 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. [3]
ICSE Maths Question Paper 2018 Solved for Class 10 45

(c) The angle of elevation from a point P of the top of a tower QR, 50 m high is 60 ° and that of the tower PT from a point Q is 30°. Find the height of the tower PT, correct to the nearest metre
ICSE Maths Question Paper 2018 Solved for Class 10 46

Answer 10

(a)  Let p(x) = 2x3 + 3x2 – 9x – 10
Factors of constant term 10 are ± 1, ± 2, ± 5
Put x = 2, we have
p(2) =2(2)3 + 3(2)2 – 9(2) – 10
= 16 + 12 – 18 – 10
= 0
∴ (x – 2) is a factor of p(x)
Put x = – 1, we have
P(-1) =2(-1)3 + 3(-1)2 – 9 (-1) – 10
= – 2 + 3 + 9 – 10 = 0
∴ (x + 1) is a factor of p(x)
Thus, (x + 1) (x – 2) i.e.,x2 – x – 2 is a factor of p(x)
ICSE Maths Question Paper 2018 Solved for Class 10 47
Hence, (x + 1), (x – 2) and (2x + 5) are the factors of given polynomial 2x3 + 3x2 – 9x – 10.
(b) Here, in ∆OPQ
OP = OQ = r
Also, OP = QR [Given]
OP = OQ = QR = r
ICSE Maths Question Paper 2018 Solved for Class 10 48

In ∆OQR, OQ = QR
∠QOR = ∠ORP = 20°
And ∠OQP = ∠QOR + ∠ORQ
= 20° + 20°
= 40°
Again, in ∆ OPQ
∠POQ = 180° – ∠OPQ – ∠OQP
= 180°- 40° – 40°
= 100°
Now, x° + ∠POQ + ∠QOR = 180° [a straight angle]
x° + 100° + 20° = 180°
x° = 180° – 120° = 60°
Hence, the value of x is 60.

(c) Here, Height of the tower (QR) = 50 m
Height of the tower (PT) = h m
Inrt. ∠ed ∆ PQR, ∠RPQ = 60°
ICSE Maths Question Paper 2018 Solved for Class 10 49
Also, inrt. ∠ed ∆ QPT, ∠TQP = 30°
ICSE Maths Question Paper 2018 Solved for Class 10 50
Hence, the required height of tower PT is 17 m (nearest to metre).

Question 11

(a) The 4th term of an A. P. is 22 and 15th term is 66. Find the first term and the common difference. Hence find the sum of the series to 8 terms. [4]
(b) Use Graph paper for this question. [6]
A survey regarding height (in cm) of 60 boys belonging to Class 10 of a school was conducted. The following data was recorded :
ICSE Maths Question Paper 2018 Solved for Class 10 51
Taking 2 cm = height of 10 cm along one axis and 2 cm = 10 boys along the other axis draw and give of the above distribution. Use the graph to estimate the following:
(i) the median
(ii) lower Quartile
(iii) if above 158 cm is considered as the tall boys of the class. Find the number of boys in the class who are tall.

Answer 11

(a) Let a and d be the first term and common difference of the required A.P.
∴ a4 = 22
⇒ a + 3d = 22 ………(i)
And a15 = 66
⇒ a + 14d = 66 ………..(ii)
Subtracting (i) from (ii), we have
(14d – 3d) = 66 – 22
11d = 44
d = 4
From (i), we have
a + 3(4) = 22
a = 22 – 12 = 10
Thus, a = 10 and d = 4
Now, Sn = \frac{n}{2} [2a + (n – 1)d]
⇒ S8\frac{8}{2} [2(10) + (8-1)4]
S8 = 4 [20 + 28]
S8 = 4 x 48 S8 = 192

(b) Given data was recorded as :
ICSE Maths Question Paper 2018 Solved for Class 10 52
Plot the points (140,4), (145,12), (150,32), (155,46), (160,53), (165,59) and (170,60). Join them free hand to get the required ogive.
Now, from the graph, we obtain :

(i) Median height (in cm) = 149.5 cm
(ii) Lower Quartile = 146 cm ‘
(iii) Number of boys who are tall e., height above 158 cm = 60 – 51 = 9.
ICSE Maths Question Paper 2018 Solved for Class 10 53

 Get Other Previous Year Solved Question Papers ICSE Maths

Board – Indian Certificate of Secondary Education (ICSE), www.cisce.org
Class – Class 10
Subject – Maths
Year of Examination – 2019, 2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011, 2010 .

  • ICSE  Maths  Question paper Solved 2019
  • ICSE  Maths  Question paper Solved 2018
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  • ICSE  Maths  Question paper Solved 2016
  • ICSE  Maths  Question paper Solved 2015
  • ICSE  Maths  Question paper Solved 2014
  • ICSE  Maths  Question paper Solved 2013
  • ICSE  Maths  Question paper Solved 2012
  • ICSE  Maths  Question paper Solved 2011
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