## Maths 2019 Solved Question Previous Year Paper ICSE

Maths 2019 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 2019 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 2019 Solved Question Paper ICSE Previous Year for practice. Because only Maths 2019 Solved Question Paper ICSE Previous Year is not enough for preparation of council exam.

## Maths 2019 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.

### Maths 2019 Solved Question Previous Year Paper ICSE

Section A [40 marks]
(Answer all questions from this Section.)

Question 1

(a) Solve the following in equation and write down the solution set : [3]
11x – 4 < 15x + 4 ≤ 3x + 14, x ∈ W
Represent the solution on a real number line.
(b) A man invests 4500 in shares of a company which is paying 7.5% dividend. [3]
If 100 shares are available at a discount of 10%. Find :
(i) Number of shares he purchases.
(ii) His annual income.
(c) In a class of 40 students, marks obtained by the students in a class test (out of 10) are given below : [4]

Calculate the following for the given distribution :
(i) Median
(ii) Mode

Total investment = ₹ 4500
Face value of a share = ₹ 100
Discount = 10%
∴ Market value of a share = ₹ (100 – 10) = ₹ 90
Now, Number of shares purchased = $\frac{4500}{90}=50$
Annual income =
= ₹ 375

Here,
Marks corresponding to cumulative frequency 20 is 6
Thus, the required median is 6.
Clearly, 6 occurs 10 times which is maximum.
Hence, mode is 6.

Question 2

(a) Using the factor theorem, show that (x – 2) is a factor of x3 + x2 – 4x – 4. [3]
Hence, factorise the polynomial completely.
(b) Prove that :
(cosec θ – sin θ) (sec θ – cos θ) (tan θ + cot θ) = 1 [3]
(c) In an Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively.
Find the : [4]
(i) first term
(ii) common difference
(iii) sum of the first 20 terms.

(a) Given polynomial is p(x) = x3 + x2 – 4x – 4
x – 2 is its factor, if p(2) = 0
p(2) = (2)3 + (2)2 – 4(2) – 4 = 8 + 4 – 8 – 4 = 0
Thus, x – 2 is a factor of p(x).
Now, x3 + x2 – 4x + 4 = x2(x +1) – 4(x + 1)
= (x + 1) (x2 – 4)
= (x + 1) (x + 2) (x – 2)
Hence, the required factors are (x + 1), (x + 2) and (x – 2).
L.H.S. = (cosec θ – sin θ) (sec θ – cos θ) (tan θ + cot θ)

Hence, first term is – 1, common difference is 3 and sum of the first 20 terms is 550.

Question 3

(a) Simplify :

(b) M and N are two points on the X axis and Y axis respectively. [3]
P(3, 2) divides the line segment MN in the ratio 2 : 3.
Find :
(i) the coordinates of M and N
(ii) slope of the line MN.
(c) A solid metallic sphere of radius 6 cm is melted and made into a solid cylinder of height 32 cm. Find the : [4]
(ii) curved surface area of the cylinder
Take π = 3.1

(b) Let the coordinates of M and N be (x, 0) and (0, y)

Thus, the coordinates of M and N are M(5,0) and N(0, 5).

Hence, the slope of the line MN is – 1.

(C) Radius of metallic sphere (R) = 6 cm
Height of cylinder (h) = 32 cm
Volume of cylinder = Volume of metallic sphere

Curved Surface area of the year = 2πrh
= 2 × 3.1 × 3 × 32 = 595.2 cm2

Question 4

(a) The following numbers, K + 3, K + 2, 3K – 7 and 2K – 3 are in proportion. Find K. [3]
(b) Solve for x the quadratic equation x2 – 4x – 8 = 0
(c) Use ruler and compass only for answering this question. [4]
Draw a circle of radius 4 cm. Mark the center as 0. Mark a point P outside the circle at a distance of 7 cm from the center. Construct two tangents to the circle from the external point P. Measure and write down the length of any one tangent

(a) Here, $\frac{K+3}{K+2}=\frac{3 K-7}{2 K-3}$
⇒ (K + 3) (2K – 3) = (K + 2) (3K – 7).
⇒ 2K2 – 3K + 6K – 9 = 3K– 7K + 6K – 14
⇒ K2 – 4K – 5 = 0
⇒ (K – 5) (K + 1) = 0
⇒ K = 5 or K = – 1

(b) Given quadratic equation is x2 – 4x – 8 = 0
By using quadratic formula, we have

$2(1 \pm \sqrt{3})=2(1 \pm 1.73205)=2(2.73205) \text { or } 2(-0.73205)$
= 5.46410 or – 1.4641
= 5.46 or – 1.46

(c) Steps of Construction :

1. Draw a circle of radius 4 cm and centre 0.
2. Draw a radius and produce it to P, such that
OP = 7 cm.
3. Bisect OP at M.
4. With M as centre and MP as radius, draw a circle to intersect the given circle at Q and R.
5. Join PQ and PR.
PQ and PR are the required tangents and length of the tangents is 5.74 cm.

### Maths 2019 Solved Question Previous Year Paper ICSE

Section – B [40 Marks]
(Attempt any four questions)

Question 5

(a) There are 25 discs numbered 1 to 25. They are put in a closed box and shaken thoroughly. A disc is drawn at random from the box.
Find the probability that the number on the disc is : [3]
(i) an odd number
(ii) divisible by 2 and 3 both
(iii) a number less than 16.
(b) Rekha opened a recurring deposit account for 20 months. The rate of interest is 9% per annum and Rekha receives 441 as interest at the time of maturity. Find the amount Rekha deposited each month.
(c) Use a graph sheet for this question. [4]
Take 1 cm = 1 unit along both x and y axis.
(i) Plot the following points :
A(0, 5), B(3, 0), C(1, 0) and D(1, -5)
(ii) Reflect the points B, C and D on the y-axis and name them as B’, C’, D’ respectively.
(iii) Write down the coordinates of B’, C’ and D’.
(iv) Join the points A, B, C, D, D’, C’, B’, A in order and give a name to the closed figure ABCDD’C’B’.

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