# Maths 2019 Solved Question Previous Year Paper ICSE

**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

**Answer 1**

Total investment = ₹ 4500

Face value of a share = ₹ 100

Discount = 10%

∴ Market value of a share = ₹ (100 – 10) = ₹ 90

Now, Number of shares purchased =

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 x^{3} + x^{2} – 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.

**Answer 2**

(a) Given polynomial is p(x) = x^{3} + x^{2} – 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, x^{3} + x^{2} – 4x + 4 = x^{2}(x +1) – 4(x + 1)

= (x + 1) (x^{2} – 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]**

(i) radius of the cylinder

(ii) curved surface area of the cylinder

Take π = 3.1

**Answer 3**

(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 cm^{2}

**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 x^{2} – 4x – 8 = 0

Give your answer correct to three significant figures.

(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

**Answer 4**

(a) Here,

⇒ (K + 3) (2K – 3) = (K + 2) (3K – 7).

⇒ 2K^{2} – 3K + 6K – 9 = 3K^{2 }– 7K + 6K – 14

⇒ K^{2} – 4K – 5 = 0

⇒ (K – 5) (K + 1) = 0

⇒ K = 5 or K = – 1

(b) Given quadratic equation is x^{2} – 4x – 8 = 0

By using quadratic formula, we have

=

= 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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