# ICSE Mathematics 2021 Specimen Paper for Class-10

**ICSE Mathematics 2021 Specimen** Paper for Class-10 Solved based on Further reduced syllabus. **Specimen Mathematics** **ICSE** Class-10 Paper for 2021. Model **Specimen Paper** for **ICSE** Board Class-10 **Mathematics**. Hence by better practice and Model Sample Paper** ICSE** **Mathematics** **2021 Specimen** is very helpful for ICSE student appearing in 2020 exam of council. Visit official website** www.cise.org **for detail information about ICSE Class-10 Mathematics.

**ICSE Mathematics 2021 Specimen** Paper for Class-10 Solved

based on Further reduced syllabus

**ICSE Mathematics 2021 Specimen** Paper for Class-10 Solved

**(Two hours and a half)**

- 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 part of the answer.
- Omission of essential working will result in loss of marks.
- The intended marks for questions or parts of questions are given in brackets [ ].

Mathematical tables are provided.

**SECTION A (40 Marks)**

**ICSE Mathematics 2021 Specimen** Paper for Class-10 Solved

**Attempt all questions from this Section.**

**Question- 1**

**(a) **Sonia had a recurring deposit account in a bank and deposited Rs. 600 per month for 2 ½ years. If the rate of interest was 10% p.a., find the maturity value of this account

** (b )**

** (c)**

The marked price of an article is 12500. A dealer in Kolkata sells the article to consumer in the same city at a profit of 8%. If the rate of GST is 18%, find

(i) the selling price (excluding tax) of the article

(ii) IGST, CGST and SGST paid by the dealer to the Central and State Government

(iii) the amount which the consumer pays for the article.

**Question- 2**

(a) The area of the curved surface of a cylinder is 4400 cm^{2}, and the circumference of its base is 110 cm. Find

(i) the height of the cylinder.

(ii) the volume of the cylinder.

(b)

A cone of maximum volume is curved out of a block of wood of size 20 cm x 10 cm x 10 cm. Find the volume of the remaining wood.

(c)

A bag contains 5 black, 7 red and 3 white balls. A ball is drawn at random from the bag, find the probability that the ball drawn is:

(i) red

(ii) black or white

(iii) not black.

**Question- 3**

(a )Express the ratios cos A, tan A and sec A in terms of sin A.

(b) A die is thrown once. What is the probability that the

(i) number is even

(ii) number is greater than 2 ?

**Question-4**

(a)

A river is 60 m wide. A tree of unknown height is on one bank. The angle of elevation of the top of the tree from the point exactly opposite to the foot of the tree on the other bank is 30°. Find the height of the tree.

(b)

Find the co-ordinates of the mid-point of the line segments joining the following pairs of points:

(i) (2, – 3), ( – 6, 7)

(ii) (5, – 11), (4, 3)

(iii) (a + 3, 5b), (2a – 1, 3b + 4)

**SECTION B (40 Marks)**

**Attempt any four questions from this Section**

**Question- 5**

(a) In the figure (i) given below, AB is a diameter of the circle APBR. APQ and RBQ are straight lines, ∠A = 35°, ∠Q = 25°. Find (i) ∠PRB (ii) ∠PBR (iii) ∠BPR.

(b) In the figure (ii) given below, it is given that ∠ABC = 40° and AD is a diameter of the circle. Calculate ∠DAC.

**Question- 6**

(a)

In the adjoining figure, ABCD is a parallelogram. P is a point on BC such that BP : PC = 1 : 2 and DP produced meets AB produced at Q. If area of ∆CPQ = 20 cm², find

(i) area of ∆BPQ.

(ii) area ∆CDP.

(iii) area of || gm ABCD.

(b)

On a map drawn to a scale of 1 : 25000, a rectangular plot of land, ABCD has the following measurements AB = 12 cm and BG = 16 cm.

Calculate:

(i) the distance of a diagonal of the plot in km.

(ii) the area of the plot in sq. km.

**Question- 7**

**(a)**

Marks obtained by 40 students in a short assessment are given below, where a and b are two missing data.

If the mean of the distribution is 7.2, find a and b.

(b)

From the following frequency distribution, find :

(i) the median

(ii) lower quartile

(iii) upper quartile

(iv) inter quartile range

**Question- 8**

**(a)**

If point A is reflected in the y-axis, the co-ordinates of its image A_{1}, are (4, – 3),

(i) Find the co-ordinates of A

(ii) Find the co-ordinates of A_{2}, A_{3} the images of the points A, A_{1}, Respectively under reflection in the line x = – 2

(b)

If point A is reflected in the y-axis, the co-ordinates of its image A_{1}, are (4, – 3),

(i) Find the co-ordinates of A

(ii) Find the co-ordinates of A_{2}, A_{3} the images of the points A, A_{1}, Respectively under reflection in the line x = – 2

**Question- 9**

(a) The difference between the squares of two numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.

(b) From a pack of 52 cards, a blackjack, a red queen and two black kings fell down. A card was then drawn from the remaining pack at random. Find the probability that the card drawn is

(i) a black card

(ii) a king

(iii) a red queen.

**Question- 10**

**(**a)

Show that (x – 2) is a factor of 3x^{2} – x – 10. Hence factorise 3x^{2} – x – 10.

(b)

If P is the solution set of – 3x + 4 < 2x – 3, x ∈ N and Q is the solution set of 4x – 5 < 12, x ∈ W, find

(i) P ∩ Q

(ii) Q – P.

**Solutions of ICSE Maths Specimen Paper -2021 **

**Ans-1**

(a)

Principal (n)= 2.5 year= 2.5*12 month=30 months

Principal (P)= Rs 600

Rate = 10% p.a.

Maturity Value= ……………

S.I.= P*n(n+1)*r*1/(2*100*12)

” ” = 600*30*31/2*100*12

Simple Interest .= RS 2335

Now Maturity Value = P*n+S.I.

Maturity Value=600*30+2325

…………………=RS 20325 Ans

(b)

(c)

(i) the selling price (excluding tax) of the article

12500 + 12500 x 8/100

12500 + 1000

13500

(ii) IGST, CGST and SGST paid by the dealer to the Central and State Government

IGST, is nil due to intra state

CGST paid by the dealer to the Central Government

13500 x 9/100

1215

SGST paid by the dealer to the State Government

13500 x 9/100

1215

(iii) the amount which the consumer pays for the article.

Amount = Selling price + CGST + SGST

13500 + 1215 +1215

15930

**Ans-2**

**(a)**

Area of the curved surface of a cylinder = 4400 cm^{2}

Circumference of base = 110 cm

**(b)**

Size of wooden block = 20 cm × 10 cm × 10 cm

Maximum diameter of the cone = 10 cm

and height (h) = 20 cm

**(c)**

In a bag,

Number of black balls = 5

and Number of red balls = 7

while number of white balls = 3

Total number of balls in the bag

= 5 + 7 + 3 = 15

(i) Probability of red balls

**Ans-3**

(a)

(b)

Dice is thrown once

Sample space = {1, 2, 3, 4, 5, 6}

(i) No. of ways in favour = 3

(∵ Even numbers are 2, 4, 6)

Total ways = 6

Probability = ^{6}⁄_{3} = ^{1}⁄_{2}

(ii) No. of ways in favour = 4

(Numbers greater than 2 are 3, 4, 5, 6)

Total ways = 6

Probability = ^{4}⁄_{6} = ^{2}⁄_{3}

**Ans-4**

(a)

Let AB be the tree and BC is the width of the river

and C is the point exactly opposite to B on the other bank

and angle of elevation is 30°.

= 36.640 = 36.64 m

Height of tree= 36.64 m

(b)

(i) Co-ordinates of the mid-point of (2, -3), ( -6, 7)

**Ans-5**

(a)

(i) ∠PRB = ∠BAP

(Angles in the same segment of the circle)

∴ ∠PRB = 35° (∵ ∠BAP = 35° given)

(ii) In ∆PRQ,

Ans-6

(a)

In the figure, ABCD is a parallelogram.

P is a point on BC such that BP : PC = 1 : 2

and DP is produced to meet ABC produced at Q.

Area ∆CPQ = 20 cm²

**(b)**

**Scale factor (k) = ^{1}⁄_{2500}**

Measurements of plot ABCD on the map are

AB = 12 cm and BC = 16 cm.

**Ans-7**

**(a)**

2a+15-3a=14

a=1

similar a+b=5

1+b=5

b=4

Solving (i) and (ii)

get a=1 , b= 4

**(b)**

**Writing frequency distribution in c.f. table :
**

**Ans-8**

**(a)**

**(i) ∵ A is reflected in the y-axis and its image is A _{1} (4, -3)**

**Co-ordinates of A will be (-4, -3)
**

**Ans-9**

**(a)**

**Let the larger number = x
then smaller number = y
Now according to the condition,
**

**(b)**

In a pack of 52 cards, a blackjack, a red queen, two black being felt down.

Then number of total out comes = 52 – (1 + 1 + 2) = 48

(i) Probability of a black card (which are 26 – 3 = 23) = ^{23}⁄_{48}

(ii) Probability of a being (4 – 2 = 2) = ^{2}⁄_{48} = ^{1}⁄_{24}

(iii) Probability of a red queen = (2 – 1 = 1) = ^{1}⁄_{18}

**Ans-10**

**(a)**

**Let x – 2 = 0, then x = 2
Substituting the value of x in f(x),
**

**(b)**

**(i) – 3 x + 4 < 2 x – 3
– 3x – 2x < – 3 – 4 => – 5x < – 7
**

**Thanks**