Maths Semester-1 ICSE Specimen Paper Solved Class-10 for practice. Step by step solutions of ICSE Class-10 specimen model sample paper . During solutions of semester-1 Maths specimen paper we explain with figure , graph, table whenever necessary so that student can achieve their goal in next upcoming exam of council .

**Maths Semester-1 ICSE Specimen Paper Solved Class-10 for practice**

Board | ICSE |

Class | 10th (x) |

Subject | Maths |

Topic | Semester-1 ICSE Specimen Paper Solved |

Syllabus | on bifurcated syllabus (after reduction) |

session | 2021-22 |

Question Type | MCQ/ Objective (as prescribe by council) |

Total question |
section-A=16 Section-B=6 Section-C=3 Total=25 |

Max mark |
section-A=1 mark x16 Que =16 Section-B=2 mark x 6 Que=12 Section-C=4 mark x 3 Que= 12 Total =25 |

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**Click Below for Answer Key of Board Paper**

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**Answer Key of Sem-1 ICSE Maths Board Paper (6th December)**

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**ICSE Maths Specimen Paper Solution Class-10 for Semester-1 (below)**

**Section-A (12 mark)**

Warning – please view Question Paper first before viewing solution

**Question-1 **

If matrix A is of order 3 x 2 and matrix B is of order 2 x 2 then the matrix AB is of order

(a) 3 x 2 (b) 3 x 1 (c) 2 x 3 (d) 1 x 3

**Solution**

Correct option is a) 3×2

**Explanation**

Order of A:3×2

Order of B:2×2

Multiplication of matrices is possible if and only if the number of columns of first matrix is equal to the number of rows of second matrix

In AB

No. of columns in A is 2

No. of rows in B is 2

∴AB exists

Order of AB is ( number of rows of A x number of columns of B)

∴ Order of AB is (3×2)

**Question-2 **

The percentage share of SGST of total GST for an Intra-State sale of an article is

(a) 25% (b) 50% (c) 75% (d) 100%

**Solution**

option (b) 50%

**Explanation**

if there is intrastate selling then total gst earn distribute equally to state SGST and central CGST

**Question-3**

𝐴𝐵𝐶𝐷 𝑖𝑠 𝑎 𝑡𝑟𝑎𝑝𝑒𝑧𝑖𝑢𝑚 𝑤𝑖𝑡ℎ 𝐴𝐵 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑡𝑜 𝐷𝐶. 𝑇ℎ𝑒𝑛 𝑡ℎ𝑒 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 𝑠𝑖𝑚𝑖𝑙𝑎𝑟 𝑡𝑜 ∆𝐴𝑂𝐵

(a) ∆𝐴𝐷𝐵 (b) ∆𝐴𝐶𝐵 (c) ∆𝐶𝑂𝐷 (d) ∆𝐶𝑂D

**Solutions**

option (c) ∆𝐶𝑂D is correct

**Explanation**

in ∆ AOB and in ∆ COD

Statement | reason |

angle BAC= angle OCD | alternate |

angle ABO= angle ODC | alternate |

So ∆ AOB similar ∆ COD | by A.A. |

**Question-4**

The mean proportion between 9 and 16 is

(a) 25 (b) 144 (c)7 (d) 12

**Solution**

option (d) 12 is correct

**explanation**

when A,B,C are in continued proportion then B is said to be the mean proportional.

let us take A=9 and C=16 and B as X. then

A:X : : X:C

9:X : : X:16

Therefore, x = 12.

So, the mean proportional of 9 and 16 is 12.

**Question-5**

A man deposited ₹ 500 per month for 6 months and received ₹3300 as the

maturity value. The interest received by him is: –

(a) 1950 (b) 300 (c) 2800 (d) none of these

**Solution**

option (b) is correct

**explanation**

total money deposited in 6 month= 500 x 6= 3000

total money received = 3300

so The interest received by him is= 3300-3000=300

**Question-6**

The solution set representing the following number line is….

(a) {x: x ∈ R, -3 ≤ x < 2}

(b) {x: x ∈ R, -3 < x < 2}

(c) {x: x ∈ R, -3 < x ≤ 2}

(d) {x: x ∈ R, -3 ≤ x ≤2}

**Solution**

option (a) {x: x ∈ R, -3 ≤ x < 2} is correct

**explanation**

shaded dot over 3 show that 3 also include while hollow dot over 2 show that 2 is not included but less than 2

**Question-7**

The first three terms of an arithmetic progression (A. P.) are 1, 9, 17, then the next two terms are

(a) 25 and 35 (b) 27 and 37 (c) 25 and 33 (d) none of these

**Solution**

option (c) 25 and 33 correct

**explanation**

in AP common deference should be same

Here deference is 9-1=8

So next term obtain by just adding 8 to previous term

**Question-8**

If ∆𝐴𝐵𝐶 ~ ∆𝑄𝑅𝑃 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛𝑎𝑙 𝑠𝑖𝑑𝑒𝑠 𝑎𝑟𝑒

(a) 𝐴𝐵/𝑄𝑅=𝐵𝐶/𝑅𝑃

(b) 𝐴𝐶/𝑄𝑅=𝐵𝐶/𝑅𝑃

(c) 𝐴𝐵/𝑄𝑅=𝐵𝐶/𝑄𝑃

(d) 𝐴𝐵/𝑃𝑄=𝐵𝐶/𝑅P

**Solution**

Option (a) 𝐴𝐵/𝑄𝑅=𝐵𝐶/𝑅𝑃 is correct

**explanation**

in ∆𝐴𝐵𝐶 ~ ∆𝑄𝑅𝑃

A𝐵/𝑄𝑅 (taking first 2 letter of similar ∆)

𝐵𝐶/𝑅𝑃 (taking last 2 letter of similar ∆)

**Question-9**

If x∈ 𝑊 , then the solution set of the inequation -x > -7, is

(a) {8,9,10…} (b) {0,1,2,3,4,5,6} (c) {0,1,2,3 …} (d) { -8, -9, -10…}

**Solution**

option (b) {0,1,2,3,4,5,6} is correct

**explanation**

-x > -7

-x by -1 < -7 by -1

sign of inequality change if multiply by negative number

x < 7

So vale of x is less than 7 which is possible in option (b) {0,1,2,3,4,5,6}

0 also included as it is Whole number

**Question-10**

The roots of the quadratic equation 4𝑥2- 7x + 2 = 0 are 1.390, 0. 359.The roots correct to 2 significant figures are

(a) 1.39 and 0.36

(b) 1.3 and 0.35

(c) 1.4 and 0.36

(d) 1.390 and 0.360

**Solution**

option (c) 1.4 and 0.36 is correct

**explanation**

in 1.390 taking 2 figure is 1.39 =1.4

and 0. 359 taking 2 figure is 0.36

**Question-11**

1.5, 3, x and 8 are in proportion, then x is equal to

(a) 6 (b) 4 (c) 4.5 (d) 16

**Solution**

option (b) 4 is correct

**explanation**

1.5/ 3,= x / 8 are in proportion

1.5 x 8 = 3 x x (cross multiplication)

on solving

x=4

**Question-12**

If a polynomial 2𝑥2 – 7x – 1 is divided by (x + 3), then the remainder is

(a) – 4 (b) 38 (c)-3 (d) 2

**solution**

option (b)38 is correct

**explanation**

when x+3=0

then x= -3

putting x=-3 in 2𝑥2 – 7x – 1

= 2(-3)²-7(-3)-1

= 2×9 + 21-1

=18+21-1

= 39-1

=38

**Question-13**

If 73 is the nth term of the arithmetic progression 3, 8, 13, 18…, then ‘n’ is

(a) 13 (b) 14 (c) 15 (d) 16

**Solution**

option (c) 15 is correct

**explanation**

here

a=3

d=8-3

=5

a_{n }= 73

a_{n} = a + (n − 1)d.

73= 3 + (n − 1) 5

73-3 = (n − 1) 5

70 = (n − 1) 5

70 / 5 = n-1

14= n-1

14+1 = n

15= n

**Question-14**

The roots of the quadratic equation x2+2x+1 = 0 are

(a) Real and distinct

(b) Real and equal

(c) Distinct

(d) Not real / imaginary

**Solution**

option (b) Real and equal is correct

**explanation**

$a=1,b=2,c=1$

$b_{2}−ac=()_{2}−××$

$=−=$

if b2−4ac = 0 then root are Real and equal

**Question-15**

Which of the following statement is not true?

(a) All identity matrices are square matrix

(b) All null matrices are square matrix

(c) For a square matrix number of rows is equal to the number of columns

(d) A square matrix all of whose elements except those in the leading diagonal are zero is the diagonal matrix

**Solution**

option ((b) All null matrices are square matrix

**explanation**

A square matrix all of whose elements except those in the leading diagonal are zero is the ~~diagonal~~ **identity or unit** matrix

**Question-16**

If (x – 2) is a factor of the polynomial x3 + 2×2 – 13 x + k, then ‘k’ is equal to

(a) -10 (b)26 (c)-26 (d) 10

**Solution**

option (d) 10 is correct

**explanation**

p(x) = x^3 + 2x^2 – 13x + k

For (x – 2) to be the factor of p(x) = x^3 + 2x^2 – 13x + k

Thus (2)^{3} + 2(2)^{2} – 13(2) + k = 0

⇒ 8 + 8 – 26 + k = 0

⇒ 16-26 +k=0

⇒ -10 = – k

⇒ k = 10

**Section-B (12 marks)**

Maths Semester-1 ICSE Specimen Paper Solved Class-10

**Question-17**

A man deposited ₹1200 in a recurring deposit account for 1 year at 5% per annum simple interest. The interest earned by him on maturity is

(a) 14790 (b) 390 (c) 4680 (d) 780

**Solution **

option (b) 390 is correct

**explanation**

Deposit per month = Rs. 1200

Period = 1 years = 12 months

∴ Total principal for 1 month = (P × n(n +1))/2

= ₹ (1200 × 12 × 13)/2

= ₹ 93600

∴ Interest = PRT/100

=(93600 x 5 x 1 )/ (100 x 12)

= ₹ 390

**Question-18**

If x2 – 4 is a factor of polynomial x3+ x2- 4x- 4, then its factors are

(a) (x-2) (x+2) (x+1)

(b) (x-2) (x+2) (x-1)

(c) (x-2) (x-2) (x+1)

(d) (x-2) (x-2) (x-1)

**Solution**

option (a) (x-2) (x+2) (x+1) is correct

**explanation**

x3 + x2 – 4x – 4

Let x + 1 = 0

∴ x = -1

On substituting value of x in the expression

∴ f(-1) = (-1)^{3 }+ (-1)^{2 }– 4(-1) -4 = 0

Clearly x + 1 is a factor of

f(x) = x^{3} + x^{2} – 4x – 4

∴ f(x) = (x + 1) (x^{2} – 4) …(By actual division)

= (x + 1) (x – 2) (x + 2)

**Question-19**

The following bill shows the GST rates and the marked price of articles A and B:

BILL: GENERAL STORE

Articles MP Rate

A ₹300 12%

B ₹1200 5%

The total amount to be paid for the above bill is: –

(a) 1548 (b) 1596 (c) 1560 (d) 1536

**Solution**

option (b) 1596 is correct

**Explanation**

Amount for A = 300 + 300 x 12/100

= 300+36=336

Amount for B = 1200 + 1200 x 5/100

= 1200 + 60 = 1260

total amount = Amount for A + Amount for B

= 336 + 1260

=1596

**Question-20**

The solution set for the linear inequation -8 ≤ x – 7 < – 4, x∈ 𝐼 is

(a) {x: x ∈ R, -1≤ x < 3}

(b) {0, 1, 2, 3}

(c) {-1, 0, 1, 2, 3}

(d) { -1, 0, 1, 2}

**Solution**

option (d) { -1, 0, 1, 2} is correct

**Explanation**

-8 ≤ x – 7 and x – 7 < -4

-8 +7 ≤ x and x < -4 +7

-1 ≤ x and x < 3

-1 ≤ x < 3

**Question-21**

If 5𝑎/7𝑏 =4𝑐/3𝑑 , then by Componendo and dividendo

(a) 5𝑎+7𝑏/5𝑎−7𝑏=4𝑐−3𝑑/4𝑐+ 3𝑑

(b) 5𝑎−7𝑏/5𝑎+7𝑏=4𝑐+3𝑑/4𝑐−3𝑑

(c) 5𝑎+7𝑏/5𝑎−7𝑏=4𝑐+3𝑑/4𝑐−3𝑑

(d) 5𝑎+7𝑏/5𝑎+7𝑏=4𝑐−3𝑑/4𝑐−3d

**Solution**

option (c) 5𝑎+7𝑏/5𝑎−7𝑏=4𝑐+3𝑑/4𝑐−3𝑑 is correct

**Explanation**

5𝑎/7𝑏 =4𝑐/3𝑑

5𝑎+7𝑏/5𝑎−7𝑏=4𝑐+3𝑑/4𝑐−3𝑑 applying Componendo and dividendo

**Question-22**

**Solutions**

option (b) [4 0−9 49] is correct

**explanation**

A² =A x A =

**Section -C**

**Maths Semester-1 ICSE Specimen Paper Solved Class-10**

**Question-23**

The distance between station A and B by road is 240 km and by train it is 300 km. A car starts from station A with a speed x km/hr whereas a train starts from station B with a speed 20km/hr more than the speed of the car

**(i) The time taken by car to reach station B is**

**Solutions**

option **(a) 240/x** is correct

**explanation**

Dis by road = 240

speed of car = x

Time = ?

Time = dis/ speed

= 240 / x

**(ii) The time taken by train to reach station A**

**Solutions**

option (d) 300 /𝑥+20 is correct

**explanation**

Dis by rail = 300

speed of train = x+20

Time = ?

Time = dis/ speed

= 300 / x+20

(iii) If the time taken by train is 1 hour less than that taken by the car, then the quadratic equation formed is

**Solutions**

option **(b) x2 + 80x –4800=0** is correct

**explanation**

According condition

Time by car – Time by train = 1

(240 / x ) – (300 / x+20) =1

on simplification

x2 + 80x –4800=0

**(iv) The speed of the car is**

(a) 60km/hr (b) 120km/hr (c) 40km/hr (d) 80km/hr

**Solutions**

option **(c) 40km/hr ** is correct

**explanation**

x2 + 80x –4800=0

x2 + 120x -40x –4800=0

x (x+120)-40(x+120)=0

(x+120) (x-40)= 0

applying zero product rule

either x+120 = 0

then x = -120 but speed can be negative hence ignore this value

or x-40=0

then x= 40

**Question-24**

In the given triangle PQR, AB || QR, QP || CB and AR intersects CB at O.

**(i) The triangle similar to ΔARQ is**

(a) ΔORC (b) ΔARP (c) ΔOBR (d) ΔQRP

**Solutions**

option **(a) ΔORC**** ** is correct

**explanation**

ΔARQ and ΔORC

∠ARQ= ∠ORC common

∠AQR= ∠OCR alternate

So ΔARQ similar to ΔORC by AA axiom

**(ii) ΔPQR ~ΔBCR by axiom**

**Solutions**

option **(b)AAA ** is correct

**explanation**

ΔPQR and ΔBCR

∠QPR= ∠CBR Alternate

∠PRQ= ∠BRC common

hence ΔPQR ~ΔBCR by AA axiom

**(iii) If QC =6 cm, CR = 4 cm, BR = 3 cm. The length of RP is**

(a) 4.5 cm (b) 8cm (c) 7.5cm (d) 5cm

**Solutions**

option ** (c) 7.5 cm**** ** is correct

**explanation**

in ΔPQR and similar ΔBCR

PQ/BC = QR/CR = PR/BR

or QR/CR = PR/BR

or 10/4 = PR/3

on simplify PR= 15/2 = 7.5

**(iv) The ratio PQ: BC is**

(a) 2 : 3 (b) 3 : 2 (c) 5 : 2 (d) 2 : 5

**Solutions**

option ** (c) 5 : 2**** ** is correct

**explanation**

PQ/BC = QR/CR

PQ/BC = 10/4

PQ/BC = 5/2 = 5:2

**Question-25**

The nth term of an arithmetic progression (A.P.) is (3n + 1)

**(i) The first three terms of this A. P. are
**(a) 5, 6, 7 (b) 3, 6, 9 (c) 1, 4, 7 (d) 4, 7, 10

**Solutions**

option ** (d) 4, 7, 10**** ** is correct

**explanation**

An= (3n + 1)

A1 = 3 x 1 +1 = 4

A2 = 3 x 2 +1= 7

A3 = 3 x 3 +1 = 10

Hence term are **4, 7, 10**

**(ii) The common difference of the A.P. is
**(a) 3 (b)1 (c) -3 (d) 2

**Solutions**

option ** (a) 3 **** ** is correct

**explanation**

common difference of the A.P = term – proceeding term

= 7-4=3

**(iii) Which of the following is not a term of this A.P.
**(a) 25 (b) 27 (c) 28 (d) 31

**Solutions**

option ** (b) 27 **** ** is correct

**explanation**

term can be obtain by adding common difference to proceeding term

hence

4, 7, 10, 13,16,19,22,25,28,31

It is clear that 27 is not a term of this AP

**(iv) Sum of the first 10 terms of this A.P. is
**(a) 350 (b) 175 (c) -95 (d) 70

**Solutions**

option ** (b) 175 **** ** is correct

**explanation**

S_{n} = (n/2)(2a + (n – 1)d)

S_{10}= (10/2) ((2 × 4) + ((10 – 1) × (3))

= (5) (8 + (27))

= 5 (35)

=175

— End of Semester-1 ICSE Maths Specimen Paper Solutions

Visit :- ICSE Class-10 textbook Solution , paper , Syllabus , Notes

thanks

please share with your friends

In no. 15 it is said thai all null matrix are square matrix how can this statement be true?

now focus on only sem -2 please

Very much helpful

⭐⭐⭐⭐⭐

thanks keep in touch

Are all solutions correct or can we consider these as correct answers to Maths Semester 1 Specimen paper

yes

Thank You

ok keep in touch

Thank a lot for this ….but I need more questions to practice for my boards!

how can we help you

Answer 1 and Answer 15 are wrong.

Answer 1 is (a) 3 x 2

Because in question A is 3×2 and B is 2×2.

Answer 15 is (b) All null matrices are square matrix.

This is wrong because a null matrix can be non-square also.

For e.g.

[0 0 0 0] is also null matrix but is not a square matrix.

during solutions

mistakely put the value of order b 2×1 in place of 2×2

hence ans become wrong

but now corrected

is the 1st and 15th one correct?

please now focus on sem-2

Thank you so much …..it would be even more better if u try to share in pdf form

thanks for suggestion but pdf can not be update time to time as syllabus/pattern change very soon in icse/isc due to cowid 19

thnks pandey tutoria

ok and now focus on sem-2 descriptive question of which specimen paper has been solved

Hey I just want 1help could u please provide me analysis of this paper or link of analysis. I mean I want to see how many question are from which chapter and how many marks per chapter,like in biology specimen we are given 8marks per chapter(2,3,4,5,6).

Thanks for the help BTW

we will try contact us on 8957797189