# ICSE Class 10 Mathematics 2022 Semester-1 Sample Paper

There are three sections in the paper. Maximum Marks are 40 and Time allowed is one and a half hours. All questions are compulsory.

### Section A [16 Marks]

**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**

- 3 x 2
- 3 x 1
- 2 x 3
- 1 x 3

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

- 25%
- 50%
- 75%
- 100%

**3. ABCD is a trapezium with AB parallel to DC.**

**Then the triangle similar to ΔAOB is**

- ΔADB
- ΔACB
- ΔCOD
- ΔCOB

**4. The mean proportion between 9 and 16 is**

- 25
- 144
- 7
- 12

**5. A man deposited ₹500 per month for 6 months and received ₹3300 as the maturity value. The interest received by him is:**

- 1950
- 300
- 2800
- none of these

**6. The solution set representing the following number line is**

- {x: x ∈ R, -3 ≤ x < 2}
- {x: x ∈ R, -3 < x < 2}
- {x: x ∈ R, -3 < x ≤ 2}
- {x: x ∈ R, -3 ≤ x ≤2}

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

- 25 and 35
- 27 and 37
- 25 and 33
- none of these

**8. If ΔABC ~ ΔQPR then the corresponding proportional sides are**

- AB/QR = BC/RP
- AC/QR = BC/RP
- AB/QR = BC/QP
- AB/PQ = BC/RP

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

- {8,9,10…}
- {0,1,2,3,4,5,6}
- {0,1,2,3 …}
- { -8, -9, -10…}

**10. The roots of the quadratic equation 4𝑥 ^{2} - 7x + 2 = 0 are 1.390, 0.359.The roots correct to 2 significant figures are**

- 1.39 and 0.36
- 1.3 and 0.35
- 1.4 and 0.36
- 1.390 and 0.360

**11. 1.5, 3, x and 8 are in proportion, then x is equal to**

- 6
- 4
- 4.5
- 16

**12. If a polynomial 2𝑥 ^{2} - 7x - 1 is divided by (x + 3), then the remainder is**

- -4
- 38
- -3
- 2

**13. If 73 is the n ^{th} term of the arithmetic progression 3, 8, 13, 18…, then ‘n’ is**

- 13
- 14
- 15
- 16

**14. The roots of the quadratic equation x ^{2} + 2x + 1 = 0 are**

- Real and distinct
- Real and equal
- Distinct
- Not real / imaginary

**15. Which of the following statement is not true?**

- All identity matrices are square matrix
- All null matrices are square matrix
- For a square matrix number of rows is equal to the number of columns
- A square matrix all of whose elements except those in the leading diagonal are zero is the diagonal matrix

**16. If (x - 2) is a factor of the polynomial x ^{3} + 2x^{2} - 13x + k, then ‘k’ is equal to**

- -10
- 26
- -26
- 10

### Section B [12 Marks]

**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**

- 14790
- 390
- 4680
- 780

**18. If x ^{2} - 4 is a factor of polynomial x^{3}+ x^{2} - 4x - 4, then its factors are**

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

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

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

- 1548
- 1596
- 1560
- 1536

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

- {x: x ∈ R, -1≤ x < 3}
- {0, 1, 2, 3}
- {-1, 0, 1, 2, 3}
- { -1, 0, 1, 2}

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

**22. If then A ^{2} is**

### Section C [12 Marks]

**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 20 km/hr more than the speed of the car.

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

- 240/x
- 300/x
- 20/x
- 300/(x+2)

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

- 240/x
- 300/x
- 20/x
- 300/(x+2)

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

- x
^{2}+ 80x - 6000 = 0 - x
^{2}+ 80x - 4800 = 0 - x
^{2}+ 240x - 1600 = 0 - x
^{2}-80x + 4800 = 0

(iv) The speed of the car is

- 60 km/hr
- 120 km/hr
- 40 km/hr
- 80 km/hr

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

Using the given diagram answer the following question:

(i) The triangle similar to ΔARQ is

- ΔORC
- ΔARP
- ΔOBR
- ΔQRP

(ii) ΔPQR ~ΔBCR by axiom

- SAS
- AAA
- SSS
- AAS

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

- 4.5 cm
- 8 cm
- 7.5 cm
- 5 cm

(iv) The ratio PQ : BC is

- 2 : 3
- 3 : 2
- 5 : 2
- 2 : 5

**25.** The n^{th} term of an arithmetic progression (A.P.) is (3n + 1)

(i) The first three terms of this A. P. are

- 5, 6, 7
- 3, 6, 9
- 1, 4, 7
- 4, 7, 10

(ii) The common difference of the A.P. is

- 3
- 1
- -3
- 2

(iii) Which of the following is not a term of this A.P.

- 25
- 27
- 28
- 31

(iv) Sum of the first 10 terms of this A.P. is

- 350
- 175
- -95
- 70