ICSE CLASS X MATHEMATICS: SAMPLE PAPER II

 Here is a fresh sample question paper designed for ICSE Class X Mathematics, matching the exact standard, topic coverage (GST, Banking/Recurring Deposits, Linear Inequations, Matrices, and Similarity), and marks distribution of the original paper.

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ICSE CLASS X MATHEMATICS: SAMPLE PAPER II

Time Allowed: 1.5 Hours | Maximum Marks: 40

Instructions: This paper is divided into two sections. Section A (20 Marks) is compulsory. Section B (20 Marks) contains three questions; answer any two.

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SECTION A (20 Marks)

(Attempt all questions from this section)

Question 1: Multiple Choice Questions (1 × 5 = 5 Marks)

i. A wholesaler in Gujarat sells an electric scooter to a dealer in the same state for ₹80,000. The dealer sells it to a customer in Rajasthan at a profit of ₹15,000. If the GST rate is 12%, the Integrated GST (IGST) paid by the dealer to the government is:

• (a) ₹1,800

• (b) ₹11,400

• (c) ₹9,600

• (d) ₹1,140

ii. Kiran opens a Recurring Deposit (RD) account in a bank for a fixed tenure. If she decides to skip two monthly installments in the middle and pays them together later with a penalty, which of the following is true?

• (a) The total principal deposited changes.

• (b) The maturity value will remain completely unchanged.

• (c) The interest calculation will be adjusted based on the delayed months for those installments.

• (d) The bank will recalculate the interest rate from month one.

iii. Given the linear inequation $x \in W$ (Whole Numbers), the solution set for $-1 \le 3x - 4 < 5$ contains how many elements?

• (a) 2

• (b) 3

• (c) 4

• (d) Infinite

iv. If $A$ is a matrix of order $3 \times 1$ and $B$ is a matrix such that the matrix multiplication $BA$ is defined and results in a matrix of order $3 \times 1$, then the order of matrix $B$ must be:

• (a) $1 \times 3$

• (b) $3 \times 3$

• (c) $3 \times 1$

• (d) $1 \times 1$

v. Two similar triangles, $\Delta ABC$ and $\Delta PQR$, have their areas in the ratio $25 : 49$. The ratio of their corresponding medians is:

• (a) $5 : 7$

• (b) $25 : 49$

• (c) $7 : 5$

• (d) $125 : 343$

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Question 2 (7 Marks)

(a) A retailer buys a laptop from a distributor for ₹60,000. He marks up the price by 20%. A customer buys this laptop and gets a 5% discount on the marked price. If the intra-state rate of GST is 18%, find:

1. The total GST paid by the retailer to the State Government (SGST).

2. The final amount (inclusive of tax) paid by the consumer. [4]

(b) Solve the following inequation and represent the solution set on a real number line: [3]

$$-1 \frac{5}{6} \le \frac{x}{2} + \frac{2}{3} < 2 \frac{1}{6}, \quad x \in R \text{ (Real Numbers)}$$

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Question 3 (8 Marks)

(a) Mr. Sharma opened a Recurring Deposit account in a nationalized bank for a period of 2 years. If the bank pays interest at the rate of 9% per annum and he receives ₹3,750 as interest at the time of maturity, find:

1. The monthly installment amount ($P$).

2. The total maturity value of the account. [4]

(b) Find the values of $x$ and $y$ if they satisfy the following matrix equation: [4]

$$3 \begin{pmatrix} x & 2 \\ 1 & 0 \end{pmatrix} \begin{pmatrix} 2 \\ -1 \end{pmatrix} + \begin{pmatrix} 4 \\ y \end{pmatrix} = \begin{pmatrix} 10 \\ 5 \end{pmatrix}$$

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SECTION B (20 Marks)

(Attempt any two questions from this section)

Question 4 (10 Marks)

(a) Case Study Based (GST & Banking):

An event planner, Rahul, needs to purchase a heavy-duty sound system listed at ₹2,000,000 from a local distributor for his corporate clients. He is presented with two commercial payment options:

• Option A: A direct discount of 15% on the list price, with GST charged at 28% on the discounted price.

• Option B: No flat discount, but the vendor offers a special dynamic corporate rebate where they effectively reduce the total GST rate from 28% down to 16% on the full list price.

1. Mathematically analyze which option saves Rahul more money and by how much.

2. If he takes the total savings from the better option and invests it into a 1-year Recurring Deposit scheme paying 7% simple interest per annum with a monthly installment of ₹1,000, will the interest generated over the year be greater than 1% of his initial savings? Justify. [5]

(b) In a triangle $ABC$, a line $DE$ is drawn parallel to base $BC$ cutting $AB$ at $D$ and $AC$ at $E$. If $AD = x + 3$, $DB = 3x - 1$, $AE = x$, and $EC = x + 1$:

1. Set up an algebraic equation to find the value of $x$.

2. Find the ratio of $\text{Area}(\Delta ADE) : \text{Area}(\text{Trapezium } BCED)$. [5]

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Question 5 (10 Marks)

(a) Given the matrices $A = \begin{pmatrix} 1 & 3 \\ -2 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 5 & 0 \\ 1 & -2 \end{pmatrix}$. Find a matrix $C$ such that: [4]

$$A^2 - 2C = 3B$$

(b) An algorithm evaluates two separate data-stream filters constraints, represented by the following inequation groups:

• Filter X: $2x - 5 \le 3$ and $3x + 7 > -2, \quad x \in I \text{ (Integers)}$

• Filter Y: $-2 < 3x - 5 \le 7, \quad x \in W \text{ (Whole Numbers)}$

Find the intersection of the solution sets of Filter X and Filter Y. List all common integral values. [6]

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Question 6 (10 Marks)

(a) High-Level Similarity Application:

A vertical lamppost of length 2.4 meters casts a shadow 1.6 meters long on the ground. At the exact same time, a neighboring telecommunication tower casts a shadow 48 meters long.

1. Using the concept of similar triangles, calculate the height of the tower.

2. A maintenance drone is hovering in a fixed position exactly midway between the top of the lamppost and the top of the tower horizontally. What is the vertical height of the drone from the ground? [5]

(b) Let $M$ be a $2 \times 2$ matrix. It is given that:

$$M \begin{pmatrix} 1 \\ 2 \end{pmatrix} = \begin{pmatrix} 5 \\ 0 \end{pmatrix} \quad \text{and} \quad M \begin{pmatrix} 0 \\ 1 \end{pmatrix} \begin{pmatrix} 2 \\ -1 \end{pmatrix}$$

1. Determine the matrix $M$.

2. Evaluate $M^2$. [5]