📚 Model Test for: Mastery Guide: Matrices, Determinants, Multiplicative Inverses & Linear System Modeling
⏱️ Official Timed Examination
Class 10 Mathematics - Ch 3: Matrices and Determinants Chapter Mock Test
Class: 10 | Subject: Mathematics | Board: Federal Board of Intermediate and Secondary Education (FBISE)
Duration
⏱️ 35 Mins
Question Pool
📝 25 MCQs
Passing Benchmark
🎯 50.0%
Scoring Engine
✓ Instant & Ranked
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Test Pattern Preview
Representative sample from official examination pool
Sample Questions & Solved Explanations
Below are representative questions drawn directly from the testing blueprint for this exam. Review these worked examples to understand the question style, difficulty calibration, and grading criteria:
Sample Q1 (SHORT)
Difficulty: MEDIUM
Simplify and express in terms of $iy$:
$$\sqrt{-3}$$
$$\sqrt{-3}$$
✓ Answer: \sqrt{3}i
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 1 (Express with imaginary unit):</strong> Write $\sqrt{-3} = \sqrt{-1 \times 3} = \sqrt{-1} \times \sqrt{3}$.</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 2 (Substitute $i = \sqrt{-1}$):</strong> $= i\sqrt{3} = \mathbf{\sqrt{3}i}$ (or $i\sqrt{3}$).</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Final Answer:</strong> $\mathbf{\sqrt{3}i}$</div>
Sample Q2 (SHORT)
Difficulty: MEDIUM
Simplify and express in terms of $iy$:
$$6\sqrt{-4}$$
$$6\sqrt{-4}$$
✓ Answer: 12i
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 1 (Express radical with $i$):</strong> $6\sqrt{-4} = 6\sqrt{-1 \times 4} = 6 \times \sqrt{-1} \times \sqrt{4}$.</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 2 (Evaluate square root):</strong> $\sqrt{4} = 2$ and $\sqrt{-1} = i$, so $6 \times 2 \times i = \mathbf{12i}$.</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Final Answer:</strong> $\mathbf{12i}$</div>
Sample Q3 (SHORT)
Difficulty: MEDIUM
Simplify and express in terms of $iy$:
$$\sqrt{-\frac{4}{9}}$$
$$\sqrt{-\frac{4}{9}}$$
✓ Answer: \frac{2}{3}i
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 1 (Separate radical factors):</strong> $\sqrt{-\frac{4}{9}} = \sqrt{-1} \times \sqrt{\frac{4}{9}}$.</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 2 (Simplify fraction):</strong> $= i \times \frac{\sqrt{4}}{\sqrt{9}} = i \times \frac{2}{3} = \mathbf{\frac{2}{3}i}$.</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Final Answer:</strong> $\mathbf{\frac{2}{3}i}$</div>
Sample Q4 (SHORT)
Difficulty: MEDIUM
Simplify and express in terms of $iy$:
$$-\sqrt{-20}$$
$$-\sqrt{-20}$$
✓ Answer: -2\sqrt{5}i
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 1 (Factor under radical):</strong> $-\sqrt{-20} = -\sqrt{-1 \times 4 \times 5} = -\sqrt{-1} \times \sqrt{4} \times \sqrt{5}$.</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 2 (Substitute values):</strong> $= -i \times 2 \times \sqrt{5} = \mathbf{-2\sqrt{5}i}$.</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Final Answer:</strong> $\mathbf{-2\sqrt{5}i}$</div>
Sample Q5 (SHORT)
Difficulty: MEDIUM
Simplify and express in terms of $iy$:
$$4 - \sqrt{-60}$$
$$4 - \sqrt{-60}$$
✓ Answer: 4 - 2\sqrt{15}i
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 1 (Factorize imaginary term):</strong> $\sqrt{-60} = \sqrt{-1 \times 4 \times 15} = \sqrt{-1} \times \sqrt{4} \times \sqrt{15} = 2\sqrt{15}i$.</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 2 (Combine real and imaginary parts):</strong> $= \mathbf{4 - 2\sqrt{15}i}$.</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Final Answer:</strong> $\mathbf{4 - 2\sqrt{15}i}$</div>
Sample Q6 (SHORT)
Difficulty: MEDIUM
Simplify and express in terms of $iy$:
$$\sqrt{-8}\sqrt{-2}$$
$$\sqrt{-8}\sqrt{-2}$$
✓ Answer: -4
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 1 (Convert both terms to $i$-notation first):</strong> $\sqrt{-8} = i\sqrt{8} = i(2\sqrt{2}) = 2\sqrt{2}i$, and $\sqrt{-2} = i\sqrt{2}$.</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 2 (Multiply complex factors):</strong> $(2\sqrt{2}i)(i\sqrt{2}) = 2(\sqrt{2} \times \sqrt{2}) i^2 = 2(2)(-1) = \mathbf{-4}$.</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Important Rule:</strong> $\sqrt{-a}\sqrt{-b} \neq \sqrt{(-a)(-b)}$; converting to $i$ first is mandatory!</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Final Answer:</strong> $\mathbf{-4}$</div>
Sample Q7 (SHORT)
Difficulty: MEDIUM
Simplify:
$$(4 - i) + (5 + 5i)$$
$$(4 - i) + (5 + 5i)$$
✓ Answer: 9 + 4i
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 1 (Group real and imaginary parts):</strong> $(4 + 5) + (-1 + 5)i$.</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 2 (Add components):</strong> $\mathbf{9 + 4i}$.</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Final Answer:</strong> $\mathbf{9 + 4i}$</div>
Sample Q8 (SHORT)
Difficulty: MEDIUM
Simplify:
$$(7 - 6i) - (5 - 6i)$$
$$(7 - 6i) - (5 - 6i)$$
✓ Answer: 2
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 1 (Distribute negative sign):</strong> $7 - 6i - 5 + 6i$.</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 2 (Combine like terms):</strong> $(7 - 5) + (-6 + 6)i = 2 + 0i = \mathbf{2}$.</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Final Answer:</strong> $\mathbf{2}$</div>
Sample Q9 (SHORT)
Difficulty: MEDIUM
Simplify:
$$(-2 + 8i) - (7 + 3i)$$
$$(-2 + 8i) - (7 + 3i)$$
✓ Answer: -9 + 5i
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 1 (Distribute negative sign):</strong> $-2 + 8i - 7 - 3i$.</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 2 (Combine components):</strong> $(-2 - 7) + (8 - 3)i = \mathbf{-9 + 5i}$.</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Final Answer:</strong> $\mathbf{-9 + 5i}$</div>
Sample Q10 (SHORT)
Difficulty: MEDIUM
Simplify:
$$(4 - 2i) - (5 - 2i)$$
$$(4 - 2i) - (5 - 2i)$$
✓ Answer: -1
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 1 (Distribute negative sign):</strong> $4 - 2i - 5 + 2i$.</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Step 2 (Combine components):</strong> $(4 - 5) + (-2 + 2)i = -1 + 0i = \mathbf{-1}$.</div>
<div style="margin-bottom: 6px; font-size: 13.5px; color: #1e293b; line-height: 1.5;">• <strong>Final Answer:</strong> $\mathbf{-1}$</div>