M.2 MPT 2022 — Questions and Worked Solutions

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Source: FPSC MPT 2022 (quantitative part). No official key was published. Every answer below is recomputed. A ⚠️ line means the answer marked in the earlier extraction does not match the working — check the booklet wording before relying on it.

Q1 · Percentage of a decimal

Question: What percentage is $0.001$?

Options: (A) 1 (B) 0.1 (C) 0.01 (D) None of these

✅ Answer: (B) 0.1

Solution:

$$0.001\times100\%=0.1\%$$

Concept: decimal → percent: multiply by 100.

⚠️ The earlier extraction marked (C) 0.01. That would be the percent form of $0.0001$, so confirm the printed number.

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Q2 · Powers of a negative number

Question: $(-3)\times(-3)\times(-3)=\ ?$

Options: (A) −3 (B) 27 (C) −27 (D) None of these

✅ Answer: (C) −27

Solution:

$$(-3)^{3}=-27$$

Concept: an odd number of negative factors gives a negative result.

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Q3 · Square root of a negative number

Question: Square root of $-25$?

Options listed: 5, −5, −2.5 (none correct)

✅ Answer: $5i$ (imaginary), i.e. "None of these" among real numbers

Solution:

$$\sqrt{-25}=\sqrt{25}\cdot\sqrt{-1}=5i$$

Concept: $i=\sqrt{-1}$. Repeated in 2025 and flagged as mis-keyed.

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Q4 · Linear equation

Question: $x=-4x+4$. Find $x$.

Options: (A) 4/5 (B) 5/4 (C) −4/3 (D) None of these

✅ Answer: (A) 4/5

Solution:

$$\begin{aligned} x&=-4x+4\\ 5x&=4\\ x&=\frac45 \end{aligned}$$

Concept: collect $x$ terms on one side.

⚠️ The earlier extraction marked (B) 5/4. The 2025 paper repeats this item and its key is (A) 4/5.

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Q5 · Average

Question: The sum of 10 values is 10. What is the average?

Options: (A) 1 (B) 5 (C) 10 (D) None of these

✅ Answer: (A) 1

Solution:

$$\bar{x}=\frac{10}{10}=1$$

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Q6 · Exponent law

Question: $x^{\frac12}\times x^{-\frac12}=\ ?$

✅ Answer: 1

Solution:

$$x^{\frac12}\cdot x^{-\frac12}=x^{\frac12-\frac12}=x^{0}=1$$

Concept: add exponents when multiplying powers of the same base. Do not be misled by the distractor 0.

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Q7 · Power of a product

Question: $(-2x)^{3}=\ ?$

Options: (A) 8x (B) −8x (C) −8x³ (D) None of these

✅ Answer: (C) −8x³

Solution:

$$(-2x)^{3}=(-2)^{3}\,x^{3}=-8x^{3}$$

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Q8 · Linear equation with fractions

Question: $\frac{x}{2}-\frac{x}{4}=2$. Find $x$.

Options: (A) 2 (B) 4 (C) 8 (D) None of these

✅ Answer: (C) 8

Solution:

$$\frac{2x-x}{4}=2\;\Rightarrow\;\frac{x}{4}=2\;\Rightarrow\;x=8$$

Concept: use the common denominator 4.

⚠️ The earlier extraction marked (B) 4, which does not satisfy the equation.

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Q9 · Fractional exponent

Question: $x^{\frac23}=64$. Find $x$.

Options: (A) 4 (B) 8 (C) 16 (D) None of these

✅ Answer: (D) None of these

Solution:

$$x=64^{\frac32}=\left(\sqrt{64}\right)^{3}=8^{3}=512$$

Concept: to remove the power $\frac23$, raise both sides to the reciprocal $\frac32$.

⚠️ If the printed question is $x^{\frac32}=64$ then $x=64^{\frac23}=16$, option (C). Marked answer 8 matches neither.

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Q100–108 · Geometry vocabulary (definition recall)

Questions: angle terms, polygon sides, triangle vertices, chord, pentagon, square.

Quick facts to recall:

• Acute angle: $<90^{\circ}$; right angle: $=90^{\circ}$; obtuse: between $90^{\circ}$ and $180^{\circ}$; straight: $180^{\circ}$; reflex: between $180^{\circ}$ and $360^{\circ}$.
• Polygon sides: triangle 3, quadrilateral 4, pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10.
• A triangle has 3 vertices and 3 sides.
• A chord joins two points on a circle; the diameter is the longest chord, $d=2r$.
• A square has 4 equal sides and 4 right angles; each interior angle is $90^{\circ}$.

$$\text{Interior angle sum of an }n\text{-gon}=(n-2)\times180^{\circ}$$

Concept: pure definition questions — learn the vocabulary once and these marks are free.