Physics Grade 11 · Unit 1 Model Paper · Athens Academy Islamabad

FBISE · Exam March 2027 · Total Marks: 80

Time allowed
2 hours 35 minutes

Section B
39 marks

Section C
24 marks

Coverage
Unit 1 only

Section A — Multiple Choice

Not printed in this paper. Section A is delivered on the Athens Academy portal.

Before you attempt this paper, complete the Unit 1 Quiz and revise the Unit 1 Flashcards on the portal. Those cover the full MCQ range for this unit — estimation, base and derived units, dimensions, precision and accuracy, and the uncertainty rules.

Section A carries 17 marks (17 MCQs × 1). Those marks are shown in the Board Marking Pattern table at the end of this paper and are recorded on the portal, not here.

Section B — Short Response Questions

Note: Attempt any THIRTEEN parts. Each part carries 3 marks. Where an OR alternative is given, attempt only one of the two. (13 × 3 = 39)

(3)★Deduce the dimensions of the constant $k$ in Coulomb's law, $F = k\,\dfrac{q_1 q_2}{r^{2}}$ , where $F$ is force (N), $q$ is charge (C) and $r$ is separation (m).

ORDefine the dimension of a physical quantity. Write the dimensions of the seven base quantities.

PHY-11-1.3Dimensions
(3)★What is meant by precision? Write the importance of taking multiple readings in an experiment. (1 + 2)

ORDistinguish between precision and accuracy. Give any two clear differences with one example.

PHY-11-1.7Precision & Accuracy
(3)★A body of mass $(27.2 \pm 0.1)~\text{kg}$ has a volume of $(2.0 \pm 0.1)~\text{m}^{3}$ . Calculate the density of the body and find the uncertainty in the density measurement.

ORThe length and width of a rectangular plate are $(5.2 \pm 0.1)~\text{cm}$ and $(3.1 \pm 0.1)~\text{cm}$ . Find its area and the uncertainty in the area.

PHY-11-1.9Uncertainty — product
(3)Show that the newton and the joule can be written in SI base units as $\text{kg m s}^{-2}$ and $\text{kg m}^{2}\,\text{s}^{-2}$ respectively.

ORExpress the units of power and pressure in terms of SI base units, showing each step.

PHY-11-1.2Derived units
(3)★Check whether the equation $v_f = v_i + at$ is dimensionally correct, showing the dimensions of every term.

ORState the principle of homogeneity of dimensions. Explain why a dimensionally correct equation need not be physically correct.

PHY-11-1.5Homogeneity
(3)What is meant by estimation of a physical quantity? Describe any one strategy with an example. (1 + 2)

OREstimate the energy required for a person of mass $70~\text{kg}$ to climb one floor of height $3~\text{m}$ , taking $g \approx 10~\text{m s}^{-2}$ .

PHY-11-1.1Estimation
(3)Distinguish between a dimensional variable and a dimensional constant. Give one example of each. (2 + 1)

ORDistinguish between a dimensionless variable and a dimensionless constant, with one example of each.

PHY-11-1.4Classification
(3)★In a timing experiment, 30 vibrations of a pendulum are recorded as $48.6~\text{s}$ using a stopwatch of least count $0.1~\text{s}$ . Find the time period and its uncertainty.

ORExplain why a timing experiment records many vibrations rather than one. Support your answer with the rule for uncertainty in timing.

PHY-11-1.9Uncertainty — timing
(3)Define uncertainty. Name the three types of error and state one cause of each. (1 + 2)

ORA reading is written as $3.06 \pm 0.02~\text{mm}$ . Explain what this statement means, and find its percentage uncertainty.

PHY-11-1.8Uncertainty — meaning
(3)State any three limitations of dimensional analysis.

ORExplain why dimensional analysis cannot determine the value of a dimensionless constant such as the $2\pi$ in $T = 2\pi\sqrt{l/g}$ .

PHY-11-1.6Limitations
(3)Four readings of a length are $3.42,\ 3.45,\ 3.40,\ 3.43~\text{cm}$ . Find the average value and the uncertainty in the average.

ORState the rule for finding the uncertainty in the average of several readings, and explain why the mean deviation is used.

PHY-11-1.9Uncertainty — average
(3)The side of a cube is measured as $(2.5 \pm 0.1)~\text{cm}$ . Find the volume of the cube and the percentage uncertainty in the volume.

ORState the rule for uncertainty in a power of a quantity, and explain why the rule acts on the percentage and not the absolute uncertainty.

PHY-11-1.9Uncertainty — power
(3)The WAPDA meter in a house records energy in kilowatt-hours. Show that $1~\text{kWh} = 3.6 \times 10^{6}~\text{J}$ .

ORDefine absolute, fractional and percentage uncertainty, and write the relation connecting them.

PHY-11-1.2Units in context

Long Questions

Note: Attempt any THREE questions. Each question carries 8 marks. (3 × 8 = 24)

(4)(a)★Define the dimension of a physical quantity. Write the dimensions of the seven base quantities in a table, and deduce the dimensions of area, volume, velocity and acceleration.

(4)(b)Classify physical quantities into dimensional variables, dimensional constants, dimensionless variables and dimensionless constants, giving two examples of each. Hence express the units of force, work and power in terms of SI base units.

PHY-11-1.3PHY-11-1.4
(3)(a)★State the principle of homogeneity of dimensions. Check the dimensional correctness of $v_f = v_i + at$ , showing every term.

(5)(b)Using dimensional analysis, derive the formula for the time period $T$ (s) of a simple pendulum, assuming it depends on mass $m$ (kg), length $l$ (m) and $g$ (m s $^{-2}$ ). State clearly why the mass does not appear in the final result, and give any two limitations of dimensional analysis shown by this derivation.

PHY-11-1.5
(4)(a)★Distinguish between precision and accuracy. Give any four differences and illustrate your answer with the readings of three weighing scales.

(4)(b)Define uncertainty. Explain absolute, fractional and percentage uncertainty, and show how each is obtained for a length measured with a metre rule.

PHY-11-1.7PHY-11-1.8
(5)(a)★State the rules for combining uncertainties in (i) a sum or difference, (ii) a product or quotient, (iii) a power, (iv) an average of many readings and (v) a timing experiment.

(3)(b)A potential difference $V = (12.0 \pm 0.1)~\text{V}$ is applied across a resistor carrying a current $I = (2.5 \pm 0.1)~\text{A}$ . Find the resistance and its uncertainty.

PHY-11-1.9

Board Marking Pattern

FBISE HSSC-I Physics — pattern followed in this paper
Section	Type	Structure	Marks
A	Multiple choice	17 MCQs × 1 — on the Athens portal, not printed here	17
B	Short response	Attempt any 13 parts × 3 marks (each with an OR alternative)	39
C	Long response	Attempt any 3 of 4 questions × 8 marks	24
Total			80

How to use this paper

Give yourself 2 hours 35 minutes and sit the whole paper in one attempt, without notes.
In Section B, read both options before choosing. The OR alternative is often the shorter answer.
Every numerical must show the six steps: Given → Required → Formula → Substitution → Calculation → ∴ Answer. Marks are given for the steps, not only the final number.
Decide first whether an uncertainty question is $+ \,/\, -$ (use absolute) or $\times \,/\, \div \,/\,$ power (use percentage). This single decision carries most of the marks.
Carry the SI unit through to the final line of every answer. A correct number without a unit loses a mark.
Roughly 1 mark ≈ 1 minute. If a 3-mark part is taking five minutes, move on and return to it.

— END OF PAPER —

Athens Academy Islamabad · Physics · Grade 11 · Unit 1 — Physical Quantities and Measurements · FBISE · Exam March 2027

Unit Model Paper — Unit 1: Physical Quantities and Measurements

Section A — Multiple Choice

Section B — Short Response Questions

Long Questions

Board Marking Pattern

📃 Chapter 1 · Physical Quantities & Measurements — Chapter Model Paper

Chapter 1: Physical Quantities & Measurements Model Paper