Senior 1 practice book · Unit 1 of 9

Introduction to Physics and Measurements of Physical Quantities

50 questions that complete the Senior 1 quiz for this unit: 30 core and 20 challenge. Easy and hard questions are mixed. Try each question, then tap “Show answer”.

Common misconceptions

A bigger number always means a bigger measurement.The unit matters as much as the number: 0.5 km is longer than 4000 cm because 0.5 km = 500 m and 4000 cm = 40 m. Convert to the same unit before you compare.
1 m² = 100 cm², because 1 m = 100 cm.Area units are squared, so the conversion factor is squared too: 1 m² = 100 cm × 100 cm = 10 000 cm². For volume, 1 m³ = 100 × 100 × 100 = 1 000 000 cm³.
A big object is always denser than a small one of the same material.Density = mass ÷ volume is a property of the material. Cutting a piece of iron in half halves its mass and its volume, so each half has the same density.
Writing more decimal places from the calculator makes an answer more accurate.An answer cannot be more precise than the measurements it came from. Round it to about the same number of significant figures as the data.
If an instrument shows a reading, that reading must be correct.Instruments can have zero errors and you can make parallax errors. Check the zero before measuring, read with your eye level with the mark, and repeat readings.

What this unit covers

Topics marked new are not tested much in the quiz, so this book gives them extra questions.

Meaning of physics, its branches and its links with other subjects, technology and daily life
Scientific investigation: hypothesis, variables, fair test and process skills
Laboratory safety rules and care of apparatus
Fundamental and derived quantities and their SI units
Prefixes and conversion of units (length, mass, area, volume, time)
Standard form (scientific notation) and significant figures
Measuring length: tape, metre rule and vernier calliper
Micrometer screw gauge: parts and reading
Measuring mass and time: balances, stopwatch, timing many swings
Volume of regular and irregular solids and of liquids
Density: calculation and floating or sinking
Errors in measurement: parallax, zero error, accuracy and precision, averages
Estimating the area of irregular shapes on squared paper and from scale maps
Scalar and vector quantities

Go to the questions

Questions (1–50)

Easier and harder questions are mixed, just like in a real exam. The 20 harder ones are marked ★ Challenge.

1True or false
If a block of iron is cut in half, each half has half the density of the whole block.
Show answer
Answer: False
Each half has half the mass and half the volume, so mass ÷ volume (density) stays the same.
Common mistakeLearners halve the mass but forget that the volume is halved too.
2True or false · ★ Challenge
A beam balance would give the same reading for a sack of beans on the Moon as on the Earth.
Show answer
Answer: True
Both the sack and the standard masses have their weight reduced by the same factor, so they still balance at the same mass.
Common mistakeLearners mix it up with a spring balance, whose reading does fall on the Moon because it measures weight.
3True or false
It is acceptable to taste a substance in the laboratory if you are sure it is harmless.
Show answer
Answer: False
Nothing in a laboratory is ever tasted or eaten, because apparatus and benches may be contaminated.
Common mistakeLearners think 'harmless' substances such as salt are safe to taste, but lab salt may be impure and the containers dirty.
4True or false
In a fair test, only one variable is changed at a time while the other variables are kept the same.
Show answer
Answer: True
Changing one variable at a time shows that any change in the result is caused by that variable.
Common mistakeChanging several things at once seems faster, but then you cannot tell which change caused the result.
5True or false · ★ Challenge
1 m² is equal to 100 cm².
Show answer
Answer: False
1 m² = 100 cm × 100 cm = 10 000 cm².
Common mistakeThe mistake is using the length factor (100) for an area; area needs the factor squared.
6Fill in the blank
Electric current is a base quantity; its SI unit, named after a French scientist, is the ______.
Show answer
Answer: ampere
Electric current is a base quantity measured in amperes (A).
Common mistakeWriting 'volt' is a common slip: the volt is the unit of voltage, and it is a derived unit.
7Multiple choice · ★ Challenge
Round 0.04682 kg to 2 significant figures.
1. A0.04 kg
2. B0.047 kg
3. C0.046 kg
4. D0.05 kg
Show answer
Answer: B. 0.047 kg
The first two significant figures are 4 and 6; the next digit is 8, so round up: 0.047 kg.
Common mistake0.046 kg comes from cutting off the digits without rounding up; 8 is 5 or more, so the 6 becomes 7.
8Fill in the blank
Repeating a measurement several times and taking the ______ reduces the effect of random errors.
Show answer
Answer: average (mean)
Random errors make some readings too high and some too low, so averaging cancels much of the error.
Common mistakeRepeating does not remove a zero error, which shifts every reading the same way; only random errors are reduced.
9Fill in the blank
A hazard symbol showing a flame means that the substance is ______ and must be kept away from fire.
Show answer
Answer: flammable
The flame symbol warns that the substance catches fire easily (flammable).
Common mistakeSome learners write 'hot'; the symbol does not mean the substance is hot, but that it can burn.
10Multiple choice · ★ Challenge
The smallest division on a metre rule is 1 mm. Which of these is a correctly recorded reading taken with it?
1. A12.4 cm
2. B12 cm
3. C12.43 cm
4. D12.432 cm
Show answer
Answer: A. 12.4 cm
A metre rule reads to the nearest millimetre, which is 0.1 cm, so 12.4 cm is correct.
Common mistake12.43 cm looks more accurate, but a metre rule cannot show hundredths of a centimetre; that needs a vernier calliper.
11Fill in the blank
The ______ of a micrometer screw gauge slips when the jaws just touch the object, so the object is not squeezed too hard.
Show answer
Answer: ratchet
Turning the ratchet stops the screw being over-tightened, which would give a reading that is too small.
Common mistakeLearners often turn the thimble directly; this squeezes the object and gives a smaller reading.
12Multiple choice
The SI unit of density is kg/m³. This shows that density is derived from:
1. AMass and time
2. BMass and length
3. CLength and time
4. DMass only
Show answer
Answer: B. Mass and length
kg is the unit of mass and m³ comes from length × length × length, so density is derived from mass and length.
Common mistakeChoosing 'mass only' ignores the m³ part of the unit, which comes from length.
13Multiple choice · ★ Challenge
Four groups each measure a rod that is really 10.0 cm long three times. Which set of readings is precise but NOT accurate?
1. A10.0 cm, 10.1 cm, 10.0 cm
2. B11.2 cm, 11.3 cm, 11.2 cm
3. C9.0 cm, 11.0 cm, 10.2 cm
4. D8.1 cm, 12.4 cm, 9.6 cm
Show answer
Answer: B. 11.2 cm, 11.3 cm, 11.2 cm
The readings 11.2, 11.3, 11.2 cm are close together (precise) but all far from 10.0 cm (not accurate).
Common mistakeChoosing 10.0, 10.1, 10.0 cm mixes up the two words: that set is both precise and accurate.
14Multiple choice
A glass beaker breaks on the bench during a practical. What is the safest thing to do?
1. APick the pieces up quickly with your bare hands
2. BLeave the pieces there and carry on with the work
3. CWash all the pieces down the sink with tap water
4. DTell the teacher; sweep up with a brush and dustpan
Show answer
Answer: D. Tell the teacher; sweep up with a brush and dustpan
Broken glass must be reported and cleared with a brush and dustpan into the broken-glass bin, never with bare hands.
Common mistakePicking up glass by hand feels quick and helpful, but it is the most common cause of cuts in the laboratory.
15Multiple choice · ★ Challenge
A small label has an area of 5 cm². What is this area in m²?
1. A5 × 10⁻⁴ m²
2. B5 × 10⁻² m²
3. C5 × 10⁻⁶ m²
4. D500 m²
Show answer
Answer: A. 5 × 10⁻⁴ m²
1 m² = 10 000 cm², so 5 cm² = 5 ÷ 10 000 = 5 × 10⁻⁴ m².
Common mistake5 × 10⁻² m² comes from dividing by 100 as for length; for area the factor is 100² = 10 000.
16Fill in the blank
A human hair is 0.00008 m thick. In standard form this is ______ m.
Show answer
Answer: 8 × 10⁻⁵
Move the decimal point 5 places to the right: 0.00008 = 8 × 10⁻⁵ m.
Common mistakeWriting 8 × 10⁵ forgets that small numbers need a negative power of ten.
17Short answer · ★ Challenge
During a practical, Uwase has long loose hair near a Bunsen flame, is eating a mandazi at the bench, and has left her bag on the floor between the benches. Identify the three unsafe practices and say how to correct each one.
Show answer
Model answer: Loose hair can catch fire: tie it back. Eating in the laboratory can take harmful substances into the body: eat only outside the lab. A bag on the floor can make people trip, especially when carrying hot or glass apparatus: store bags in the place provided.
Common mistakeLearners often name the hazard but forget to give the correction; each unsafe practice needs a matching safe action.
18Multiple choice
Reading a scale with your eye to one side of the mark, instead of directly in front of it, causes:
1. AZero error
2. BRounding error
3. CCalibration error
4. DParallax error
Show answer
Answer: D. Parallax error
Looking at the scale from an angle makes the pointer or liquid level appear against the wrong mark; this is parallax error.
Common mistakeZero error is tempting, but that is when an instrument does not read zero before you start measuring.
19Multiple choice
Which instrument is most suitable for measuring the length of the football pitch at Amahoro Stadium?
1. AA vernier calliper
2. BA micrometer screw gauge
3. CA 30 cm ruler
4. DA long measuring tape
Show answer
Answer: D. A long measuring tape
A pitch is about 100 m long, so a long measuring tape is needed; the other instruments are for small lengths.
Common mistakeA ruler can be moved along many times, but that adds many errors; the tape measures the whole length at once.
20Multiple choice · ★ Challenge
When its jaws are closed, a vernier calliper reads +0.03 cm. It then reads 1.25 cm for the diameter of a bead. What is the true diameter?
1. A1.28 cm
2. B1.22 cm
3. C1.25 cm
4. D0.03 cm
Show answer
Answer: B. 1.22 cm
True reading = reading − zero error = 1.25 − 0.03 = 1.22 cm.
Common mistake1.28 cm comes from adding the zero error; a positive zero error makes every reading too big, so it must be subtracted.
21Multiple choice
Ishimwe writes: 'newton, ampere, kelvin and kilogram are all SI base units.' Which unit in his list is wrong?
1. AAmpere
2. BKelvin
3. CNewton
4. DKilogram
Show answer
Answer: C. Newton
The newton (N) is a derived unit (kg m/s²); the ampere, kelvin and kilogram are base units.
Common mistakeThe newton is so common that learners think it is basic, but it is built from kg, m and s.
22Short answer · ★ Challenge
A large log floats on Lake Kivu but a small pebble sinks. Explain why, using the idea of density.
Show answer
Model answer: Floating depends on density, not size. The wood of the log has a density less than that of water, so it floats; the rock of the pebble has a density greater than water, so it sinks, however small it is.
Common mistakeSaying the log floats because it is big, or the pebble sinks because it is heavy, confuses mass with density.
23Multiple choice
A micrometer screw gauge can measure lengths to the nearest:
1. A0.1 mm
2. B0.001 mm
3. C0.01 mm
4. D1 mm
Show answer
Answer: C. 0.01 mm
The thimble has 50 divisions and one turn moves 0.5 mm, so each division is 0.5 ÷ 50 = 0.01 mm.
Common mistake0.1 mm is the precision of a vernier calliper; the micrometer is ten times more precise.
24Multiple choice · ★ Challenge
On a micrometer screw gauge, the sleeve scale shows 5.5 mm and the 28th thimble division lines up with the datum line. What is the reading?
1. A5.28 mm
2. B5.528 mm
3. C33.5 mm
4. D5.78 mm
Show answer
Answer: D. 5.78 mm
Reading = sleeve + thimble = 5.5 + 28 × 0.01 = 5.5 + 0.28 = 5.78 mm.
Common mistake5.28 mm comes from forgetting the 0.5 mm half-division already showing on the sleeve.
25Multiple choice
Keza says: 'I think bean seeds sprout faster in warm soil than in cold soil.' Before she tests it, this statement is:
1. AA conclusion
2. BAn observation
3. CA hypothesis
4. DA measurement
Show answer
Answer: C. A hypothesis
A hypothesis is a testable idea made before the experiment; a conclusion comes after the results.
Common mistakeCalling it a conclusion is the common error: nothing has been tested yet, so it cannot be a conclusion.
26Fill in the blank
1 cm³ of a liquid is also called one ______ (mL).
Show answer
Answer: millilitre
1 mL = 1 cm³ and 1000 mL = 1 L.
Common mistakeLearners sometimes write 'centilitre', but 1 cL = 10 cm³.
27Multiple choice · ★ Challenge
How many significant figures are there in the reading 0.0450 m?
1. A2
2. B3
3. C4
4. D5
Show answer
Answer: B. 3
Leading zeros do not count; 4, 5 and the final 0 do, so there are 3 significant figures.
Common mistakeAnswering 5 counts the leading zeros, which only show the place value and are not significant.
28Multiple choice
A student investigates how the strings of an inanga make sound and how the sound reaches the audience. Which branch of physics is she studying?
1. AOptics (light)
2. BElectricity and magnetism
3. CHeat (thermal physics)
4. DWaves and sound
Show answer
Answer: D. Waves and sound
The production and travel of sound are studied in the branch called waves and sound.
Common mistakeChoosing optics comes from thinking of anything we sense; optics is about light, not sound.
29Multiple choice
Which pair correctly matches a branch of physics with something it explains?
1. AOptics – how spectacles help a person see clearly
2. BMechanics – why a phone battery runs flat
3. CHeat – how a radio picks up a signal from far away
4. DElectricity – why a bicycle slows down on braking
Show answer
Answer: A. Optics – how spectacles help a person see clearly
Spectacles use lenses to bend light, which is part of optics.
Common mistakeLinking braking to electricity is tempting because bikes can have lights, but braking is about forces (mechanics).
30Short answer · ★ Challenge
Explain how you could measure the length of a winding road on a map of Rwanda using a piece of thread and a ruler, and how you would get the real length.
Show answer
Model answer: Lay the thread carefully along every bend of the road on the map, mark the start and end, then straighten the thread and measure it with the ruler. Multiply this length by the map scale (for example 1 cm : 2 km) to get the real length.
Common mistakeA straight ruler laid from start to end measures the straight-line gap, not the length along the bends, so it gives too small a value.
31Multiple choice
Ndayisaba groups together quantities that need a direction to be fully described. Which group is correct?
1. AForce, weight, displacement
2. BMass, time, speed, area
3. CForce, mass, velocity
4. DDistance, area, weight, time
Show answer
Answer: A. Force, weight, displacement
Force, weight and displacement all need a direction to be fully described.
Common mistake'Force, mass, velocity' is tempting, but mass has no direction, so it is a scalar.
32Multiple choice · ★ Challenge
A 30 g piece of wood has a volume of 50 cm³. Water has a density of 1.0 g/cm³. What happens when the wood is put in water?
1. AIt sinks, because its density is 1.7 g/cm³
2. BIt floats, because its density is 1.7 g/cm³
3. CIt floats, because its density is 0.6 g/cm³
4. DIt sinks, because its mass is more than 1 g
Show answer
Answer: C. It floats, because its density is 0.6 g/cm³
ρ = m/V = 30 ÷ 50 = 0.6 g/cm³, which is less than 1.0 g/cm³, so it floats.
Common mistake1.7 g/cm³ comes from dividing volume by mass (50 ÷ 30); density is mass ÷ volume.
33True or false
One way to estimate an area on squared paper is to count a square if half or more of it is covered and ignore it if less than half is covered.
Show answer
Answer: True
The squares counted and ignored roughly balance out, giving a good estimate.
Common mistakeLearners often count every square that is touched at all, which gives an estimate that is too large.
34Multiple choice
The distance from the Earth to the Sun is about 150 000 000 km. Written in standard form this is:
1. A15 × 10⁷ km
2. B1.5 × 10⁷ km
3. C1.5 × 10⁹ km
4. D1.5 × 10⁸ km
Show answer
Answer: D. 1.5 × 10⁸ km
Move the decimal point 8 places: 150 000 000 = 1.5 × 10⁸.
Common mistake15 × 10⁷ has the right value but is not standard form, because the first number must be between 1 and 10.
35Short answer · ★ Challenge
Mugisha wants to find out whether the length of a pendulum affects the time for one swing. Name the independent variable, the dependent variable and two variables he must keep the same.
Show answer
Model answer: Independent variable: the length of the pendulum. Dependent variable: the time for one swing (period). Control variables: the mass of the bob and the size of the swing (angle of release); also use the same string and the same stopwatch.
Common mistakeMany learners swap the independent and dependent variables; the one you choose to change is independent, the one you measure is dependent.
36Multiple choice
Gold has a density of 19.3 g/cm³. What is the mass of 2.0 cm³ of gold?
1. A38.6 g
2. B9.65 g
3. C21.3 g
4. D0.104 g
Show answer
Answer: A. 38.6 g
m = ρV = 19.3 × 2.0 = 38.6 g.
Common mistake9.65 g comes from dividing the density by the volume; mass = density × volume.
37Multiple choice · ★ Challenge
A packet of sugar is labelled 0.75 kg. A baker uses 150 g of sugar for each cake. How many cakes can she make from the packet?
1. A5 cakes
2. B50 cakes
3. C2 cakes
4. D0.5 cakes
Show answer
Answer: A. 5 cakes
0.75 kg = 750 g, so number of cakes = 750 ÷ 150 = 5.
Common mistakeGetting 50 comes from turning 0.75 kg into 7500 g; 1 kg = 1000 g, so 0.75 kg = 750 g.
38Multiple choice
A beam balance finds the mass of an object by comparing it with:
1. AThe pull of a spring inside it
2. BStandard masses on the other pan
3. CThe volume of water it pushes aside
4. DThe time it takes to fall
Show answer
Answer: B. Standard masses on the other pan
A beam balance balances the object against known standard masses.
Common mistakeThinking of a spring is the error: a spring balance measures weight using a spring, a beam balance does not.
39Short answer
Explain, with one example each, how physics is used in (a) medicine and (b) farming in Rwanda.
Show answer
Model answer: (a) Hospitals use X-ray machines and ultrasound scanners, which are built on physics of radiation and sound waves. (b) Farmers use solar-powered pumps to irrigate crops and weigh harvests on balances; both depend on physics (energy and forces).
Common mistakeLearners often give a chemistry or biology example (such as fertiliser) that does not use any physics idea.
40Multiple choice · ★ Challenge
To find the volume of a cork that floats, a student uses a heavy sinker. Readings: water alone 60 cm³; water and sinker 68 cm³; water, sinker and cork tied together 83 cm³. What is the volume of the cork?
1. A15 cm³
2. B23 cm³
3. C83 cm³
4. D8 cm³
Show answer
Answer: A. 15 cm³
Volume of cork = 83 − 68 = 15 cm³; the sinker's own volume (8 cm³) is not included.
Common mistake23 cm³ comes from 83 − 60, which wrongly includes the volume of the sinker.
41Multiple choice
A stone is too big to go into a measuring cylinder. Which apparatus should be used to find its volume?
1. AA beam balance and a long metre rule
2. BA vernier calliper used on its own
3. CAn overflow can and a measuring cylinder
4. DA spring balance and a stopwatch
Show answer
Answer: C. An overflow can and a measuring cylinder
The stone is lowered into a full overflow (displacement) can; the water pushed out is collected and measured in a measuring cylinder.
Common mistakeA ruler only works for regular shapes; an irregular stone has no length, width and height to multiply.
42Short answer · ★ Challenge
A calculator gives the density of a stone as 2.6666667 g/cm³, from a mass of 40 g and a volume of 15 cm³ (both to 2 significant figures). Write the density to a sensible number of significant figures and explain your choice.
Show answer
Model answer: ρ = 40 ÷ 15 = 2.7 g/cm³ (2 significant figures). The data are only given to 2 significant figures, so the answer cannot be more precise than that; the extra digits from the calculator are meaningless.
Common mistakeCopying every calculator digit suggests a precision that the measurements do not have.
43Short answer
A weather report says, 'The temperature in Kigali today is 25 °C towards the east.' Explain what is wrong with this statement.
Show answer
Model answer: Temperature is a scalar quantity: it has size (magnitude) only and no direction. Saying 'towards the east' makes no sense; the report should just say 25 °C.
Common mistakeLearners think every quantity with a number can have a direction, but only vectors such as force or velocity do.
44Short answer · ★ Challenge
Which instrument, a vernier calliper or a micrometer screw gauge, would you use to measure (a) the thickness of a 100-franc coin and (b) the inside diameter of a cup? Give a reason for each.
Show answer
Model answer: (a) Micrometer screw gauge: the coin is thin (about 2 mm), and the micrometer reads to 0.01 mm. (b) Vernier calliper: it has inside jaws that fit into the cup, which a micrometer does not have.
Common mistakeMany learners choose the micrometer for both because it is more precise, forgetting that it cannot measure inside diameters.
45Short answer
Speed is measured in m/s and area in m². Explain why both are called derived quantities and name the base quantities each comes from.
Show answer
Model answer: They are derived because they are calculated from base quantities. Speed = distance ÷ time comes from length and time; area = length × width comes from length only (length × length).
Common mistakeSome learners say area is a base quantity because it has only one unit symbol, but m² is metre × metre.
46Multiple choice
A water tank on a Kigali building holds 4.2 m³. How many litres is this?
1. A42 L
2. B420 L
3. C4200 L
4. D42 000 L
Show answer
Answer: C. 4200 L
1 m³ = 1000 L, so 4.2 m³ = 4.2 × 1000 = 4200 L.
Common mistakeChoosing 420 L comes from using 1 m³ = 100 L; a cube 1 m on each side holds 1000 litres.
47Short answer · ★ Challenge
A plan of a farm in Bugesera is drawn on 1 cm squared paper with a scale of 1 cm : 10 m. The farm covers about 30 squares. Estimate the real area of the farm in m². Explain your working.
Show answer
Model answer: Each 1 cm square stands for 10 m × 10 m = 100 m² on the ground. Area ≈ 30 × 100 = 3000 m².
Common mistakeUsing 10 m² for each square forgets that the scale applies to both the length and the width of the square.
48Short answer
Explain how to use an electronic balance to find the mass of salt in a beaker without weighing the beaker separately.
Show answer
Model answer: Place the empty beaker on the balance and press the 'tare' (zero) button so the display reads 0.0 g. Then add the salt; the display now shows only the mass of the salt.
Common mistakeForgetting to tare means the reading includes the mass of the beaker, so the mass of salt is too large.
49Short answer · ★ Challenge
A cylindrical tin has a radius of 7 cm and a height of 10 cm. Calculate its volume in cm³ and in litres (take π = 22/7).
Show answer
Model answer: V = πr²h = 22/7 × 7² × 10 = 22/7 × 49 × 10 = 1540 cm³. In litres: 1540 ÷ 1000 = 1.54 L.
Common mistakeUsing the diameter (14 cm) instead of the radius gives four times the correct volume.
50Multiple choice
A pupil draws round her shoe on 1 cm squared paper. The outline covers 36 full squares and 20 part squares. Counting each part square as half a square, what is the area of the sole?
1. A56 cm²
2. B36 cm²
3. C26 cm²
4. D46 cm²
Show answer
Answer: D. 46 cm²
Area = 36 + 20 × ½ = 36 + 10 = 46 cm².
Common mistake56 cm² counts every part square as a whole square, which makes the estimate too large.