PRELIMINARY STAGE 2024
Contest 4
Tsito SHTS: 55 points (Winner)
Methodist Girls’ SHS, Mamfe: 48 points
Notre Dame Seminary SHS: 45 points
Contest 5
Tema Methodist SHS: 54 points (Winner)
Shama SHS: 37 points
Bolgatanga SHS: 28 points
Contest 6
Wallahs Academy: 32 points (Winner)
O’Reilly SHS: 29 points
Adanwomase SHS: 25 points
ROUND 4 - TRUE OR FALSE
FIRST SET OF QUESTIONS
PREAMBLE
A student measures the length of an object five times and records her results.
1. The student's best estimate of the length of the object is the average of her five results.
ANSWER: TRUE
EXPLANATION:
Taking the average of multiple measurements reduces random errors and gives a better estimate of the true length.
2. If the student makes a sixth measurement of the length of the object, the outcome will be the average of her five previous results.
ANSWER: FALSE
EXPLANATION:
Each measurement is independent.
The sixth measurement may differ due to random errors; it is not automatically equal to the previous average.
3. If the student makes a sixth measurement of the length of the object, the average of all her six results might be a better estimate of the object's length than the average of her five previous results.
ANSWER: TRUE
EXPLANATION:
Including more measurements generally improves the estimate by further reducing random errors, giving a more accurate average.
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PRACTICE QUESTIONS
PREAMBLE 1
A student uses a stopwatch to time 20 oscillations of a pendulum and repeats the timing four more times.
1. Dividing the time for 20 oscillations by 20 reduces the effect of the reaction-time error on each period.
ANSWER: TRUE
EXPLANATION:
The same reaction-time error is shared over 20 periods.
2. Repeating the timing removes a systematic error caused by a stopwatch that runs slow.
ANSWER: FALSE
EXPLANATION:
A slow stopwatch gives every reading the same bias; averaging cannot remove it.
3. The mean of the five timings is a better estimate than any single timing.
ANSWER: TRUE
EXPLANATION:
Averaging reduces the effect of random errors.
PREAMBLE 2
A student measures the diameter of a wire at several places along its length with a micrometer screw gauge.
1. Measuring at several places allows for the wire not being perfectly uniform.
ANSWER: TRUE
EXPLANATION:
The mean diameter represents the whole wire better than one reading.
2. A zero error on the micrometer is removed by averaging the readings.
ANSWER: FALSE
EXPLANATION:
A zero error shifts every reading by the same amount; it must be subtracted, not averaged away.
3. The micrometer screw gauge reads to a smaller division than a metre rule.
ANSWER: TRUE
EXPLANATION:
A micrometer reads to 0.01 mm; a metre rule reads to 1 mm.
PREAMBLE 3
Two students measure the same length. Student A's readings are close to each other but far from the true value; student B's readings are spread out, but their mean is close to the true value.
1. Student A's readings are precise but not accurate.
ANSWER: TRUE
EXPLANATION:
Close agreement is precision; closeness to the true value is accuracy.
2. Student B's readings are more precise than student A's readings.
ANSWER: FALSE
EXPLANATION:
Student B's readings are more spread out, so they are less precise.
3. Student A's results probably contain a systematic error.
ANSWER: TRUE
EXPLANATION:
Consistent readings that are all off the true value point to a systematic error.
PREAMBLE 4
A student records the mass of a beaker five times on a digital balance and gets the same reading every time.
1. The reading must be the true mass of the beaker.
ANSWER: FALSE
EXPLANATION:
Repeatable readings can still share a systematic error, such as a zero error.
2. The balance could still have a zero error.
ANSWER: TRUE
EXPLANATION:
A zero error would affect every reading equally, so it would not show up as scatter.
3. Taking more readings will change the mean of the results.
ANSWER: FALSE
EXPLANATION:
If every further reading is the same, the mean stays the same.