Q. A car travels at a speed of 80 km/h. How long will it take to travel 240 km?
A.
2 hours
B.
3 hours
C.
4 hours
D.
5 hours
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Solution
Time = Distance / Speed = 240 km / 80 km/h = 3 hours.
Correct Answer: B — 3 hours
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Q. A length is measured as 5.67 m with an uncertainty of 0.01 m. What is the percentage error?
A.
0.18%
B.
0.2%
C.
0.15%
D.
0.25%
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Solution
Percentage error = (Uncertainty / Measured value) * 100 = (0.01 / 5.67) * 100 ≈ 0.176%.
Correct Answer: B — 0.2%
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Q. A student measures the length of a table as 1.20 m with an uncertainty of 0.02 m. What is the total length if he measures 3 tables?
A.
3.60 m
B.
3.58 m
C.
3.62 m
D.
3.64 m
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Solution
Total length = 3 * 1.20 m = 3.60 m. The uncertainty for 3 tables = 3 * 0.02 m = 0.06 m.
Correct Answer: A — 3.60 m
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Q. A thermometer reads 25.0 °C with an uncertainty of ±0.5 °C. What is the range of possible true values?
A.
24.5 °C to 25.5 °C
B.
24.0 °C to 25.0 °C
C.
25.0 °C to 26.0 °C
D.
25.5 °C to 26.5 °C
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Solution
The range of possible true values is from 25.0 - 0.5 to 25.0 + 0.5, which is 24.5 °C to 25.5 °C.
Correct Answer: A — 24.5 °C to 25.5 °C
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Q. A volume is measured as 250.0 mL with an uncertainty of 1.0 mL. What is the minimum possible volume?
A.
249.0 mL
B.
250.0 mL
C.
251.0 mL
D.
248.0 mL
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Solution
Minimum possible volume = Measured volume - Uncertainty = 250.0 mL - 1.0 mL = 249.0 mL.
Correct Answer: A — 249.0 mL
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Q. If a car travels 150 km with a time measurement of 2.5 hours, what is the speed with an uncertainty of ±0.1 hours?
A.
60 km/h
B.
62 km/h
C.
58 km/h
D.
64 km/h
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Solution
Speed = Distance / Time = 150 km / 2.5 h = 60 km/h.
Correct Answer: A — 60 km/h
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Q. If a car travels 60 km in 1 hour, how far will it travel in 3 hours?
A.
120 km
B.
180 km
C.
150 km
D.
200 km
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Solution
Distance = speed × time = 60 km/h × 3 h = 180 km.
Correct Answer: B — 180 km
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Q. If a length is measured as 150.0 cm, how many significant figures does this measurement have?
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Solution
The measurement 150.0 cm has 4 significant figures because the trailing zero after the decimal point is significant.
Correct Answer: C — 4
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Q. If a measurement is recorded as 0.00456 m, how many significant figures are in this measurement?
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Solution
The leading zeros are not significant. Therefore, 0.00456 has 3 significant figures.
Correct Answer: B — 3
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Q. If a measurement is recorded as 12.30 cm, what is the absolute error if the true value is 12.5 cm?
A.
0.2 cm
B.
0.3 cm
C.
0.1 cm
D.
0.4 cm
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Solution
Absolute error = |Measured value - True value| = |12.30 - 12.5| = 0.2 cm.
Correct Answer: B — 0.3 cm
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Q. If a weight is recorded as 0.050 kg, how many significant figures does this weight have?
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Solution
The leading zeros are not significant. Therefore, 0.050 kg has 2 significant figures.
Correct Answer: B — 2
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Q. If the diameter of a circle is measured as 10.0 cm with an uncertainty of 0.1 cm, what is the circumference with uncertainty?
A.
31.4 cm ± 0.3 cm
B.
31.4 cm ± 0.2 cm
C.
31.4 cm ± 0.1 cm
D.
31.4 cm ± 0.4 cm
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Solution
Circumference = π * diameter = π * 10.0 cm ≈ 31.4 cm. Uncertainty in circumference = π * 0.1 cm ≈ 0.314 cm.
Correct Answer: A — 31.4 cm ± 0.3 cm
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Q. If the price of a shirt is $40 after a 20% discount, what was the original price?
A.
$50
B.
$60
C.
$70
D.
$80
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Solution
Let the original price be x. Then, x - 0.2x = 40, which gives 0.8x = 40. Thus, x = 40 / 0.8 = $50.
Correct Answer: A — $50
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Q. If the radius of a circle is 7 cm, what is its circumference? (Use π ≈ 3.14)
A.
43.96 cm
B.
21.98 cm
C.
31.4 cm
D.
14 cm
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Solution
Circumference = 2πr = 2 × 3.14 × 7 cm = 43.96 cm.
Correct Answer: A — 43.96 cm
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Q. If the sum of the angles in a triangle is 180 degrees, what is the measure of the third angle if the other two angles are 50 degrees and 70 degrees?
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Solution
The third angle can be found by subtracting the sum of the other two angles from 180 degrees: 180 - (50 + 70) = 60 degrees.
Correct Answer: A — 60
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Q. If the sum of two numbers is 30 and their difference is 10, what are the numbers?
A.
20 and 10
B.
25 and 5
C.
15 and 15
D.
18 and 12
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Solution
Let the numbers be x and y. We have x + y = 30 and x - y = 10. Solving these gives x = 20 and y = 10.
Correct Answer: A — 20 and 10
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Q. If the weight of an object is measured as 50.0 kg with an uncertainty of 0.5 kg, what is the relative error?
A.
1%
B.
0.5%
C.
2%
D.
0.1%
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Solution
Relative error = (Uncertainty / Measured value) * 100 = (0.5 / 50.0) * 100 = 1%.
Correct Answer: B — 0.5%
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Q. In a physics experiment, a mass is measured as 2.50 kg with an uncertainty of 0.05 kg. What is the maximum possible mass?
A.
2.55 kg
B.
2.50 kg
C.
2.45 kg
D.
2.60 kg
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Solution
Maximum possible mass = Measured mass + Uncertainty = 2.50 kg + 0.05 kg = 2.55 kg.
Correct Answer: A — 2.55 kg
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Q. In the calculation 100.0 - 0.045, how many decimal places should the answer have?
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Solution
The number 100.0 has 1 decimal place, so the answer should also be rounded to 1 decimal place.
Correct Answer: A — 0
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Q. In the calculation 12.11 - 0.3, how many decimal places should the answer have?
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Solution
The number with the least decimal places is 0.3 (1 decimal place), so the answer should be rounded to 1 decimal place.
Correct Answer: A — 1
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Q. In the expression 3.4567 + 2.1, how many significant figures does the result have?
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Solution
The result of 3.4567 + 2.1 is 5.5567. However, since 2.1 has only 2 significant figures after the decimal, the result should be rounded to 5.6, which has 3 significant figures.
Correct Answer: B — 3
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Q. In the expression 3.4567, how many significant figures are there?
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Solution
The number 3.4567 has 4 significant figures. The leading digit is not counted as significant.
Correct Answer: C — 4
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Q. In the expression 3x + 5 = 20, what is the value of x?
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Solution
To find x, subtract 5 from both sides: 3x = 20 - 5 = 15. Then divide by 3: x = 15 / 3 = 5.
Correct Answer: A — 5
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Q. In the expression 5.00 × 10^3 + 2.1 × 10^2, how many significant figures should the final answer have?
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Solution
The term 2.1 × 10^2 has 2 significant figures, so the final answer should be rounded to 2 significant figures.
Correct Answer: B — 3
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Q. In the expression 5x + 3y = 15, if x = 2, what is the value of y?
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Solution
Substituting x = 2 into the equation gives 5(2) + 3y = 15, which simplifies to 10 + 3y = 15. Thus, 3y = 5, and y = 5/3.
Correct Answer: C — 3
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Q. What is the result of multiplying 2.5 by 3.456, considering significant figures?
A.
8.64
B.
8.6
C.
8.65
D.
8.7
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Solution
2.5 has 2 significant figures and 3.456 has 4 significant figures. The result should be rounded to 2 significant figures, giving 8.6.
Correct Answer: B — 8.6
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Q. What is the value of x in the equation 3x - 7 = 2?
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Solution
Adding 7 to both sides gives 3x = 9. Dividing by 3 gives x = 3.
Correct Answer: A — 1
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Q. When dividing 6.022 × 10^23 by 3.0, how many significant figures should the answer have?
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Solution
The number 3.0 has 2 significant figures, so the result should also be reported with 2 significant figures.
Correct Answer: B — 2
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Q. When rounding the number 0.006789 to three significant figures, what is the result?
A.
0.00678
B.
0.00679
C.
0.0067
D.
0.0068
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Solution
Rounding 0.006789 to three significant figures gives 0.00679.
Correct Answer: B — 0.00679
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