Physics, Foundation Programme – Problem Solving Exercises 1
1. Make a cross if the number belongs to the given subset of real numbers:
3 -3 3.33 10
Natural number
Integer
Rational number
Irrational number
a:
3 -3 3.33 10
Natural number x x
Integer x x x
Rational number x x x x x
Irrational number x x
2. Evaluate the expressions:
a) a:
b) a: 29
c) a: 7
d) a: -64
3. What is the prime factorization of each number:
a) 35 a:
b) 16 a:
c) 18 a:
4. Find the greatest common factor (GCF) for each pair of numbers.
a) 8 and 24 a: 8
b) 20 and 25 a: 5
c) 16 and 40 a: 8
5. Find the least common multiple (LCM) of numbers:
a) 6 and 7 a: 42
b) 16 and 24 a: 48
c) 10 and 35 a: 70
6. Express each fraction in the simplest form:
a) a: 1/5
b) a: 1/3
c) a: 9/10
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7. Write a mixed number for each improper fraction:
a) a: 4+4/5
b) a: 2+9/12=2+3/4
8. Write improper fraction for each mixed number:
a) a: 17/10
b) a: 33/5
9. Add or subtract, express in the simplest form:
a) a: 8/16=1/2
b) a: 10/60=1/6
c) a: 28/60=7/15
d) a: 2/9
e) a: 4+3/10
f) a: 8+3/4
10. Find the multiplicative reciprocal:
a) a: 7/5
b) a: 2/11
c) 4 a: 1/4
11. Multiply or divide, express in the simplest form:
a) a: 14/45
b) a: 1/2
c) a: 15/44
d) a: 28+3/4
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e) a: 49+1/2
f) a: 3/10
g) a: 27/38
h) a: 7/8
12. Round each decimal to the indicated place.
a) 1.7432; tenth a: 1.7
b) 49.096; hundredths a: 49.10
c) 158,890; 3 significant digits a:159,000
d) 19.39498; 5 significant digits a: 19.395
13. Simplify the following expression using the correct number of significant digits:
a) 5.012 km + 3.4 km + 2.33 km a: 10.7 km
b) 45 g – 8.3 g a: 37 g
c) 54 m / 6.5 s a: 8.3 m/s
14. Express each number using scientific notation
a) 12,589.3 a:
b) 545,250,000,000,000 a:
c) 0.0000000939 a:
d) 0.000052 a:
15. Express each number using decimal form
a) a: 0.00000390
b) a: 0.00872
c) a: 79,000
16. While heated, water in a pot increased temperature from 50 degrees of Celsius to 90 degrees of
Celsius in 10 minutes. Write the fact as an unit rate.
FP Physics - Problem Solving Exercises 1WA 3/4 Masaryk University
A: 4 degC/min
17. A car accelerated from 0 meters per second (m/s) to 30 meters per second (m/s) in 5 seconds (s).
Express the fact as an unit rate.
A: 6 m/s2
18. Give the percent of each number:
a) 30% of 90 a: 27
b) 5% of 300 a:15
c) 25% of 64 a: 16
19. 20 is 25% of what number? A:80
20. 36 is 18% of what number? A: 200
21. What percent of 50 is 2.5? a: 5%
22. What percent of 52 is 13? a: 25%
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